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PostPosted: Thu Apr 21, 2011 11:56 pm 
Offline
Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
This is Part D of the Assassin Forum Archive, moving on to include puzzles posted on this site and provide easy links to the puzzles and threads. Please read the first part of the Archive Index to get the background to this archive including Mike (mhparker)'s original post about ratings.

Old SSv3.2.1 scores:
Score = SudokuSolver v3.2.1 Score, rounded to nearest 0.05
E = Easy
H = Hard
In these tables, Rating is the lowest of the ratings given by Afmob,
Andrew and Mike, including estimates for puzzles by Afmob and Mike

+--------------------------+--------------------------+--------------------------+
| Puzzle Rating Score | Puzzle Rating Score | Puzzle Rating Score |
+--------------------------+--------------------------+--------------------------+
| MO#1 1.00 1.00 | Cycl V2 1.50 | A102X 1.00 1.05 |
| MO#2 1.25 1.05 | A101 1.25 1.25 | A103 E1.50 1.75 |
| Cycl V1 H1.00 | A102 H1.00 1.10 | A103 E1.50 1.75 |
+--------------------------+--------------------------+--------------------------+
Page #1

+--------------------------+--------------------------+--------------------------+
| Puzzle Rating Score | Puzzle Rating Score | Puzzle Rating Score |
+--------------------------+--------------------------+--------------------------+
| A104HBN! 1.00 1.20 | A106V2 H1.50 2.15 | A107V2 E1.50 1.25 |
| A105 E1.50 1.35 | MO#3 1.00 0.95 | A108 1.25 0.90 |
| A106 1.25 1.35 | A107 H1.00 1.05 | A108V2 1.75 1.60 |
+--------------------------+--------------------------+--------------------------+
Page #2

+--------------------------+--------------------------+--------------------------+
| Puzzle Rating Score | Puzzle Rating Score | Puzzle Rating Score |
+--------------------------+--------------------------+--------------------------+
| SOK1 E1.00 0.80 | A110XV2 H1.25 1.30 | A112V2 1.25 2.50 |
| SOK1 var 0.75 | A111 1.25 1.25 | A113 1.50 1.55 |
| A109 1.00 1.15 | A112 0.75 1.35 | A113-Lite 1.00 1.05 |
| A110X 1.00 0.80 | | |
+--------------------------+--------------------------+--------------------------+
Page #3

+--------------------------+--------------------------+--------------------------+
| Puzzle Rating Score | Puzzle Rating Score | Puzzle Rating Score |
+--------------------------+--------------------------+--------------------------+
| MO#4 1.00 1.05 | A114 Twin 0.75 | A115V0.9 1.00 0.90 |
| A114 1.00 0.85 | A114V3 4.15 | A115V2 1.50 1.75 |
| A114V2 E1.50 1.30 | A115 1.50 1.55 | MO#5 H0.75 1.00 |
+--------------------------+--------------------------+--------------------------+
Page #4

+--------------------------+--------------------------+--------------------------+
| Puzzle Rating Score | Puzzle Rating Score | Puzzle Rating Score |
+--------------------------+--------------------------+--------------------------+
| A116 Mars H1.00 1.15 | A118V0.9 H1.00 0.90 | A119V2 1.25 1.65 |
| A116 Venus 1.25 1.90 | HS2x | A119V3 |
| A117 1.25 1.30 | HS2x Lite H1.25 1.35 | SOK2 1.25 |
| A118 1.25 1.30 | A119 1.00 0.90 | |
+--------------------------+--------------------------+--------------------------+
Page #5

+--------------------------+--------------------------+--------------------------+
| Puzzle Rating Score | Puzzle Rating Score | Puzzle Rating Score |
+--------------------------+--------------------------+--------------------------+
| A120 1.25 1.25 | HS3x 1.50 2.00 | A123 H1.25 2.50 |
| A120V2 H1.50 | A122 1.00 1.65 | A123V0.9 1.25 1.55 |
| A121 1.00 1.20 | A122V1.5 1.25 1.85 | A123V2 2.00 2.70 |
+--------------------------+--------------------------+--------------------------+
Page #6

+--------------------------+--------------------------+--------------------------+
| Puzzle Rating Score | Puzzle Rating Score | Puzzle Rating Score |
+--------------------------+--------------------------+--------------------------+
| MO#6 H1.00 0.95 | A124V2 1.75 2.60 | A125V0 0.75 0.70 |
| A124 1.00 1.40 | A125 H1.00 1.10 | A125V2 1.25 1.60 |
+--------------------------+--------------------------+--------------------------+
Page #7

Puzzle rating table, with links to archive entries; each of these has a link to the puzzle thread.

Abbreviations used in Rating Table:
Est = Estimated rating by puzzle maker
E = Easy
H = Hard
Az = azpaull
F = Frank
G = gary w
Go = goooders
M = Mike (mhparker)
N = Nasenbaer
P = Para
U = udosuk
SOK = Special Occasion Killer
Score = SudokuSolver v3.3.0 score, rounded to nearest 0.05
! indicates that the Score has changed at least 0.10 from the SS v3.2.1 score
R indicates lowest score out of 4 rotations of puzzle, for some harder puzzles
** in the Afmob column indicates that these puzzles were made by him,
for these ones the estimate is his rating.
+------------------------+-----------+-------+-------+-------+-----------------------+-------+
| Puzzle | Made By | Est | Afmob | Andrew| Other Raters | Score |
+------------------------+-----------+-------+-------+-------+-----------------------+-------+
| Messy One #1 | Ed | | 1.00 | 1.00 |(M)1.00 | !0.85 |
| Messy One #2 | Afmob | H1.00 | ** | H1.25 |(M)1.25(Ed)1.25 | 1.10 |
| Cyclone V1 | Mike | 1.25 | H1.00 | H1.00 | | |
| Cyclone V2 | Mike | 1.75 | | H1.50 |(M)1.50 | |
| Assassin 101 | Nasenbaer | | H1.00 | 1.25 |(M)1.25 | !1.10 |
| Assassin 102 | Afmob | H1.00 | ** | 1.25 |(G)1.25(Ed)1.25(N)1.25 | !0.65 |
| Assassin 102X | Mike | 1.25 | 1.00 | H1.00 | | 1.10 |
| Assassin 103 | Mike | 1.25 | E1.50 | 1.50 | | !1.50 |
| Human Solvable 1 | HATMAN | | 1.75 | 1.75 | |!R4.10 |
+------------------------+-----------+-------+-------+-------+-----------------------+-------+
Page #1

+------------------------+-----------+-------+-------+-------+-----------------------+-------+
| Puzzle | Made By | Est | Afmob | Andrew| Other Raters | Score |
+------------------------+-----------+-------+-------+-------+-----------------------+-------+
| Assassin 104HBN! | Ed | 1.00 | 1.00 | 1.00 |(M)1.0 | 1.20 |
| Assassin 105 | Nasenbaer | H1.25 | E1.50 | 1.50 |(Go)1.0(M)1.50(G)1.0 | 1.35 |
| Assassin 106 | Afmob | 1.25 | ** | 1.00 |(M)1.25(Ed)1.25(G)1.25 | !1.20 |
| Assassin 106V2 | Afmob | H1.50 | ** | H1.50 | |!R2.45 |
| Messy One #3 | Nasenbaer | | 1.00 | H1.00 |(G)1.0 | 0.95 |
| Assassin 107 | Mike | 1.25 | H1.00 | H1.25 |(Ed)E1.0 | 1.05 |
| Assassin 107V2 | Mike | 1.75 | E1.50 | 1.50 | | !1.45 |
| Assassin 108 | Nasenbaer | | 1.25 | H1.25 |(Ed)H1.25(G)1.50 | !1.10 |
| Assassin 108V2 | Nasenbaer | | 1.75 | 1.75 | | !1.75 |
+------------------------+-----------+-------+-------+-------+-----------------------+-------+
Page #2

+------------------------+-----------+-------+-------+-------+-----------------------+-------+
| Puzzle | Made By | Est | Afmob | Andrew| Other Raters | Score |
+------------------------+-----------+-------+-------+-------+-----------------------+-------+
| SOK1 | Nasenbaer | | E1.00 | E1.00 | | 0.80 |
| SOK1 var | Nasenbaer | | | 0.75 | | 0.75 |
| Assassin 109 | Afmob | E1.25 | 1.25 | H1.25 |(M)1.0 | 1.10 |
| Assassin 110X | Ed | | 1.00 | 1.00 |(M)1.0 | !1.00 |
| Assassin 110XV2 | Ed | 1.50 | H1.25 | H1.25 | | 1.35 |
| Assassin 111 | Nasenbaer | E1.50 | 1.25 | H1.50 |(G)1.25 | 1.30 |
| Assassin 112 | Afmob | H0.75 | ** | 0.75 |(F)H0.75(G)H0.5 | !0.80 |
| Assassin 112V2 | Afmob | 1.25 | ** | 1.50 |(M)1.50 | 2.50 |
| Assassin 113 | Para | H1.25 | 1.50 | 1.50 |(Go)1.50(Ed)2.0 | 1.55 |
| Assassin 113-Lite | Para | 1.00 | | 1.00 | | 1.10 |
+------------------------+-----------+-------+-------+-------+-----------------------+-------+
Page #3

+------------------------+-----------+-------+-------+-------+-----------------------+-------+
| Puzzle | Made By | Est | Afmob | Andrew| Other Raters | Score |
+------------------------+-----------+-------+-------+-------+-----------------------+-------+
| Messy One #4 | Para | 1.00 | H1.00 | 1.00 |(G)1.0(Ed)H1.0 | 0.95 |
| Assassin 114 | Nasenbaer | E1.00 | 1.00 | H1.00 | | !1.15 |
| Assassin 114V2 | Nasenbaer | E1.25 | E1.50 | 1.50 |(M)1.50 | 1.30 |
| Assassin 114 Twin | Nasenbaer | H1.25 | | 0.75 |(U)0.50(P)H0.50(N)0.75 | |
| Assassin 114V3 | Nasenbaer | | | | No walkthroughs posted|!R5.30 |
| Assassin 115"Beijing" | udosuk | H1.25 | H1.50 | 1.50 |(Az)H1.25 | !1.85 |
| Assassin 115V0.9 | udosuk | H0.75 | | E1.25 |(M)1.0(U)0.75 | !1.00 |
| Assassin 115V2 | udosuk | E1.75 | 1.50 | 1.50 | | 1.80 |
| Messy One #5 | Nasenbaer | 0.75 | H0.75 | H0.75 |(Az)1.0 | 0.95 |
+------------------------+-----------+-------+-------+-------+-----------------------+-------+
Page #4

+------------------------+-----------+-------+-------+-------+-----------------------+-------+
| Puzzle | Made By | Est | Afmob | Andrew| Other Raters | Score |
+------------------------+-----------+-------+-------+-------+-----------------------+-------+
| Assassin 116 Mars | Afmob | H1.00 | ** | H1.00 |(U)E1.0 | 1.25 |
| Assassin 116 Venus | Ed | 1.50 | H1.50 | 1.50 |(M)1.25 | !1.70 |
| Ass. 117 Hammer Throw | Ed | E1.25 | 1.25 | 1.25 | | 1.40 |
| Assassin 118 | J-C | | 1.25 | 1.25 |(Az)H1.0 | 1.35 |
| Assassin 118V0.9 | J-C | | | H1.00 |(U)E1.0 | !1.35 |
| Human Solvable 2X | HATMAN | | | |(U)H1.25 | 2.45 |
| Human Solvable 2X Lite | Afmob | H1.25 | ** | | |!R2.75 |
| Assassin 119 | Afmob | 1.00 | ** | 1.00 |(U)E1.0 | !1.10 |
| Assassin 119V2 | Afmob | 1.25 | ** | 1.50 |(U)H1.50 | 1.70 |
| Assassin 119V3 | Afmob | | | | | DNF |
| SOK2 | Nasenbaer | | 1.00 | 1.00 | | 1.20 |
+------------------------+-----------+-------+-------+-------+-----------------------+-------+
Page #5

+------------------------+-----------+-------+-------+-------+-----------------------+-------+
| Puzzle | Made By | Est | Afmob | Andrew| Other Raters | Score |
+------------------------+-----------+-------+-------+-------+-----------------------+-------+
| Ass. 120 "Twin Towers" | Ed | 1.25 | E1.25 | 1.25 | | 1.35 |
| Assassin 120V2 | Ed | | H1.50 | 1.75 |(Ed)1.75 | 3.70 |
| Assassin 121 | Nasenbaer | 1.00 | 1.00 | H1.00 | | 1.20 |
| Assassin 121V2 | Nasenbaer | 1.25 | 1.25 | 1.25 | | 1.30 |
| Human Solvable 3X | HATMAN | H0.75 | 1.50 | 1.50 |(N)1.50(Ed)1.50 |!R3.65 |
| Assassin 122 | Afmob | 1.00 | ** | 1.25 |(Ed)H1.0 | 1.85 |
| Assassin 122V1.5 | Afmob | H1.25 | ** | 1.25 | | 1.90 |
| Ass. 123 "Roulette" | udosuk | | H1.25 | |(Ed)E1.50 |!R3.25 |
| Assassin A123V0.9 | udosuk | | | 1.25 | | 1.55 |
| Assassin 123V2 | udosuk | | 2.00 | 2.50 | |!R3.85 |
+------------------------+-----------+-------+-------+-------+-----------------------+-------+
Page #6

+------------------------+-----------+-------+-------+-------+-----------------------+-------+
| Puzzle | Made By | Est | Afmob | Andrew| Other Raters | Score |
+------------------------+-----------+-------+-------+-------+-----------------------+-------+
| Messy One #6X | Ed | | H1.00 | | | 1.00 |
| Assassin 124 | Frank | | 1.00 | H1.00 | | !1.10 |
| Assassin 124V2 | Frank | | H1.75 | 1.75 | | !2.95 |
| Assassin 125 | Para | 1.00 | H1.00 | E1.25 | | 1.05 |
| Assassin 125V0 | Para | 0.75 | | 0.75 | | 0.70 |
| Assassin 125V2 | Para | 1.50 | 1.25 | 1.50 | | 1.55 |
+------------------------+-----------+-------+-------+-------+-----------------------+-------+
Page #7


Some of the selected quotes in the puzzle entries have been edited to remove "spoilers"; the full rating comments are included with the walkthroughs. In some cases the puzzle makers gave hints; these are included in tiny text in the selected quotes.

Many thanks to Ed for providing the original rating tables, including links to the puzzle threads. I think it was a great idea that in the rating tables he provided separate columns for Afmob and myself, the most regular posters of walkthroughs. Thanks also to Børge for generating so many diagrams, which are also in the Images with "udosuk Style Killer Cages" thread.

If you solve any of these puzzles and decide that there aren't enough walkthroughs for that puzzle or, better still, that you've found an interesting way to solve it which hasn't been posted, please feel free to post your walkthrough in the puzzle thread. Your comments and walkthrough will then be added to this archive.


Last edited by Andrew on Mon Jan 14, 2013 9:16 pm, edited 31 times in total.

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PostPosted: Fri Apr 22, 2011 12:09 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Messy One #1 by Ed (April 2008) here
Puzzle Diagram:
Image
The original diagram is no longer available;
Ed has replace it by Børge's B&W diagram.
Images with "udosuk style Killer Cages" by Børge:
Image     Image
Code: Select, Copy & Paste into solver:
3x3:d:k:2817:2817:3330:4867:4867:6916:6916:6916:6916:773:4614:3330:3847:4867:6916:4872:4872:4872:773:4614:4614:3847:4867:4105:4105:4105:4872:4874:2315:2315:2060:4867:5389:5389:5646:5646:4874:4623:3856:3856:2060:5389:5389:3601:5646:4874:4623:3346:3346:3346:2060:3601:3601:5646:6931:4623:4623:6931:7188:4885:4885:4885:3350:6931:6931:6931:6931:7188:4885:5143:4885:3350:4632:4632:4632:4632:7188:7188:5143:5143:5143:
Solution:
+-------+-------+-------+
| 8 3 6 | 4 5 7 | 2 9 1 |
| 2 9 7 | 6 1 8 | 5 4 3 |
| 1 5 4 | 9 3 2 | 6 8 7 |
+-------+-------+-------+
| 9 4 5 | 1 6 3 | 8 7 2 |
| 3 6 8 | 7 2 9 | 1 5 4 |
| 7 2 1 | 8 4 5 | 3 6 9 |
+-------+-------+-------+
| 4 1 9 | 3 8 6 | 7 2 5 |
| 6 7 2 | 5 9 1 | 4 3 8 |
| 5 8 3 | 2 7 4 | 9 1 6 |
+-------+-------+-------+
Quote:
Ed: Start of an occasional series - Messy One. Must get a SudokuSolver Score from 0.95-1.05 and is messy (NOT symmetrical).

Afmob: We can't have a Killer on our new home without a walkthrough, can we? ;)
Nice idea Ed though it will be quite difficult to get the SS rating right since the range of accepted ratings is quite small. This is probably one of the rare cases where it's harder to create a Killer than to solve it.
Rating: 1.0.

Mike: Nice, enjoyable, and (above all!) messy killer, Ed! Thanks!
Just to give Afmob a bit of company, here's my WT. I used a move (step 5), which almost certainly is not necessary, but which added to the fun, so I thought "why not?".
Like Afmob, I'll rate this one at 1.0.

Andrew: This was a fun puzzle and a fairly easy one. Even so the solving path is fairly well defined so that my route was very similar to those already posted by Afmob and Mike.
I'll also rate Messy One #1 at 1.0. I thought about a lower rating but it's still a reasonably long path and harder than newspaper puzzles ... so I feel that 1.0 is justified.
It's my first walkthrough for many months, probably over a year, that doesn't include the word killer ...

Walkthrough by Afmob:
Messy One #1 Walkthrough:

1. R123
a) Outies = R4C5 = 6
b) 3(2) = {12} locked C1+N1
c) 11(2) <> 9
d) 19(5) = 136{27/45} -> 1,3 locked for N2

2. R456 !
a) Innies = 8(2) <> 4,8,9
b) Outies N56 = 9(2) = [63/72/81]
c) 9 locked in 19(3) @ N4 for C4 -> 19(3) = 9{37/46}
d) 9(2) <> 3
e) ! Outies N56 = 9(2) <> {36} because it'S a Killer pair of 19(3)
f) 15(2) = {78} locked for R5
g) Outies N6 = 12(2) <> 1,2,6; R4C6 <> 4,5
h) 13(3) must have 1 xor 2 because R6C3 = (12) -> R6C45 <> 1,2
i) 1,2 locked in 8(3) @ N5 = {125} locked for N5+D\
j) Outies N6 = 12(2) <> 7

3. C456 !
a) 15(2) @ N1 = {69} locked for C4+N2 because R5C4 = (78) blocks {78}
b) ! Outies N9 = 7(2) = {16/25} because {34} blocked by Killer pair of Outies N6
c) 28(4) = {4789} locked for N8 because {5689} blocked by Killer pair of Outies N9
d) Innies N89 = 10(3) = {235} locked for C4+N8
e) 3 locked in Outies N6 @ C6 = 12(2) = {39} locked for C4+N5+21(4)
f) 13(3) = 4{18/27} -> 4 locked for R6
g) R4C4 = 1

4. N4
a) 9(2) <> 8
b) Hidden Single: R5C3 = 8 @ N4, R5C4 = 7, R1C4 = 4
c) 13(3) = {148} -> R6C3 = 1, R6C4 = 8, R6C5 = 4
d) Hidden Single: R9C6 = 4 @ C6

5. N12
a) 19(5) = {13456} -> {135} locked for C5+N2
b) 11(2) <> 7; R1C2 <> 6
c) 13(2) <> 5; R2C3 <> 9
d) 5 locked in R13C2 for C2
e) Hidden Single: R4C3 = 5 @ N4 -> R4C2 = 4

6. R456
a) R5C5 = 2, R6C6 = 5
b) Innies = 8(2) = [62] -> R5C2 = 6, R6C2 = 2
c) 19(3) = {379} locked for C1
d) Innies N6 = 9(2) = [81] -> R4C7 = 8, R5C7 = 1
e) Outies N4 = 10(2) <> 4,8; R6C2 <> 9

7. R789
a) 18(4) must have 5 xor 6 because R9C1 = (56) -> R9C34 <> 5,6
b) 5 locked in R78C4 for 27(6)
c) Hidden Single: R9C1 = 5 @ N9
d) 18(5) = 35{19/28} -> 3 locked for R9
e) 19(5) = 136{27/45} because R78C6 = (16); R7C8 = (25) and R7C7+R8C8 <> 6
-> 3 locked for N9+D\
f) Hidden Single: R9C8 = 1 @ N7
g) 18(4) = {2358} -> R9C2 = 8; 2 locked for R9
h) 20(4) = {1469} -> R8C7 = 4, {69} locked for R9+N9
i) 13(2) = {58} locked for C9+N9

8. R123
a) Hidden Single: R1C1 = 8 @ N1 -> R1C2 = 3
b) 27(5) = 178{29/56} -> R2C6 = 8, R1C9 = 1
c) R1C5 = 5
d) 27(5) = {12789} -> {279} locked for R1, 9 locked for N3
e) Hidden Single: R7C2 = 1 @ N7 -> R7C3 = 9

9. Rest is singles.

Rating: 1.0. I used Killer pairs to crack it.
Walkthrough by Mike (mhparker):
Just to give Afmob a bit of company, here's my WT. I used a combined cage move (step 5), which almost certainly is not necessary, but which added to the fun, so I thought "why not?".

Like Afmob, I'll rate this one at 1.0.

Here's the way I did it:

May 15, 2008: Corrections from Andrew applied (many thanks!)

Messy One #1 Walkthrough

Prelims

a) 3(2) at R2C1 = {12}, locked for C1 and N1
b) 11(2) at R1C1 = {38/47/56} (no 9)
c) 13(2) at R1C3 and R7C9 = {49/58/67} (no 1..3)
d) 15(2) at R2C4 and R5C3 = {69/78} (no 1..5)
e) 9(2) at R4C2 = {18/27/36/45} (no 9)
f) 8(3) at R4C4 = {125/134}, 1 locked for D\ and N5
g) 28(4) at R7C5 = {4789/5689} (no 1..3), {89} locked for N8

1. Outie N23: R4C5 = 6
1a. cleanup: no 9 in R5C3; no 3 in R4C23

2. Innies/Outies N789: R7C23 = 10(2) = {19/28/37/46} (no 5)
2a. R56C2 = 8(2) = {17/26/35} (no 4,8,9)

3. Split innies N4: R56C3 = 9(2) = [63/72/81]
3a. -> no 4..9 in R6C3

4. 9 in N4 locked in 19(3) at R4C1 = {379/469} (no 5,8)
4a. 9 locked in R456C1 for C1

5. 9(2) at R4C2 = {18/27/45}
5a. -> combined cage 19(3) at R4C1 (step 4) and 9(2) at R4C2 blocks {17} combo for R56C2 (step 2a)
5b. -> R56C2 = {26/35} (no 1,7)

6. 19(3) at R4C1 (step 4) and R56C2 (step 5b) form killer pair on {36} within N4
6a. -> no 3,6 elsewhere in N4
6b. cleanup: no 9 in R5C4

7. Naked pair (NP) at R5C34 = {78}, locked for R5

8. 15(2) at R2C4 = {69} (no 7,8), locked for C4 and N2 (Note: {78} combo blocked by R5C4)

9. Innies C6789: R69C6 = 9(2) = [18/27/36/45/54]
9a. -> no 9 in R9C6

10. Outies N6: R45C6 = 12(2) = {39} (no 2,4,5,7,8), locked for C6, N5 and 21(4)
(Note: other combos impossible, because the 9 of C6 is locked in this hidden cage)
10a. split 9(2) at R45C7 = [45/54/72/81] (no 6; no 1,2 in R4C7)
10a. cleanup: no 6 in R9C6 (step 9)

11. 2 in N5 locked in 8(3) at R4C4 = {125} (no 4) (last combo), locked for D\ and N5
11a. cleanup: no 6 in R1C2, no 5 in R9C6 (step 9)

12. 28(4) at R7C5 = {4789} (no 5) (last combo), locked for N8

13. Outies N9: R78C6 = {16} (no 2,5), locked for C6, N8 and 19(5)
(Note: other combos impossible, because the 6 of C6/N8 is locked in this hidden cage)

14. Naked triple (NT) at R789C4 = {235}, locked for C4
14a. -> R4C4 = 1
14b. cleanup: no 8 in R4C23

15. Hidden single (HS) in N4 at R5C3 = 8
15a. -> R5C4 = 7; R6C3 = 1 (step 3)
15b. cleanup: no 5 in R12C3

16. 5 in C1 locked in R789C1 for N7

17. HS in C3 at R4C3 = 5
17a. -> R4C2 = 4
17b. cleanup: no 7 in R1C1; no 3 in R56C2 (step 5b); no 4,5 in R5C7 (step 10a); no 6 in R56C1 (step 4)

>>>>> Aside:
It's tempting at this stage to think that there is a Unique Rectangle (UR, type I) available on {39}
at R45C16, leading to R4C1 = 7, but this is not the case (and in fact is the wrong answer). the reason
for this is that one of the corners of the would-be UR (namely, R4C6) lies on one of the two diagonals.
This is something one has to watch out for when trying to use UR on a Sudoku-X.
<<<<<

18. 2 in R4 locked in R4C89 for N6
18a. -> R45C7 (step 10a) = [81]

19. HS in N9 at R9C8 = 1

20. 3 in C5 locked in R123C5
20a. -> split 13(4) at R1C4+R123C5 = {1345} (no 2,7,8)
(Note: must have 3, and {1237} unplaceable due to R1C4)
20b. -> R1C4 = 4; R123C5 = {135}, locked for C5 and N2
20c. cleanup: no 9 in R2C3, no 7 in R1C2

21. Split 7(2) at R5C5+R6C6 = [25]
21a. -> R56C2 = [62]; R6C45 = [84]

22. HS in C6/N8 at R9C6 = 4

23. 2 of R1 locked in 27(5) at R1C6 = {12789/23589/23679}
23a. 9 locked in R1C789 for R1 and N3
23b. no 2 in R2C6
23c. cleanup: no 4 in R2C3

24. HS in N1 at R3C3 = 4
24a. -> split 14(2) at R23C2 = [95] (last permutation)
24b. cleanup: no 6 in R1C1

All singles and simple cage sums left now.
Walkthrough by Andrew:
I'll also rate Messy One #1 at 1.0. I thought about a lower rating but it's still a reasonably long path and harder than newspaper puzzles or those on http://www.sudoku.org.uk so I feel that 1.0 is justified.

I wasn't going to post my walkthrough, but have changed my mind so here it is. I've included eliminations on the diagonals for those who do their own eliminations manually; ones on the diagonals are particularly easy to overlook, I often forget them.

Prelims

a) R1C12 = {29/38/47/56}, no 1
b) R12C3 = {49/58/67}, no 1,2,3
c) R23C1 = {12}, locked for C1 and N1, clean-up: no 9 in R1C12
d) R12C4 = {69/78}
e) R4C23 = {18/27/36/45}, no 9
f) R5C34 = {69/78}
g) R78C9 = {49/58/67}, no 1,2,3
h) R456C1 = {289/379/469/478/568}, no 1
i) 8(3) diagonal cage in N5 = {125/134}, 1 locked for N5 and D\
j) 28(4) cage in N8 = {4789/5689}, no 1,2,3, 8,9 locked for N8
k) 19(5) cage at R1C4 = {12349/12358/12367/12457/13456}, 1 locked for N2
l) 19(5) cage at R7C6 = {12349/12358/12367/12457/13456}, must contain 1

1. 45 rule on R123 1 outie R4C5 = 6, clean-up: no 3 in R4C23, no 9 in R5C3

2. 28(4) cage in N8 = {4789/5689}
2a. 6 of {5689} must be in R9C6 -> no 5 in R9C6

3. 45 rule on R789 2 innies R7C23 = 10 = {19/28/37/46}, no 5
3a. R56C2 = 8 = {17/26/35}, no 4,8,9

4. 45 rule on N9 2 outies R78C6 = 7 = {16/25/34}, no 7
4a. R7C78 + R8C8 = 12 = {129/138/147/156/237/345} (cannot be {246} which clashes with R78C6)
4b. 1 of {129} must be in R7C8 -> no 9 in R7C8

5. 45 rule on N4 2 innies R56C3 = 9 = [63/72/81], no 9 in R5C3, R6C3 = {123}

6. 9 in N4 locked in R456C1, locked for C1
6a. R456C1 = {379/469}, no 5,8
6b. R56C3 (step 5) = [72/81] (cannot be [63] which clashes with R456C1), no 3,6, clean-up: no 9 in R5C4

7. Naked pair {78} in R5C34, locked for R5, clean-up: no 1 in R6C2 (step 3a)
7a. R23C4 = {69} (cannot be {78} which clashes with R5C4), locked for C4 and N2

8. 45 rule on N6 2 outies R45C6 = 12 = {39}/[75/84], no 2, no 4,5 in R4C6
8a. R45C7 = 9 = [36/45/54/72/81], no 9, no 1,2 in R4C7, no 3 in R5C7

9. 45 rule on N8 3 innies R789C4 = 10 = {127/235} (cannot be {145} which clashes with 28(4) cage), no 4, 2 locked for C4 and N8, clean-up: no 5 in R78C6 (step 4)
9a. R7C78 + R8C8 (step 4a) = {129/156/237/345} (cannot be {138/147} which clash with R78C6), no 8

10. 45 rule on N5 3 innies R5C4 + R6C45 = 19 = {379/478} (cannot be {289} because 2,9 only in R6C5), no 2,5, 7 locked for N5, clean-up: no 5 in R5C6 (step 8)
10a. 9 of {379} must be in R6C5 -> no 3 in R6C5

11. 2,5 in N5 locked in 8(3) diagonal cage = {125} (only remaining combination), locked for D\, clean-up: no 6 in R1C2

12. R7C78 + R8C8 (step 9a) = {237/345} (cannot be {129/156} because 1,2,5 only in R7C8), no 1,6,9
12a. 2,5 only in R7C8 -> R7C8 = {25}
12b. 3 locked in R7C7 + R8C8, locked for N9, D\ and 19(5) cage -> no 3 in R78C6, clean-up: no 8 in R1C2, no 4 in R78C6 (step 4)
12c. 3 in N1 locked in R13C2, locked for C2, clean-up: no 5 in R56C2 (step 3a), no 7 in R7C3 (step 3)

13. Naked pair {16} in R78C6, locked for C6 and N8, clean-up: no 7 in R789C4 (step 9), no 5 in 28(4) cage in N8 (step 2)

14. Naked triple {235} in R789C4, locked for C4 -> R4C4 = 1, clean-up: no 8 in R4C23, no 9 in R6C5 (step 10)

15. R5C3 = 8 (hidden single in N4), R5C4 = 7, R6C3 = 1 (step 6b), clean-up: no 5 in R12C3, no 7 in R6C2 (step 3a), no 2,9 in R7C2 (step 3)

16. Naked pair {26} in R56C2, locked for C2, N4 and 18(4) cage -> no 2,6 in R7C3, clean-up: no 7 in R4C23, no 4 in R456C1 (step 6a), no 4,8 in R7C2, no 4 in R7C3 (both step 3)
16a. Naked pair {45} in R4C23, locked for R4, clean-up: no 4,5 in R5C7 (step 8a)
16b. Naked triple {379} in R456C1, locked for C1, clean-up: no 4 in R1C2
16c. 5 in C1 locked in R789C1, locked for N7

17. Naked pair {48} in R6C45, locked for R6 and N5

18. Naked pair {39} in R45C6, locked for C6 and 21(4) cage -> no 3 in R4C7, clean-up: no 6 in R5C7 (step 8a)

19. Naked pair {39} in R5C16, locked for R5

20. Naked pair {39} in R4C6 and R7C3, locked for D/

21. 2 in R4 locked in R4C89, locked for N6 -> R5C7 = 1, R4C7 = 8 (step 8a)
21a. R9C8 = 1 (hidden single in N9)
21b. 8 in N9 locked in R789C9, locked for C9

22. 1,3 in C5 locked in R123C5 with 6 in R4C5 -> 19(5) cage = {13456} (only remaining combination, cannot be {12367} because R1C4 only contains 4,8) -> R1C4 = 4, R123C5 = {135}, locked for C5 and N2 -> R5C5 = 2, locked for D/, R6C6 = 5, R56C2 = [62], R6C45 = [84], 8 locked for D/, clean-up: no 7 in R1C2, no 9 in R2C3
22a. R9C6 = 4 (hidden single in C6)

23. 18(3) cage in N1 = {378/459/567} (cannot be {369/468} which clash with R1C12)
23a. 3,5 only in R3C2 -> R3C2 = {35}
23b. Naked pair {35} in R13C2, locked for C2 -> R4C23 = [45]
[R4C3 had been a hidden single in C3 since step 16c.]
23c. 4 of {459} must be in R3C3 -> no 9 in R3C3
23d. 4 in N1 locked in R23C3, locked for C3

24. 3 in R9 locked in R9C34
24a. 18(4) cage at R9C1 = {2358/2367}, no 9
24b. 2,3 only in R9C34 -> R9C34 = {23}, locked for R9

25. 5 in C4 locked in R78C4, locked for 27(6) cage -> no 5 in R78C1

26. R9C1 = 5 (hidden single in C1), locked for D/, R9C2 = 8 (step 24a)
26a. Naked pair {46} in R78C1, locked for C1 and N7 -> R1C1 = 8, R1C2 = 3, R3C2 = 5

27. Naked pair {17} in R78C2, locked for C2 and N7 -> R2C2 = 9, R3C3 = 4 (step 23), both locked for D\, R23C4 = [69], R12C3 = [67], R2C8 = 4, R5C89 = [54], R7C8 = 2, clean-up: no 9 in R78C9
27a. R3C7 = 6 (hidden single in D/)

28. Naked pair {37} in R7C7 + R8C8, locked for N9 -> R9C79 = [96], R9C5 = 7, R8C7 = 4 (hidden single in C7), R78C1 = [46], R78C6 = [61], R78C2 = [17], 7 locked for D/, R7C3 = 9 (step 3), locked for D/

and the rest is naked singles without using the diagonals.


Last edited by Andrew on Thu Sep 26, 2013 7:33 pm, edited 2 times in total.

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PostPosted: Fri Apr 22, 2011 12:15 am 
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Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Messy One #2 by Afmob (April 2008) here
Puzzle Diagram:
Image
Images with "udosuk style Killer Cages" by Børge:
Image     Image
Code: Select, Copy & Paste into solver:
3x3::k:6144:6144:6146:6146:6146:2565:4614:4614:4614:6144:6144:2315:2315:7693:2565:2565:4614:4625:3858:6144:3604:3604:7693:5143:5143:4625:4625:3858:1820:3604:7693:7693:7693:5143:5143:4625:3858:1820:6182:6182:6182:3881:3881:5143:6700:4653:4653:2095:2864:6182:6182:6700:6700:6700:4653:4663:2095:2864:3130:3130:3130:1085:7486:4663:4663:3905:3905:4931:2116:2116:1085:7486:4663:2377:2377:3905:4931:4931:4931:7486:7486:
Solution:
+-------+-------+-------+
| 2 1 8 | 7 9 6 | 5 4 3 |
| 9 7 4 | 5 8 3 | 1 6 2 |
| 6 5 3 | 4 2 1 | 9 8 7 |
+-------+-------+-------+
| 8 4 7 | 6 5 9 | 3 2 1 |
| 1 3 9 | 2 4 7 | 8 5 6 |
| 5 6 2 | 3 1 8 | 7 9 4 |
+-------+-------+-------+
| 7 2 6 | 8 3 5 | 4 1 9 |
| 4 9 5 | 1 7 2 | 6 3 8 |
| 3 8 1 | 9 6 4 | 2 7 5 |
+-------+-------+-------+
Quote:
Afmob: Here is my entry to the beauty of the asymmetrical.
If you don't find the cracking move which is available right from the start, then you'll have a harder time than SS suggests.
SS Score: 1.04. Estimated rating: (Hard) 1.0, depends on how long it takes you to find that move.
Hint: Look at Innies/Outies of R1234.

Mike: Nice puzzle, Afmob! Don't think I saw the cracking move you intended though, because I didn't see anything like that that was available "right from the start". Haven't read your TT hint.
Nevertheless very enjoyable and still only about a 1.25 rating the way I did it...

gary W: I thought this one was excellent. Many thanks Afmob

Andrew: Thanks Afmob for a challenging puzzle. Yes, it's available from the diagram at the start. That move isn't a difficult one but it's hard to spot (my step 30). Maybe that's because the eye is drawn away from the move.
I'll rate the way I solved it as Hard 1.25.
I used 16 different 45 tests, still slightly short of my record!

Ed: Agree. It was my key move and was very hard to find.
Here's an alternative way to get past Mike's step 8. It is the same as Andrew used, just gets to it a lot quicker. I'd still give this way a 1.25 rating.

Walkthrough by Mike (mhparker):
Don't think I saw the cracking move you intended though, because I didn't see anything like that that was available "right from the start". Haven't read your TT hint.

Nevertheless very enjoyable and still only about a 1.25 rating the way I did it. Certainly didn't need any chains. My moves 8 - 10 were what did it for me.

Edit: Added steps 9a/9b and simplified step 10, as proposed by Afmob. Thanks once again!
Edit2: Typo fixed in step 5. Thanks, Andrew!

Messy One #2 Walkthrough

Prelims

a) 24(3) at R1C3 = {789}, locked for R1
b) 10(3) at R1C6 = {127/136/145/235} (no 8,9)
c) 9(2) at R2C3 and R9C2 = {18/27/36/45} (no 9)
d) 7(2) at R4C2 = {16/25/34} (no 7..9)
e) 15(2) at R5C6 = {69/78} (no 1..5)
f) 26(4) at R5C9 = {2789/3689/4589/4679/5678} (no 1)
g) 8(2) at R6C3 and R8C6 = {17/26/35} (no 4,8,9)
h) 11(2) at R6C4 = {29/38/47/56} (no 1)
i) 4(2) at R7C8 = {13}, locked for C8 and N9; cleanup: no 5,7 in R8C6
j) 29(4) at R7C9 = {5789}, locked for N9; cleanup: no 1,3 in R8C6


1. Naked pair (NP) at R8C67 = {26}, locked for R8

2. Naked triple (NT) at R789C7 = {246}, locked for C7; cleanup: no 9 in R5C6

3. Innie C12: R9C2 = 8
3a. -> R9C3 = 1
3b. cleanup: no 7 in R67C3, no 8 in R2C4

4. 8 in N9 locked in R78C9 for C9

5. Innies N789: R7C134 = 21(3) = {579/678} (no 2..4)
(Note: {489} unplaceable)
5a. only 1 of {56}, which must go in R7C3
5b. -> no 5,6 in R7C14
5c. 7 locked in R7C14 for R7
5d. cleanup: no 5,6 in R6C3; no 5..9 in R6C4

6. Innie/Outie (I/O) diff. N89: R7C4 = R8C3 + 3
6a. -> R7C4 = {78} (no 9); R8C3 = {45} (no 3,7,9)
6b. cleanup: no 2 in R6C4

7. Innies N7: R7C13+R8C3 = 18(3) = {459/567}
7a. -> 5 locked in R78C3 for C3 and N7
7b. cleanup: no 4 in R2C4

8. Hidden killer mutual on {26} within N7:
8a. {26} in N7 locked in R7C23+R9C1
8b. -> R7C23 must contain at least one of {26} (no eliminations yet)

9. 12(3) at R7C5 = {129/345} (no 6,8)
(Note: {138} unplaceable, {156} blocked by R7C3, {246} blocked by R7C23 (step 8b))
9a. can only have 1 of {24}, which must go in R7C7
9b. -> no 2,4 in R7C56

10. Hidden pair (HP) in R7 at R7C27 = {24} (no 3,6,9)

11. Hidden single (HS) in R7 at R7C3 = 6
11a. -> R6C3 = 2
11b. cleanup: no 3,7 in R2C4; no 5 in R45C2

12. Innies N7 (step 7): R7C1+R8C3 = 12(2) = [75]
12a. -> R67C4 = [38]

13. HS in R8/C9/N9 at R8C9 = 8

14. Split 11(2) at R6C12 = {56} (no 1,4,8,9) (last combo), locked for R6 and N4
14a. cleanup: no 1 in R45C2

15. NP at R45C2 = {34}, locked for C2 and N4

16. R78C2 = [29]
16a. -> split 7(2) at R89C1 = {34}, locked for C1

17. R7C7 = 4
17a. -> split 8(2) at R7C56 (step 9) = {35} (no 1,9), locked for C7 and N8

18. R78C8 = [13]
18a. -> R89C1 = [43]

19. Naked single at R7C9 = 9
19a. -> split 12(2) at R9C89 = {57}, 7 locked for R9

20. Split 10(2) at R89C4 = [19] (last permutation)
20a. cleanup: no 8 in R2C3

21. NS at R8C5 = 7

22. NS at R1C4 = 7

23. HP in N1 at R23C3 = {34} (no 7..9)
23a. cleanup: no 2 in R2C4

24. 1 in R6 locked in R6C56 for N5

25. HS in R5 at R5C1 = 1
25a. -> spilt 14(2) at R34C1 = [59/68]
25b. -> no 2,8,9 in R3C1

26. NP at R36C1 = {56}, locked for C1
26a. -> R1C1 = 2 (NS)

27. Naked quad at R5C7+R6C789 = {4789}, locked for N6
27a. 4 locked in R6C89 for R6

28. I/O diff. R1234: R5C8 = R4C2 + 1
28a. -> R4C2 = 4, R5C8 = 5
28b. -> R5C2 = 3

29. R9C89 = [75]

30. Split 15(4) at R3C67+R4C78 = {1239/1248} (no 6,7)
(Note: {2346} unplaceable)
30a. -> R4C8 = 2
30b. 4 of {1248} only available in R3C6
30c. -> no 8 in R3C6

31. NS at R5C9 = 6
31a. cleanup: no 9 in R5C7

32. NP at R5C67 = {78}, locked for R5
32a. -> R5C3 = 9

33. R4C13 = [87]
33a. -> R3C1 = 6 (cage sum)

34. R1C35 = [89]

This next move intended to get to all singles more quickly:

35. R4C456 = {569} = 20
35a. -> R23C5 = 10(2) (30(5) cage split)
35b. 8 in N2 locked in R23C5
35c. -> split 10(2) at R23C5 = {28}, locked for C5 and N2

Only naked singles and a couple of simple cage sums left now.
Solving outline by gary W:
1.O r789-> r7c134=21 and only combos are 957 and 768.So r6c3=2/3.
2.r5c128=9.So r5c8=5/6.
3.r789c7={246} only perm.
4.Thus 15/2 cage n5/6 cannot be {69} because the 26/4 cage in n6 must have a 5 or a 9.
So r5c67={78}.Thus 26/4 cage n6 <> 1 OR 2 in it.
5.I-O r6789-> r6c56=r5c9+3 so<> {12}
6Now,if r5c12={12} this forces {12} into r6c56 ..impossible.So r5c12={13}.-> r6c3=2 etc and it's a mop-up from here.
Walkthrough by Andrew:
Yes, it's available from the diagram at the start. That move isn't a difficult one but it's hard to spot (my step 30). Maybe that's because the 15(3) and 7(2) cages sticking out into R5C12 draw the eye away from the move.

Mike's step 8 was unusual and very powerful because it leads to a key combination elimination from the 12(3) cage in R7. I'm not sure if I've seen a hidden killer pair used that way before; it's something I'll try to look out for in future. I'm guessing that most/all software solvers wouldn't currently find that step. It looks to be the sort of thing that only an expert human solver would consider to be useful.

I'll rate the way I solved it as Hard 1.25. It's clearly easier with Mike's step 8 which I think was more powerful than the move that Afmob hinted at. If it's 1.25 with Mike's step then it's also 1.25 with Afmob's breakthrough step.

Prelims

a) R2C34 = {18/27/36/45}, no 9
b) R45C2 = {16/25/34}, no 7,8,9
c) R5C67 = {69/78}
d) R67C3 = {17/26/35}, no 4,8,9
e) R67C4 = {29/38/47/56}, no 1
f) R78C8 = {13}, locked for C8 and N9
g) R8C67 = [17/26/35/62], no 4,8,9, no 5,7 in R8C6
h) R9C23 = {18/27/36/45}, no 9
i) R1C345 = {789}, locked for R1
j) 10(3) cage at R1C6 = {127/136/145/235}, no 8,9
k) 26(4) cage in N6 = {2789/3689/4589/4679/5678}, no 1
l) 29(4) cage in N9 = {5789}, locked for N9, clean-up: no 1,3 in R8C6

1. 45 rule on C12 1 innie R9C2 = 8, R9C3 = 1, clean-up: no 8 in R2C4, no 7 in R67C3
1a. 8 in N9 locked in R78C9, locked for C9

2. Naked pair {26} in R8C67, locked for R8

3. Naked triple {246} in R789C7, locked for C7, clean-up: no 9 in R5C6

4. 1 in N6 locked in R4C79, locked for R4, clean-up: no 6 in R5C2

5. R7C567 = {129/147/156/237/246/345} (cannot be {138} which clashes with R7C8), no 8

6. 45 rule on N36 2 innies R25C7 = 1 outie R3C6 + 8
6a. Max R25C7 = 16 -> max R3C6 = 8

7. 45 rule on N7 3 innies R7C13 + R8C3 = 18 = {279/369/459/567}
7a. 2 of {279} must be in R7C3 -> no 2 in R7C1

8. 45 rule on N3 2 innies R23C7 = 1 outie R4C9 + 9
8a. Max R23C7 = 16 -> max R4C9 = 7
8b. Min R4C9 = 1 -> min R23C7 = 10 -> no 1 in R3C7

9. 45 rule on N89 1 innie R7C4 = 1 outie R8C3 + 3, R8C3 = {345}, R7C4 = {678}, R6C4 = {345}

10. R7C13 + R8C3 (step 6) = {369/459/567} (cannot be {279} because 7,9 only in R7C1), no 2, clean-up: no 6 in R6C3
10a. 7,9 can only be in R7C1 -> R7C1 = {79}
10b. 6 of {369} must be in R7C3 -> no 3 in R7C3, clean-up: no 5 in R6C3
[Could also eliminate {369} with complex block using step 9 but it goes soon with simple steps.]

11. 18(3) cage at R6C1 = {189/279/369/378/459/567} (cannot be {468} because R7C1 only contains 7,9)
11a. 8 of {189} must be in R6C1 -> no 1 in R6C1

12. 45 rule on R1234 3 outies R5C128 = 9 = {126/135/234}, no 7,8,9
12a. 2 of {234} must be in R5C8 (R5C12 cannot be {23} which clashes with R6C3) -> no 4 in R5C8
12b. 5 of {135} must be in R5C8 -> no 5 in R5C12, clean-up: no 2 in R4C2

13. 45 rule on R789 3 innies R7C134 = 21 = {579/678}, 7 locked for R7
13a. 6 of {678} must be in R7C3 -> no 6 in R7C4, clean-up: no 5 in R6C4, no 3 in R8C3 (step 9)

14. R7C13 + R8C3 (step 7) = {459/567}, 5 locked in R78C3, locked for C3 and N7, clean-up: no 4 in R2C4

15. 15(3) cage at R8C3 = {159/249/258/348/357/456} (cannot be {168/267} because R8C3 only contains 4,5)
15a. 6 of {456} must be in R9C4, for all other combinations 4,5 must be in R8C3 -> no 4,5 in R9C4

16. Max R1C789 = 15 -> no 2 in R2C8

17. 14(3) cage at R3C3 = {149/158/167/239/248/257/347/356}
17a. 1 of {149} must be in R3C4
17b. 9 of {239} must be in R34C3 (R34C3 cannot be {23} which clashes with R6C3)
17c. -> no 9 in R3C4

18. 45 rule on R89 3 outies R7C289 = 12 = {129/138/156/246/345}
18a. 2 of {129} must be in R7C2 -> no 9 in R7C2

19. 45 rule on R789 1 innie R7C1 = 2 outies R6C34 + 2
19a. R7C1 = {79} -> R6C34 = 5,7 = [23/34], 3 locked for R7

20. 45 rule on N47 3 innies R458C3 = 1 outie R3C1 + 15
20a. Max R458C3 = 22 -> max R3C1 = 7

21. 15(3) cage at R8C3 (step 15) = {159/249/258/348/456} (cannot be {357} because R89C4 = {37} clashes with R67C4), no 7
21a. 8 of {348} must be in R8C4 -> no 3 in R8C4

22. 45 rule on R789 4 outies R6C1234 = 16 and must contain [23/34] in R6C34 (step 19a) = {1348/2347/2356} -> R6C12 = {18/27/56} (cannot be {47} because 18(3) cage cannot be {47}7), no 4,9

23. 26(4) cage in N6 = {3689/4589/4679/5678} (cannot be {2789} which clashes with R5C7), no 2
23a. Killer triple 7,8,9 in R5C7 and 26(4) cage, locked for N6

24. 45 rule on C89 2 outies R16C7 = 2 innies R45C8 + 5
24a. Min R45C8 = 6 -> min R16C7 = 11, no 1 in R1C7, no 5 in R6C7
24b. Max R16C7 = 14 -> max R45C8 = 9
24c. R45C8 = {24/25/26/45}

25. Hidden killer triple 7,8,9 in R23C7, R5C7 and R6C7 -> R23C7 must contain one of 7,8,9
25a. R23C7 = R4C9 + 9 (step 8)
25b. Max R23C7 = 14 (cannot be {78} which contains two of 7,8,9) -> max R4C9 = 5
25c. R4C9 = {12345} -> R23C7 = 10,11,12,13,14 = [19/38/39/57/58/59/75] (cannot be [37/73] because R2C7 must be 1 when R4C1 = 1), no 3 in R3C7

26. 45 rule on C9 4 (3+1) outies R369C8 + R6C7 = R1C9 + 28
26a. Max R369C8 + R6C7 = 24 + 9 = 33 -> max R1C9 = 5
26b. Min R369C8 + R6C7 = 29 -> min R369C8 = 20, no 2 in R3C8

27. 45 rule on N36 2 outies R35C6 = 1 innie R2C7 + 7
27a. R2C7 = {1357} -> R35C6 must be even and cannot be [77] -> no 7 in R3C6

28. 45 rule on R6789 2 innies R6C56 = 1 outie R5C9
28a. Min R5C9 = 3 -> min R6C56 = 6, cannot be {12} -> at least one of 1,2 must be in R6C123

29. R5C128 (step 12) = {126/135/234}
29a. R5C12 cannot be {12} which clashes with R6C123 (step 28a) -> no 6 in R5C8

30. 45 rule on R1234 2 outies R5C18 = 1 innie R4C2 + 2, IOU no 2 in R5C8 -> R5C8 = 5, R5C12 = {13} (step 29), locked for R5 and N4 -> R6C3 = 2, R7C3 = 6, R4C8 = {24} (step 24c), clean-up: no 3,7 in R2C4, no 5 in R4C2
30a. R8C3 = 5 (hidden single in C3)
30b. 5 in N9 locked in R79C9, locked for C9

31. R6C4 = 3 (hidden single in R6), R7C4 = 8, R7C1 = 7 (step 13)
31a. R7C1 = 7 -> R6C12 = {56} (step 11), locked for R6 and N4 -> R4C2 = 4, R5C2 = 3, R5C1 = 1, R7C2 = 2, R8C2 = 9, R7C7 = 4, R4C8 = 2
31b. R7C7 = 4 -> R7C56 = {35} (step 5), locked for R7 and N8 -> R7C89 = [19], R8C8 = 3, R9C8 = 7, R89C9 = [85], R89C1 = [43], R8C45 = [17], R9C4 = 9 (step 15), R1C4 = 7, clean-up: no 8 in R2C3

32. 26(4) cage in N6 (step 23) = {4679} (only remaining combination) -> R5C9 = 6, clean-up: no 9 in R5C7
32a. Naked triple {479} in R6C789, locked for R6 and N6 -> R5C7 = 8, R5C6 = 7, R5C3 = 9, R4C13 = [87], R1C35 = [89], R3C1 = 6 (cage sum), R6C12 = [56], R12C1 = [29], clean-up: no 2 in R2C4

33. R4C3 = 7 -> R3C34 = [34] (step 17) (cannot be {25} because 2,5 only in R3C4), R5C45 = [24], R2C3 = 4, R2C4 = 5, R4C456 = [659], R7C56 = [35]

34. 30(5) cage at R2C5 = {25689} (only remaining combination) -> R23C5 = {28}, locked for C5 and N2

35. 20(5) cage at R3C6 = {12359} (only remaining combination) -> R34C7 = [93] , R3C6 = 1

and the rest is naked singles.
Alternative ending by Ed:
I haven't got time to do a full WT.

Messy One #2 (ALT ending)
Mike's steps 1-7: should be to here
Code:
.-------------------------------.-------------------------------.-------------------------------.
| 123456789 12345679  789       | 789       789       1234567   | 135789    2456789   12345679  |
| 123456789 12345679  234678    | 123567    123456789 1234567   | 1357      2456789   12345679  |
| 123456789 12345679  2346789   | 123456789 123456789 123456789 | 135789    2456789   12345679  |
:-------------------------------+-------------------------------+-------------------------------:
| 123456789 123456    2346789   | 123456789 123456789 123456789 | 135789    2456789   12345679  |
| 123456789 123456    2346789   | 123456789 123456789 678       | 789       2456789   2345679   |
| 123456789 12345679  23        | 34        123456789 123456789 | 35789     2456789   2345679   |
:-------------------------------+-------------------------------+-------------------------------:
| 79        23469     56        | 78        12345689  12345689  | 246       13        589       |
| 3479      3479      45        | 1345789   1345789   26        | 26        13        5789      |
| 234679    8         1         | 2345679   2345679   2345679   | 246       579       579       |
'-------------------------------.-------------------------------.-------------------------------'

ALT steps

8. "45" r1234: 3 outies r5c128 = h9(3)r5 = {126/135/234}(no 7..9)

9. "45" r1234: r5c18 - 2 = r5c8
9a. since 1 innie & 1 outie are in the same house (n4) -> r5c8 cannot = 2 (IOU)
9b. h9(3)r5 = 1 of 4/5/6 (step 8) -> no (456) in r5c12
9c. no (123) in r4c2

10. Naked triple (123) in n4: all locked for n4
10a. 1 locked for r5
10b. 1 locked in h9(3)r5 = 1{26/35}(no 4)

11. 18(3)n4 must have 7/9 = {459/567}(no 8)
11a. must have only 1 of 7/9 -> no 7 or 9 in r6c12
11b. r6c12 = 5{4/6}
11c. 5 locked for n4 & r6
11d. no 2 r5c2

12. "45" n789: 4 outies r6c1234 = h16(4) & must have 5 (step 11c) & no 1
12a. ={2356} only = {56}[23]
12c. r7c1 = 7 (cage sum)

Cracked now.


Last edited by Andrew on Tue Apr 26, 2011 1:04 am, edited 1 time in total.

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PostPosted: Fri Apr 22, 2011 12:23 am 
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Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Cyclone V1 by Mike (mhparker) (April 2008) here
Puzzle Diagram:
Image
Images with "udosuk style Killer Cages" by Børge:
Image     Image
Code: Select, Copy & Paste into solver:
2x4::k:4096:4096:5378:5378:5378:5378:2054:2054:4096:3337:5378:3595:3595:2573:2573:2054:5392:3337:2578:3595:1300:1300:6422:6422:5392:4121:2578:3867:3867:4637:4637:6422:5392:4121:4121:3867:3867:2853:4637:6422:5392:5392:1834:1834:3628:2853:3118:6422:2864:1329:1329:3628:3628:6453:3118:2871:2864:2864:6453:6453:6453:6453:2871:2871:
Solution:
+---------+---------+
| 5 8 4 6 | 7 3 1 2 |
| 3 7 1 2 | 8 4 6 5 |
+---------+---------+
| 7 6 8 4 | 3 2 5 1 |
| 1 5 2 3 | 6 8 7 4 |
+---------+---------+
| 2 4 7 5 | 1 6 3 8 |
| 8 3 6 1 | 2 5 4 7 |
+---------+---------+
| 4 2 3 7 | 5 1 8 6 |
| 6 1 5 8 | 4 7 2 3 |
+---------+---------+
Quote:
Mike: Welcome to my first puzzle(s) on the SS forum!
Tried to create a nice killer with a whirling cage pattern, and always ended up with one row and column left over. So decided to simply cut them out and go for an 8 x 8 killer instead!
Est. rating: 1.25.
Have fun with those "36" tests! :-)

Afmob: Thanks Mike for providing a nice Killer which had an interesting move (step 2f). But I don't know if I tackle V2 because I am used to solve Killers with SumoCue and it's quite tedious to make eliminations with other programms, so I had quite a fight to solve it using JSudoku. Rating: Hard 1.0.

Andrew: It shouldn't be any harder using my Excel worksheet than a standard 9 x 9 killer; the eliminations get done by me either way. I guess the hardest thing may be getting used to 2 x 4 blocks instead of 3 x 3 nonets.
Thanks Mike for a fun puzzle. ... Thanks for that table, Mike!
In a position similar to where Afmob found his interesting move I found a different variation. It wasn't quite as direct as Afmob's one but mine also led to a fairly quick solution.
I agree with Afmob and rate Cyclone Killer V1 at Hard 1.0.

Mike wrote: BTW, here is a killer combination table for 8x8, which you may find useful:
3(2) = {12}
4(2) = {13}
5(2) = {14/23}
6(2) = {15/24}
6(3) = {123}
7(2) = {16/25/34}
7(3) = {124}
8(2) = {17/26/35}
8(3) = {125/134}
9(2) = {18/27/36/45}
9(3) = {126/135/234}
10(2) = {28/37/46}
10(3) = {127/136/145/235}
10(4) = {1234}
11(2) = {38/47/56}
11(3) = {128/137/146/236/245}
11(4) = {1235}
12(2) = {48/57}
12(3) = {138/147/156/237/246/345}
12(4) = {1236/1245}
13(2) = {58/67}
13(3) = {148/157/238/247/256/346}
13(4) = {1237/1246/1345}
14(2) = {68}
14(3) = {158/167/248/257/347/356}
14(4) = {1238/1247/1256/1346/2345}
15(2) = {78}
15(3) = {168/258/267/348/357/456}
15(4) = {1248/1257/1347/1356/2346}
15(5) = {12345}
16(3) = {178/268/358/367/457}
16(4) = {1258/1267/1348/1357/1456/2347/2356}
16(5) = {12346}
17(3) = {278/368/458/467}
17(4) = {1268/1358/1367/1457/2348/2357/2456}
17(5) = {12347/12356}
18(3) = {378/468/567}
18(4) = {1278/1368/1458/1467/2358/2367/2457/3456}
18(5) = {12348/12357/12456}
19(3) = {478/568}
19(4) = {1378/1468/1567/2368/2458/2467/3457}
19(5) = {12358/12367/12457/13456}
20(3) = {578}
20(4) = {1478/1568/2378/2468/2567/3458/3467}
20(5) = {12368/12458/12467/13457/23456}
21(3) = {678}
21(4) = {1578/2478/2568/3468/3567}
21(5) = {12378/12468/12567/13458/13467/23457}
21(6) = {123456}
22(4) = {1678/2578/3478/3568/4567}
22(5) = {12478/12568/13468/13567/23458/23467}
22(6) = {123457}
23(4) = {2678/3578/4568}
23(5) = {12578/13478/13568/14567/23468/23567}
23(6) = {123458/123467}
24(4) = {3678/4578}
24(5) = {12678/13578/14568/23478/23568/24567}
24(6) = {123468/123567}
25(4) = {4678}
25(5) = {13678/14578/23578/24568/34567}
25(6) = {123478/123568/124567}
26(4) = {5678}
26(5) = {14678/23678/24578/34568}
26(6) = {123578/124568/134567}
27(5) = {15678/24678/34578}
27(6) = {123678/124578/134568/234567}
28(5) = {25678/34678}
28(6) = {124678/134578/234568}
28(7) = {1234567}
29(5) = {35678}
29(6) = {125678/134678/234578}
29(7) = {1234568}
30(5) = {45678}
30(6) = {135678/234678}
30(7) = {1234578}
31(6) = {145678/235678}
31(7) = {1234678}
32(6) = {245678}
32(7) = {1235678}
33(6) = {345678}
33(7) = {1245678}
34(7) = {1345678}
35(7) = {2345678}
36(8) = {12345678}


Andrew suggested using Ruud's combination calculator with 9 forbidden; however that's no longer available.
Walkthrough by Afmob:
Thanks Mike for providing a nice Killer which had an interesting move (step 2f -> Grouped X-Wing).

Note: I used B for Blocks since there are no Nonets.

Cyclone V1 Walkthrough:

1. R678
a) Innies B7 = 20(3) = {578} locked for B7
b) Outies R78 = 6(2) = [15/24]
c) 12(2): R7C7 <> 4,5
d) 14(3): R7C5 <> 1,2,3 because R6C5 = (12)
e) Killer pair (78) locked in 14(3) + R7C7 for R7
f) 7(2) <> {25} because it's a Killer pair of Outies R78
g) Killer pair (14) locked in 7(2) + Outies R78 for R6
h) Outies R8 = 11(3) <> 5 because {245} blocked by Killer pair (24) of 5(2)
i) 5 locked in 14(3) @ R7 = 5{18/27}

2. C5678 !
a) Outies C78 = 12(2) = [48/75/84]
b) 10(2) = [46/73/82]
c) 11(2) <> {47} because it's a Killer pair of Outies C78
d) Killer pair (58) locked in Outies C78 + 11(2) for C6
e) Using Outies R78 = 6(2): Innies B46 = 7(2) <> 7,8
f) ! 7 locked in 18(3) + 25(5) for B46 (Grouped X-Wing)
-> 18(3) = 7{38/56}; R45C7 <> 5,8
-> 7 locked for C78
g) R7C7 = 8 -> R6C7 = 4
h) 14(3) @ R6C5 = {257} -> R6C5 = 2
i) Innies B46 = [16/43/61]
j) Killer pair (58) locked in R4C6 + 11(2) for C6
k) 10(2) <> 2

3. C1234
a) 7(2) = {16} locked for R6+B5
b) Innies B35 = Outies B46 = 8(2) <> 4,8; R4C4 <> 2,7
c) Outies C12 = 10(2) = [73/82]
d) 5(2) = {23} locked for R7+B7

4. R12
a) 8(3) = {125} locked for B2 because {134} blocked by Killer pair (34) of 10(2)
b) Outies R12 = 10(2) = [64/73/82]
c) Outies R1 = 9(3) = 1{26/35} since {234} blocked by Killer pair (34) of 10(2)
d) 13(2): R2C2 <> 8
e) 8 locked in 14(3) @ R2 = {248} -> 2 locked for C4
f) Outies R12 = 10(2) <> 7
g) 13(2): R2C2 <> 6

5. C5678
a) Naked triple (367) locked in R245C7 for C7
b) 5 locked in R78C5 for B8
c) 11(3): 6{14/23} -> 6 locked for C8+B8; R78C8 <> 1,2
d) 6 locked in R4C57 for R4

6. B3
a) 16(3) <> 2

7. Rest is singles and simple cage sums.

Rating: Hard 1.0. I used Killer pairs and a Grouped X-Wing.
Walkthrough by Andrew:
In a position similar to where Afmob found his grouped X-wing, I found a different grouped X-wing. It wasn't quite as direct as Afmob's one but mine also led to a fairly quick solution.

I agree with Afmob and rate Cyclone Killer V1 at Hard 1.0.

Here is my walkthrough. I originally used some combined cages but have replaced them with simpler steps which weren’t significantly slower.

Prelims

a) R23C2 = {58/67}
b) R2C67 = {28/37/46}, no 1,5
c) R34C3 = {28/37/46}, no 1,5
d) R3C56 = {14/23}
e) R56C6 = {38/47/56}, no 1,2
f) R6C34 = {16/25/34}, no 7,8
g) R67C7 = {48/57}, no 1,2,3,6
h) R7C23 = {14/23}
i) 8(3) cage in Octet 2 (O2) = {125/134}, 1 locked for O2
j) 18(3) cage at R4C6 = {378/468/567}, no 1,2

1. 36 rule on O2 3 innies R1C56 + R2C5 = 18 = {378/468/567}, no 2

2. 36 rule on R12 2 outies R3C24 = 10 = [64/73/82], no 5 in R3C2, R3C4 = {234}, clean-up: no 8 in R2C2
2a. Max R3C4 = 4 -> min R2C45 = 10, no 1 in R2C4
2b. Killer single 4 in R3C4 and R3C56, locked for R3, clean-up: no 6 in R4C3

3. 36 rule on C8 3 outies R138C7 = 8 = {125/134}, no 6,7,8

4. Killer pair 4,5 in R138C7 and R67C7, locked for C7, clean-up: no 6 in R2C6

5. 36 rule on C78 2 outies R24C6 = 12 = {48}/[75], no 2,3,6, no 7 in R4C6, clean-up: no 7,8 in R2C7
5a. R56C6 = {38/56} (cannot be {47} which clashes with R24C6), no 4,7
5b. Killer pair 5,8 in R24C6 and R56C6, locked for C6

6. 36 rule on C12 2 outies R57C3 = 10 = [64/73/82], R5C3 = {678}, no 1 in R7C3, clean-up: no 4 in R7C2

7. 1 in R2 locked in R2C138
7a. 36 rule on R1 3 outies R2C138 = 9 = {126/135}, no 4,7,8
7b. Max R2C1 = 6 -> min R1C12 = 10, no 1

8. 36 rule on R78 2 outies R6C57 = 6 = [15/24], clean-up: no 4,5 in R7C7
8a. R6C34 = {16/34} (cannot be {25} which clashes with R6C57), no 2,5
8b. Killer pair 1,4 in R6C34 and R6C57, locked for R6

9. 14(3) cage at R6C5 = {158/167/248/257} (cannot be 347/356} because R6C5 only contains 1,2), no 3
9a. R6C5 = {12} -> no 1,2 in R7C45
9b. Killer pair 7,8 in R7C45 and R7C7

10. 36 rule on R8 3 outies R7C168 = 11 = {146/236} (cannot be {245} which clashes with R7C23), no 5, 6 locked for R7
10a. Killer pair 3,4 in R7C168 and R7C23, locked for R7

11. 36 rule on C678 4 innies R1378C6 = 13 = {1237/1246} (cannot be {1345} which clashes with R56C6)
11a. Hidden killer pair 1,2 in R3C6 and R78C6 for C6, R78C6 cannot be {12} because 25(5) cage at R7C6 cannot contain both 1 and 2 -> R78C6 contains one of 1,2, R3C6 = {12}, clean-up: no 1,2, in R3C5
11b. R78C6 contains one of 1,2 -> no 1,2 in R8C345
11c. 25(5) cage at R7C6 = {13678/14578/23578/24568} (cannot be {34567} which doesn’t contain 1,2), 8 locked in R8C345, locked for R8

12. 36 rule on O7 3 innies R7C4 + R8C34 = 20 = {578}, locked for O7

13. 36 rule on O46 4 innies R456C5 + R6C7 = 13, R6C57 = 6 (step 8) -> R45C5 = 7 = {16/25} (cannot be {34} which clashes with R3C5), no 3,4,7,8, R45C4 = 8 = {17/35} (cannot be {26} which clashes with R45C5), no 2,4,6,8
13a. R45C45 = 15{27/36}

14. Grouped X-Wing for 5 in R45C45 and R7C45, locked for C45
14a. Killer triple 5,7,8 in R45C4, R7C4 and R8C4, locked for C4
14b. 8 in C4 locked in R78C4, locked for O7

15. 14(3) cage at R2C4 = {248/347}, no 6
15a. 7,8 can only be in R2C5 -> R2C5 = {78}
15b. 4 locked in R23C4, locked for C4, clean-up: no 3 in R6C3

16. 5 in O2 locked in 8(3) cage = {125}, clean-up: no 8 in R2C6
16a. 8 in O2 locked in R12C5, locked for C5

17. R8C4 = 8 (hidden single in R8)
17a. Naked pair {57} in R7C45, locked for R7 -> R7C7 = 8, R6C7 = 4, R6C5 = 2 (step 8), clean-up: no 5 in R45C5, no 3 in R6C4
17b. 5 locked in R45C4 (step 13a and step 13) = {35}, locked for C4 -> R7C45 = [75], R8C3 = 5

18. Naked pair {24} in R23C4, locked for C4, R2C5 = 8 (step 15)

19. Naked pair {16} in R6C34, locked for R6 and O5

20. 21(5) cage at R1C3 = {12378/12468/13467}
20a. 8 of {12378/12468} must be in R1C3 -> no 2 in R1C3

21. 36 rule on C1 3 outies R168C2 = 16 = {178/358/367} (cannot be {268/457} which clash with R23C2), no 2,4

22. 4 in C2 locked in R45C2 -> 16(3) cage at R4C2 = {457} (only remaining combination} -> R5C3 = 7, R45C2 = {45}, locked for C2, clean-up: no 8 in R3C2, no 3 in R34C3

23. Naked triple {358} in R5C4 + R6C12, locked for O5 -> R5C12 = [24], R4C2 = 5, R45C4 = [35]

24. 11(3) cage in O7 = {146} (only remaining combination), locked for O7 -> R7C23 = {23}, locked for R7
24a. R8C2 = 1 (hidden single in C2}, naked pair {46} in R78C1, locked for C1

25. Naked pair {38} in R6C12, locked for R6 and 21(5) cage at R3C1 -> R6C68 = [57], R5C6 = 6

and the rest is naked singles

Maybe I'll now try V2.


Last edited by Andrew on Tue Apr 26, 2011 1:12 am, edited 1 time in total.

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PostPosted: Fri Apr 22, 2011 12:30 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Cyclone V2 by Mike (mhparker) (April 2008) here (below Cyclone V1)
Puzzle Diagram:
Image
Images with "udosuk style Killer Cages" by Børge:
Image     Image
Code: Select, Copy & Paste into solver:
2x4::k:3328:3328:5890:5890:5890:5890:4102:4102:3328:1801:5890:3339:3339:1805:1805:4102:4880:1801:2834:3339:2324:2324:5398:5398:4880:4377:2834:4379:4379:3613:3613:5398:4880:4377:4377:4379:4379:2341:3613:5398:4880:4880:3114:3114:3628:2341:2606:5398:3888:2097:2097:3628:3628:6709:2606:1847:3888:3888:6709:6709:6709:6709:1847:1847:
Solution:
+---------+---------+
| 1 4 5 6 | 2 7 3 8 |
| 8 2 3 7 | 4 1 6 5 |
+---------+---------+
| 3 5 7 2 | 1 8 4 6 |
| 6 8 4 1 | 3 2 5 7 |
+---------+---------+
| 2 3 6 5 | 8 4 7 1 |
| 7 1 8 4 | 6 5 2 3 |
+---------+---------+
| 4 7 1 3 | 5 6 8 2 |
| 5 6 2 8 | 7 3 1 4 |
+---------+---------+
Quote:
Mike: Welcome to my first puzzle(s) on the SS forum!
Tried to create a nice killer with a whirling cage pattern, and always ended up with one row and column left over. So decided to simply cut them out and go for an 8 x 8 killer instead!
Est rating: 1.75.
Have fun with those "36" tests! :-)
Afmob (after going through my WT) also commented about the 1.75 rating being too high. I agree, but would still rate it as 1.5, because there's at least one important move in there that is difficult to see.

Andrew: Cyclone Killer #2 was a really challenging puzzle. It took me a few sessions but I eventually got it out.
Mike's step 15b was a nice one; it really broke the puzzle open. I also missed Mike's step 12a but found a couple of similar steps. I realised later that my step 27 is the complement of Mike's step 12a.
Mike rated this puzzle at 1.5, after feedback from Afmob. I agree with that. It was Hard 1.5 the way I solved it.

Mike wrote: BTW, here is a killer combination table for 8x8, which you may find useful:
3(2) = {12}
4(2) = {13}
5(2) = {14/23}
6(2) = {15/24}
6(3) = {123}
7(2) = {16/25/34}
7(3) = {124}
8(2) = {17/26/35}
8(3) = {125/134}
9(2) = {18/27/36/45}
9(3) = {126/135/234}
10(2) = {28/37/46}
10(3) = {127/136/145/235}
10(4) = {1234}
11(2) = {38/47/56}
11(3) = {128/137/146/236/245}
11(4) = {1235}
12(2) = {48/57}
12(3) = {138/147/156/237/246/345}
12(4) = {1236/1245}
13(2) = {58/67}
13(3) = {148/157/238/247/256/346}
13(4) = {1237/1246/1345}
14(2) = {68}
14(3) = {158/167/248/257/347/356}
14(4) = {1238/1247/1256/1346/2345}
15(2) = {78}
15(3) = {168/258/267/348/357/456}
15(4) = {1248/1257/1347/1356/2346}
15(5) = {12345}
16(3) = {178/268/358/367/457}
16(4) = {1258/1267/1348/1357/1456/2347/2356}
16(5) = {12346}
17(3) = {278/368/458/467}
17(4) = {1268/1358/1367/1457/2348/2357/2456}
17(5) = {12347/12356}
18(3) = {378/468/567}
18(4) = {1278/1368/1458/1467/2358/2367/2457/3456}
18(5) = {12348/12357/12456}
19(3) = {478/568}
19(4) = {1378/1468/1567/2368/2458/2467/3457}
19(5) = {12358/12367/12457/13456}
20(3) = {578}
20(4) = {1478/1568/2378/2468/2567/3458/3467}
20(5) = {12368/12458/12467/13457/23456}
21(3) = {678}
21(4) = {1578/2478/2568/3468/3567}
21(5) = {12378/12468/12567/13458/13467/23457}
21(6) = {123456}
22(4) = {1678/2578/3478/3568/4567}
22(5) = {12478/12568/13468/13567/23458/23467}
22(6) = {123457}
23(4) = {2678/3578/4568}
23(5) = {12578/13478/13568/14567/23468/23567}
23(6) = {123458/123467}
24(4) = {3678/4578}
24(5) = {12678/13578/14568/23478/23568/24567}
24(6) = {123468/123567}
25(4) = {4678}
25(5) = {13678/14578/23578/24568/34567}
25(6) = {123478/123568/124567}
26(4) = {5678}
26(5) = {14678/23678/24578/34568}
26(6) = {123578/124568/134567}
27(5) = {15678/24678/34578}
27(6) = {123678/124578/134568/234567}
28(5) = {25678/34678}
28(6) = {124678/134578/234568}
28(7) = {1234567}
29(5) = {35678}
29(6) = {125678/134678/234578}
29(7) = {1234568}
30(5) = {45678}
30(6) = {135678/234678}
30(7) = {1234578}
31(6) = {145678/235678}
31(7) = {1234678}
32(6) = {245678}
32(7) = {1235678}
33(6) = {345678}
33(7) = {1245678}
34(7) = {1345678}
35(7) = {2345678}
36(8) = {12345678}


Andrew suggested using Ruud's combination calculator with 9 forbidden; however that's no longer available.
Walkthrough by Mike:
Here is my walkthrough for the Cyclone V2:

Edit: Typos corrected (many thanks, Afmob!)

Edit2: Afmob (after going through my WT) also commented about the 1.75 rating being too high. I agree, but would still rate it as 1.5, because there's at least one important move in there that is difficult to see.

Edit3: Yet more typos corrected (muchas gracias, Andrew!)

[collapse=Cyclone V2 Walkthrough]Prelims

a) 7(2) at R2C2 and R2C6 = {16/25/34} (no 7,8)
b) 19(5) at R3C1 = {12358/12367/12457/13456} (1 locked)
c) 11(2) at R3C3 = {38/47/56} (no 1,2)
d) 17(3) at R4C2 = {278/368/458/467} (no 1)
e) 12(2) at R6C3 = {48/57} (no 1..3,6)
f) 10(2) at R6C8 = {28/37/46} (no 1,5)
g) 8(2) at R7C2 = {17/26/35} (no 4,8)
h) 26(5) at R8C6 = {14678/23678/24578/34568} (8 locked)
i) 7(3) at R7C8 = {124}, locked for B8; cleanup: no 6,8 in R6C8


1. Outies R12: R3C24 = 7(2) = {16/25/34} (no 7,8)

2. Outies C12: R57C3 = 7(2) = [25/43/52/61] (no 7,8)
2a. -> no 3 in R5C3, no 6 in R7C3
2b. cleanup: no 1,2 in R7C2

3. Outies C78: R24C6 = 3(2) = {12} (no 3..8), locked for C6
3a. cleanup: no 1..4 in R2C7; no 7,8 in R3C5 and R56C6
3b. 9(2) at R56C6 = {36/45} = {(3/5)..}

4. 14(3) at R4C6: max. R4C6 = 2 -> min. R45C7 = 12
4a. -> no 1..3 in R45C7

5. Outies R78: R6C57 = 8(2) = [17/62] (no 3..5,8)
(Note: [53] blocked by R56C6 (step 3b))
5a. -> no 2,7 in R6C5
5b. cleanup: no 6,7 in R7C7

6. Outies R8: R7C168 = 12(3) = {147/246/345} (no 8)
(Note: {156/237} blocked by R8C23; {138} blocked by R7C7)
6a. 4 locked for R8
6b. 6,7 of {147/246} must go in R8C6
6c. -> no 6,7 in R7C1

7. 8 in 26(5) (prelim h) locked in R8C3456 for R8

8. 8 locked in innies B7: R7C4+R8C34 = 13(3) = {148/238} (no 5..7)

9. 14(3) at R6C5 = {158/167/356} (no 2)
(Note: {257} unplaceable)
9a. possible permutations R6C5+R7C45 are: [185/617/635]
9b. -> R7C5 = {57} (no 3,6,8)

10. 15(3) at R7C1 = {267/357/456} (no 1)
10a. 2 of {267} must go in R7C1
10b. -> no 2 in R8C12

11. Innies B1235: R45C4 = 6(2) = {15/24} (no 3,6..8)
11a. -> R45C5 = 11(2) (17(4) cage split) = {38/47} (no 1,2,5,6)
(Note: {56} blocked by R67C5 (step 9a))

12. 2 in B6 locked in R6C7+R56C8
12a. -> R6C7+R56C8 and 7(3) at R7C8 (prelim i) form grouped X-Wing on 2 within C78
12b. -> no 2 elsewhere in C78

13. Outies C1: R168C2 = 11(3) = {137/146/245} (no 8) = {(3/4)..}
(Note: {128} unplaceable, {236} blocked by R23C2)
13a. -> {34} combo blocked for 7(2) at R2C2 (prelim a)
13b. -> 7(2) at R2C2 = {16/25} (no 3,4)
13c. cleanup: no 3,4 in R3C4 (step 1)
13d. R3C24 (step 1) = {16/25} = {(5/6)..}

14. 11(2) at R3C3 (prelim c) = {38/47} (no 5,6)
(Note: {56} blocked by R3C24 (step 13d))

15. Innie/Outie (I/O) difference B12: R2C2 = R3C4
15a. 6 in C4 locked in R123C4
15b. -> (from R2C2 = R3C4 above) 6 locked in R12C4+R2C2 for B1

16. Hidden single (HS) in C3 at R5C3 = 6
16a. -> R7C3 = 1 (step 2)
16b. -> R7C2 = 7
16c. cleanup: no 3 in R6C6

17. Naked single (NS) at R7C5 = 5
17a. cleanup: no 4 in R3C6

18. HS in R7 at R7C6 = 6
18a. cleanup: no 3 in R5C6 and R3C5; no 3 in R7C1 (step 6)

19. 8 in C2 locked in split 11(2) at R45C2 = {38} (no 2,4,5), locked for C2

20. 11(2) at R3C3 (step 14) = {47} (no 3,8) (last combo), locked for C3 and B3
(Note: {38} blocked by R4C2)
20a. cleanup: no 2 in R5C4 (step 11); no 5,8 in R6C4

21. Naked pair (NP) at R56C6 = {45}, locked for C6 and B6
21a. cleanup: no 4 in R3C5; no 7 in R4C5 (step 11a)

22. 15(3) at R7C1 = {456} (no 2,3) (last combo), 4 locked for B7
22a. -> R7C18 = [42]

23. HS in C7 at R6C7 = 2
23a. -> R7C7 = 8 (cage sum)
23b. -> R7C4 = 3, R6C5 = 6 (step 5 or 14(3) cage sum)
23c. cleanup: no 3 in R3C6

24. NS at R5C7 = 7
24a. -> split 7(2) at R4C67 = [16/25] (no 4)
24b. cleanup: no 4 in R4C5 (step 11a)

25. NP at R45C5 = {38}, locked for C5
25a. -> R9C56 = [73]

26. NP at R4C25 = {38}, locked for R4
26a. NP at R5C25 = {38}, locked for R5

27. NS at R5C8 = 1
27a. -> R9C78 = [14]

28. HS in R4 at R4C3 = 4
28a. -> R3C3 = 7
28b. cleanup: no 2 in R3C5

Only naked singles and simple cage sums left now.
Walkthrough by Andrew:
Mike's step 15b was a nice one; it really broke the puzzle open. I also missed Mike's grouped X-wing (step 12a) but found a couple of other ones. I realised later that my step 27 is the complement of Mike's step 12a.

Mike rated this puzzle at 1.5, after feedback from Afmob. I agree with that. It was Hard 1.5 the way I solved it.

Here is my walkthrough. I hope I've made the more difficult moves, particularly the ones that cover two octets, clear enough. Edit: Step 45 re-phrased for clarity.

Edit2: Mike pointed out that there were flaws in the original step 37 and the first part of step 40, both now in red. Fortunately I found a workaround for step 37 and was able to include Mike's suggestion for the first part of step 40. Mike also gave a quicker way to the first placement, which I've included after step 32. Thanks for all of those, Mike!


Prelims

a) R23C2 = {16/25/34}, no 7,8
b) R2C67 = {16/25/34}, no 7,8
c) R34C3 = {38/47/56}, no 1,2
d) R6C34 = {48/57}, no 1,2,3,6
e) R67C7 = {28/37/46}, no 1,5
f) R7C23 = {17/26/35}, no 4,8
g) 17(3) cage at R4C2 = {278/368/458/467}, no 1
h) 7(3) cage in Octet 8 (O8) = {124}, locked for O8, clean-up: no 6,8 in R6C7

1. 36 rule on C8 3 outies R138C7 = 8 = {125/134}, 1 locked for C7, clean-up: no 6 in R2C6

2. 36 rule on R12 2 outies R3C24 = 7 = {16/25/34}, no 7,8 in R3C4

3. 36 rule on O35 4 innies R3C24 + R45C4 = 13, R3C24 = 7 (step 2) -> R45C4 = 6 = {15/24}, no 3,6,7,8
3a. R45C4 = 6 -> R45C5 = 11 = {38/47/56}, no 1,2

4. 36 rule on R78 2 outies R6C57 = 8 = [17/53/62], R6C5 = {156}, no 4 in R6C7, clean-up: no 6 in R7C7
4a. Killer pair 2,3 in R138C7 and R67C7, locked for C7, clean-up: no 4,5 in R2C6

5. 36 rule on C12 2 outies R57C3 = 7 = [25/43/52/61], no 7,8, no 3 in R5C3, no 6 in R7C3, clean-up: no 1,2 in R7C2

6. 36 rule on C78 2 outies R24C6 = 3 = {12}, locked for C6, clean-up: no 4 in R2C7, no 7,8 in R3C5, no 7,8 in R56C6

7. 17(3) cage at R4C2 = {278/368/458/467}
7a. 2 of {278} must be in R5C3 -> no 2 in R45C2

8. 36 rule on R1 3 outies R2C138 = 16 = {178/358/367/457} (cannot be {268} which clashes with R2C67), no 2

9. 26(5) cage at R7C6 = {23678/34568} (cannot be {14678/24578} which clash with 7(3) cage in O8), no 1
9a. R8C34 must contain 2 or 4

10. 1 in 7(3) cage in O8 must be in R8C78 (R8C78 cannot be {24} which clashes with R8C34), no 1 in R7C8
10a. 1 in O8 locked in R8C78, locked for R8
10b. Killer pair 2,4 in R8C34 and R8C78, locked for R8

11. 15(3) cage in O7 = {168/258/267/348/357/456}
11a. 1,2,4 of {168/258/267/348/456} must be in R7C1 -> no 6,8 in R7C1

12. 36 rule on C1 3 outies R168C2 = 11 = {128/137/146/245} (cannot be {236} which clashes with R23C2)
12a. 5,6,8 in {128/146/245} must be in R8C2 -> no 5,6,8 in R16C2

13. 16(3) cage in O2 = {178/358/367/457} (cannot be {268} which clashes with R2C67), no 2
13a. 1 of {178} must be in R1C7 -> no 1 in R12C8

14. 21(5) cage at R3C7 = {12567/13458/13467/23457} (cannot be {12378} which clashes with 16(3) cage in O2, cannot be {12468} which clashes with 8(3) cage in O8)
14a. 16(3) cage in O2 (step 13) = {358/367/457} (cannot be {178} which clashes with 21(5) cage at R3C7), no 1

15. R138C7 (step 1) = {125/134}
15a. 5 of {125} must be in R1C7 -> no 5 in R3C7

16. 36 rule on R8 3 outies R7C168 = 12 = {147/246/345} (cannot be {138/156} because R7C8 only contains 2,4, cannot be {237} which clashes with R7C23), no 8, 4 locked for R7
16a. 1 of {147} must be in R7C1 -> no 7 in R7C1

17. 26(5) cage at R7C6 (step 9) = {23678/34568}, 8 locked in R8C3456, locked for R8

18. 15(3) cage in O7 (step 11) = {267/357/456}, no 1
[I missed a clean-up (using step 16) here, see comment after step 26.]

19. 8 in C2 locked in R45C2, locked in 17(3) cage (step 7) = {278/368/458}
19a. 6 of {368} must be in R5C3 -> no 6 in R45C2

20. R168C2 (step 12) = {137/146/245}
20a. R23C2 = {16/25} (cannot be {34} which clashes with R168C2), no 3,4, clean-up: no 3,4 in R3C4 (step 2)

21. 36 rule on R12 3 innies R2C245 = 13 = {148/238/247/346} (cannot be {157/256} which clash with R2C67), no 5, clean-up: no 2 in R3C2, no 5 in R3C4 (step 2)
21a. R2C2 = {126} -> no 1,2,6 in R2C45

22. Hidden pair {12} in R1C5 and R2C6 for O2 -> R1C5 = {12}

23. 36 rule on O2 3 innies R1C56 + R2C5 = 13 = {148/238/247} (cannot be {157/256} which clash with R2C67, cannot be {346} because R1C5 only contains 1,2), no 5,6

24. 8 in O7 locked in R7C4 + R8C34
24a. 36 rule on O7 3 innies R7C4 + R8C34 = 13 = {148/238}, no 5,6,7
24b. R8C34 must contain 2 or 4 (step 9a) -> no 2 in R7C4

25. 8 in R7 locked in R7C457
25a. 36 rule on R78 3 innies R7C457 = 16 = {178/358}, no 6
25b. 5 of {358} must be in R7C5 -> no 3 in R7C5

26. 1 in R7 must be in R7C23 = [71] or in R7C457 = 1{78} -> 7 locked in R7C257, locked for R7
[I then realised that I only got this because I’d missed the clean-up after step 18. I’ve left it like this because it’s an interesting step.]

27. 2 in C56 locked in R13C5 and R24C6, locked for B24

28. Hidden killer pair 1,2 in R6C57 and R56C8 for O6 -> R6C57 and R56C8 must each contain one of {12} (R56C8 cannot be {12} which clashes with R78C8)
28a. R6C57 (step 4) = [17/62] (cannot be [53] which doesn’t contain 1 or 2), clean-up: no 7 in R7C7
28b. Killer pair 1,2 in R56C8 and R78C8, locked for C8
28c. 4 of 7(3) cage must be in R78C8 (R78C8 cannot be {12} which clashes with R56C8), no 4 in R8C7
28d. 4 in O8 locked in R78C8, locked for C8

29. Hidden grouped X-Wing in 1 for C78 -> 21(5) cage at R3C7 and 7(3) cage in O8 must both contain 1
29a. 21(5) cage at R3C7 (step 14) = {12567/13458/13467} (cannot be {23457} which doesn’t contain 1)
[This was there after step 14a but I’ve only just spotted it. Since it doesn’t lead to any immediate candidate eliminations I haven’t moved it.]

30. 16(3) cage in O2 (step 14a) = {358/367} (cannot be {457} which clashes with 21(5) cage at R3C7), no 4, 3 locked for O2

31. R138C7 (step 1) = {125/134}
31a. 4 of {134} must be in R3C7 -> no 3 in R3C7

32. 36 rule on R123 4 innies R3C1378 = 20 = {1478/3458/3467} (cannot be {1568/2468/2567} which clash with R3C24, cannot be {2378} because R3C7 only contains 1,4), no 2, 4 locked for R3, clean-up: no 5 in R3C56

[Mike pointed out that from here there is a much quicker route to my first placement.
33. 14(3) at R6C5+R7C45 = [185/617/635]
33a. R67C5 = {(5/6)..}
33b. -> {56} combo blocked for h11(2) at R45C5 (step 3a)
33c. -> no 5,6 in R45C5
34. 5 in C5 locked in R78C5 for O8
35. 5 in C6 locked in 9(2) at R5C6 = {45}, locked for C6 and N6
36. HS in O2 at R2C5 = 4
I'm not sure why I didn't look at the permutations for the 14(3) cage at R6C5; I'd looked at them for R7C457.]


33. R7C457 (step 25a) = {178/358}
33a. 5,7 can only be in R7C5 -> R7C5 = {57}

34. 4 in C5 can only be in R2C5 or R45C5
34a. If 4 in R45C5, then R45C5 = {47}
34b. -> no 7 in R2C5

35. R2C245 (step 21) = {148/238/247/346}
35a. 13(3) cage at R2C4 = {148/238/247/346}
35b. 4 of {148} must be in R2C5 (R23C4 cannot be [41] which clashes with R45C4)
35c. 3,7 of {247/346} must be in R2C4
35d. -> no 4 in R2C4

36. Combined cage R12368C2 = 18 = {12357/12456}, 5 locked for C2, clean-up: no 4 in R5C3 (step 19), no 3 in R7C3
36a. R34C3 = {38/47} (cannot be {56} which clashes with R57C3), no 5,6

37. Killer singles 8 in R45C2 (step 19), R34C3 or R6C34, locked for O35
37a. 19(5) cage at R3C1 = {12367/12457/13456}


[Mike pointed out that there is a flaw in step 37. Because of the geometrical arrangement it’s possible for R34C3 to be {47} with R6C34 = [57] when there is an 8 in the 19(5) cage = {12358}. Fortunately I found a workaround which showed that this combination is impossible.]

37. 8 locked in R45C2 (step 19)
37a. If R34C3 or R6C34 contain 8 => no 8 in 19(5) cage at R3C1 = {12367/12457/13456}
37b. If neither of R34C3 or R6C34 contain 8 then both must contain 7 => R34C3 = {47} => R6C34 = [57] => 19(5) cage at R3C1 must contain 8 = {12358} with 5 in R34C1 => R3C24 = {16}, locked for R3 => R3C7 = 4 => R3C56 = [27] -> R3C57 clash with R3C3
37c. -> R3C1 = {12367/12457/13456}, no 8


38. 8 in C1 locked in R12C1, locked for O1
38a. 13(3) cage at R1C1 = {148/238}, no 5,6,7

39. R2C245 (step 21) = {238/247/346} (cannot be {148} because R2C4 only contains 3,7), no 1, clean-up: no 6 in R3C2, no 1 in R3C4 (step 2)

40. Hidden killer singles 7 in 19(5) cage at R3C1, 17(3) cage at R4C2, R34C3 and R6C34 for O35, R34C3 or R6C34 contain 7 -> 19(5) cage at R3C1 or 17(3) cage at R4C2 must contain 7
40a. 2 and 7 are linked in 19(5) cage at R3C1 (step 37a) and 17(3) cage at R4C2 (step 19) -> 19(5) cage at R3C1 or 17(3) cage at R4C2 contains 2 and 7
40b. Hidden killer singles 2 in 19(5) cage at R3C1, 17(3) cage at R4C2 and R345C4, 19(5) cage at R3C1 or 17(3) cage at R4C2 contains 2 -> R345C4 must contain 2
40c. 2 locked in R345C4, locked for C4


[After checking my workaround for step 37, Mike pointed out that there is a similar flaw in this step and in this case provided a workaround using the same basic approach that I’ve put into the first part of step 40.]

40. Hidden killer pairs 7,8 in 19(5) cage at R3C1, 17(3) cage at R4C2, R34C3 and R6C34 for O35, R34C3 and R6C34 must contain two occurrences of 7,8 -> 19(5) cage at R3C1 and 17(3) cage at R4C2 must contain two occurrences of 7,8 of which one is 8 locked in R45C2 so either 19(5) cage at R3C1 or 17(3) cage at R4C2 contains 7
40a. 2 and 7 are linked in 19(5) cage at R3C1 (step 37a) and 17(3) cage at R4C2 (step 19) -> either 19(5) cage at R3C1 or 17(3) cage at R4C2 contains 2 and 7
40b. Hidden killer singles 2 in 19(5) cage at R3C1, 17(3) cage at R4C2 and R345C4, 19(5) cage at R3C1 or 17(3) cage at R4C2 contains 2 -> R345C4 must contain 2
40c. 2 locked in R345C4, locked for C4


41. R7C4 + R8C34 (step 24a) = {148/238}
41a. 2 of {238} must be in R8C3 -> no 3 in R8C3
41b. 4 of {148} must be in R8C3 (R78C4 cannot be [14] which clashes with R45C4], no 8 in R8C3, no 4 in R8C4
41c. 8 in O7 locked in R78C4, locked for C4, clean-up: no 4 in R6C3

42. Killer pair 2,6 in R2C2 and R2C67, locked for R2

43. R2C138 (step 8) = {178/358/457}
43a. 4 of {457} must be in R2C1 -> no 4 in R2C3

44. 36 rule on C123 4 innies R1268C3 = 18 = {1467/2358/2457} (cannot be {1278/2367} which clash with R34C3, cannot be {1368} because R8C3 only contains 2,4, cannot be {1458/3456} which clash with R57C3)
44a. 6 of {1467} must be in R1C3 -> no 1 in R1C3
44b. 2,4 of {2457} must be in R18C3
44c. Combining steps 44a and 44b, no 7 in R1C3

45. 13(3) cage at R2C4 (step 35a) = {238/247/346}
45a. Hidden killer triple 1,2,3 in R23C4, R45C4 and R78C4 for C4, R45C4 must contain 1 or 2, R78C4 must contain 1 or 3 -> R23C4 can only contain one of 2,3 -> no 8 in R2C5 (step 45)

45b. R2C5 = 4, R23C4 = [36/72] (step 45), clean-up: no 7 in R45C5
45c. Killer triple 1,2,3 in R23C4, R45C4 and R78C4, locked for C4
45d. R2C5 = 4 -> R1C56 = [18/27] (step 23)

46. 5 in O1 locked in R1C34 + R2C3 -> 23(5) cage at R1C3 must contain 5
46a. 23(5) cage at R1C3 = {12578/13568/23567} (cannot be {13478/23468} which don’t contain 5, cannot be {14567} which clashes with R1C56), no 4
[I could now make further candidate eliminations but the next step is more direct.]

47. 4 in O1 locked in R1C12
47a. 13(3) cage at R1C1 (step 38a) = {148} (only remaining combination), locked for O1

48. Grouped X-Wing on 1 in 13(3) cage at R1C1 and 19(5) cage at R3C1, locked for C12 -> R3C2 = 5, R2C2 = 2, R2C6 = 1, R2C7 = 6, R2C1 = 8, R4C6 = 2, R1C5 = 2, R1C6 = 7 (step 45c), R2C4 = 7 (step 39), R3C4 = 2 (step 45a), clean-up: no 4 in R45C4, no 1 in R5C4 (both step 3)
48a. R45C4 = [15], R16C4 = [64], R6C3 = 8, clean-up: no 3 in R34C3, no 6 in R45C5 (step 3a)

49. R1C8 = 8 (hidden single in R1)

50. R7C3 = 1 (hidden single in C3), R7C2 = 7, R7C5 = 5, R56C2 = [31], R1C12 = [14], R4C2 = 8, R45C5 = [38], clean-up: no 6 in R3C56

and the rest is naked singles.


Last edited by Andrew on Thu Apr 28, 2011 3:59 am, edited 2 times in total.

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PostPosted: Fri Apr 22, 2011 12:41 am 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Assassin 101 by Nasenbaer (May 2008) here
Puzzle Diagram:
Image

Attention: in n5 there is a 14(3)-cage on D\ in r4c4 r5c5 r6c6 (you almost can't see it in the picture, sorry about that).

Attention: this is a Killer-X which means that the numbers on each of the diagonals D/ and D\ are not allowed to repeat itself!
Images with "udosuk style Killer Cages" by Børge:
Image     Image
Code: Select, Copy & Paste into solver:
3x3:d:k:1792:1792:3074:3074:5636:4101:4101:4871:4871:1792:5642:5642:3074:5636:4101:2319:2319:4871:4626:5642:4372:4372:5636:3351:3351:2319:4378:4626:4626:4372:3614:3103:3103:3351:4378:4378:3108:3108:3108:4903:3614:3103:4138:4138:4138:3629:3629:3631:4903:4903:3614:4147:3892:3892:3629:4663:3631:3631:2874:4147:4147:2365:3892:3903:4663:4663:3394:2874:4676:2365:2365:4423:3903:3903:3394:3394:2874:4676:4676:4423:4423:
Solution:
+-------+-------+-------+
| 1 2 8 | 3 6 5 | 9 4 7 |
| 4 7 6 | 1 9 2 | 3 5 8 |
| 3 9 5 | 8 7 4 | 2 1 6 |
+-------+-------+-------+
| 9 6 4 | 2 5 1 | 7 8 3 |
| 8 3 1 | 7 4 6 | 5 9 2 |
| 2 5 7 | 9 3 8 | 1 6 4 |
+-------+-------+-------+
| 7 1 3 | 4 8 9 | 6 2 5 |
| 5 8 9 | 6 2 7 | 4 3 1 |
| 6 4 2 | 5 1 3 | 8 7 9 |
+-------+-------+-------+
Quote:
Nasenbaer: A little bit earlier than I intended but I'm not at home so it's now or never to give you the first Assassin for this forum.
Back to the roots - that's what we should call this Assassin. After I created and solved it I realized that I had seen this design before (except for the diagonals) - in Assassin 2! Ed convinced me to go along with it (the old ones are often the best - the design, not Ed :lol: ), so here it is:
SSolver 3.0 rating: 1.23

Afmob: Thanks Nasenbaer for providing the first Assassin on this forum.
I think SudokuSolver's rating is a bit too high. After looking at SS solving path it is my step 6b which SS misses and which explains the difference between my and SudokuSolver's suggested rating. Rating: (Hard?)1.0.

Mike: Actually, the Assassin 2X is (like Ed :lol:) not all that old... Fortunately (talking about being old...) my memory is obviously even shorter, so had to "re-invent the wheel" again! :roll:
As to the rating, I'd personally score it at 1.25, because it took quite a lot of chipping away at the candidates before the puzzle finally gave in, with lots of small moves being required, making the puzzle IMO too "finicky" for a 1.0 rating.
I didn't keep a WT this time, but would like to take this opportunity to thank Nasenbaer for a challenging but rewarding "re-match"!

Andrew: Thanks for posting the first Assassin on this forum! I think it's also the first time that the "Assassin of the Week" has been a Killer-X. It will be good to have them as the main puzzle occasionally, maybe once a month.
Yes, it's very like Assassin 2, A2X and A2X-Lite except that the split cage is on the other diagonal.
I'll agree with Mike and rate A101 at 1.25. My solving path is fairly similar to Afmob's, so maybe there's one clear path, but a number of my steps are very different.

Walkthrough by Afmob:
A101 Walkthrough:

1. N5
a) Innies R1234 = 1{25/34} -> 1 locked for R4+N5
b) Innies R6789 = 20(3) <> 2
c) Innies C1234 = 18(3): R56C4 <> 2,3,5 because R4C4 <= 5 and 19(3) can't have 5 and 9
d) Innies+Outies C1234: 1 = R6C5 - R4C4 -> R4C4 <> 1 and R6C5 <> 7,8,9
e) Innies+Outies R1234: 4 = R5C6 - R4C4 -> R5C6 = (6789)
f) Innies+Outies R6789: -1 = R5C4 - R6C6 -> R5C4 <> 9 and R6C6 <> 3,4,6
g) Innies+Outies C6789: -3 = R4C5 - R6C6 -> R6C6 <> 9 and R4C5 <> 1,3
h) Hidden Single: R4C6 = 1
i) 12(3) <> 8
j) Innies R1234 = 8(3): R4C4 <> 4

2. N5 !
a) Innies+Outies C1234: 1 = R6C5 - R4C4 -> R6C5 <> 5
b) ! Innies R1234 = 8(3) = {125} locked for R4+N5 because {134} blocked by Killer pair (34) of 19(3)
c) 12(3) <> 7
d) 14(3) <> 6,9 because R6C6 = (78)
e) 14(3) = {248} because R4C4 = (25) and they are only possible there -> R4C4 = 2, R6C6 = 8, R5C5 = 4
f) 19(3) = {379} -> R5C4 = 7, R6C4 = 9, R6C5 = 3
g) R4C5 = 5, R5C6 = 6, R1C1 = 1

3. R123
a) 22(3) @ N2 = {679} locked for C5+N2
b) 16(3) must have one of (789) and it's only possible @ R1C7 -> R1C7 = (789)
c) 22(3) @ N1 = 9{58/67} -> 9 locked for N1

4. R456
a) 12(3) = 1{29/38} - > 1 locked for R5+N4
b) 16(3) @ R5 = 5{29/38} -> 5 locked for N6
c) 15(3) = {168/249/267/456} because R6C89 <> 3,5,8,9
-> R7C9 <> 1,3,4

5. R789
a) 11(3) = {128} locked for N8
b) 13(3) <> 1,7,8,9 because 7 <= R89C4 <= 11
c) 14(3) @ R6C1 = {248/257/356/347} because R6C12 = (24567)
-> R7C1 <> 4,6,9
d) Innies N7 = 12(3) <> 8
e) Outies R89 = 11(3) <> 9
f) 18(3) @ N7: R8C3 <> 1,2 because 9 only possible there
g) Hidden Single: R5C3 = 1 @ C3
h) 18(3) @ N9 = {279/369/378/459/567} because R89C6 <> 6,8
-> R9C7 <> 1,3,7
i) Innies N7 = 12(3): R9C3 <> 6 because 4 only possible there
j) 6 locked in 13(3) for C4

6. C123 !
a) Outies C12 = 16(3) = 1{69/78}
b) ! Killer pair (67) locked in Outies C12 + 14(3) @ R6C3 for C3
c) 17(3) = 5{39/48} -> 5 locked for R3
d) Hidden Single: R2C4 = 1 @ N2
e) 12(3) = {138} -> 3,8 locked for R1
f) Innies N1 = 16(3) = {358} locked for N1 because R13C3 = (358) -> R3C3 = 5

7. R123
a) Naked triple (679) locked in R2C235 for R2
b) Outies R12 = {179/269/467} -> R3C8 = (124)
c) 9(3) = 3{15/24} -> 3 locked for R2+N3
d) Hidden Single: R2C9 = 8 @ R2
e) 16(3) = 5{29/47} -> 5 locked for C6

8. C789
a) 15(3) <> 1
b) Hidden Single: R6C7 = 1 @ N6
c) 16(3) @ R6C7 = {169} -> R7C6 = 9, R7C7 = 6
d) 15(3) = 6{27/45} -> 6 locked for R6+N6
e) 18(3) = {378} because R6C89 = (347) -> R9C7 = 8, 3 locked for C6+N8
f) R8C8 = 3
g) 17(3) = {179} @ N9 locked for N9
h) 9(3) = {234} locked for N9
i) R7C9 = 5 -> R6C89 = {46} locked for R6+N6

9. N13
a) 13(3) = {247} -> R4C7 = 7, R3C7 = 2, R3C6 = 4
b) R2C8 = 5
c) 19(3) = {478} -> R1C9 = 7, R1C8 = 4
d) R9C9 = 9
e) 18(3) must have 3 xor 8 and R3C1 = (38) -> R4C12 <> 3,8

10. Rest is singles without considering the diagonals.

Rating: (Hard?)1.0. I used Killer pairs and Innies+Outies Difference.
Walkthrough by Andrew:
I was a bit surprised that Afmob rated it at (Hard?) 1.0. Step 1c felt to me like it was part of a higher rated puzzle. I was surprised that SS didn't find Afmob's step 6b.

I'll agree with Mike and rate A101 at 1.25.

Here is my walkthrough. The solving path is fairly similar to Afmob's, so maybe there's one clear path, but a number of my steps are very different. I've included eliminations on the diagonals for those who do their own eliminations; those on the diagonals are so easy to overlook.

Prelims

a) 7(3) cage in N1 = {124}, locked for N1
b) 22(3) cage in N1 = {589/679}, 9 locked for N1
c) R123C5 = {589/679}, 9 locked for C5 and N2
d) 19(3) cage in N3 = {289/379/469/478/568}, no 1
e) 9(3) cage in N3 = {126/135/234}, no 7,8,9
f) 19(3) cage in N5 = {289/379/469/478/568}, no 1
g) R789C5 = {128/137/146/236/245}, no 9
h) 9(3) cage in N9 = {126/135/234}, no 7,8,9

1. 45 rule on R89 3 outies R7C258 = 11 = {128/137/146/236/245}, no 9

2. 45 rule on N9 3 innies R7C79 + R9C7 = 19 = {289/379/469/478/568}, no 1

3. 45 rule on C6789 3 outies R4C45 + R5C5 = 11 = {128/137/146/236/245}, no 9

4. 45 rule on R1234 3 innies R4C456 = 8 = {125/134}, 1 locked for R4 and N5

5. 45 rule on R6789 3 innies R6C456 = 20 = {389/479/569/578}, no 2

6. 45 rule on R6789 1 innie R6C6 = 1 outies R5C4 + 1, no 9 in R5C4

7. 45 rule on R1234 1 outies R5C6 = 1 innie R4C4 + 4 -> R5C6 = {56789}

8. 45 rule on C1234 1 outie R6C5 = 1 innie R4C4 + 1, no 1 in R4C4, no 7,8 in R6C5, clean-up: no 5 in R5C6 (step 7)

9. 45 rule on C6789 1 innie R6C6 = 1 outie R4C5 + 3, no 3,9 in R6C6, clean-up: no 2,8 in R5C4 (step 6)

10. 19(3) cage in N5 = {379/469/478/568}
10a. 3 of {379} must be in R6C5 -> no 3 in R56C4, clean-up: no 4 in R6C6 (step 6), no 1 in R4C5 (step 9)
10b. 8,9 only in R6C4 -> R6C4 = {89}

11. R4C6 = 1 (hidden single in R4), locked for D/
11a. R4C5 + R5C6 = [29/38/47/56]

12. 45 rule on C6789 2 remaining innies R56C6 = 14 = [68/86/95], no 7, clean-up: no 3 in R4C4 (step 7), no 4 in R4C5 (step 9), no 6 in R5C4 (step 6), no 4 in R6C5 (step 8)

13. 19(3) cage in N5 (step 10) = {379/469/568} (cannot be {478} because 4,7 only in R5C4)
13a. 6 of {568} must be in R6C5 -> no 5 in R6C5, clean-up: no 4 in R4C4 (step 8), no 8 in R5C6 (step 7), no 3 in R4C5 (step 11a), no 6 in R6C6 (step 9), no 5 in R5C4 (step 6)

14. Naked pair {25} in R4C45, locked for R4 and N5 -> R6C6 = 8, locked for D\, R6C4 = 9, locked for D/, R5C6 = 6, R6C5 = 3, R5C4 = 7 (step 13), R5C5 = 4, locked for both diagonals, R4C5 = 5 (step 11a), R4C4 = 2, locked for D\ -> R1C1 = 1, locked for D\, clean-up: no 8 in R123C5

15. Naked triple {679} in R123C5, locked for C5 and N2
15a. Naked triple {128} in R789C5, locked for N8

16. 9(3) cage in N9 = {126/135/234}
16a. 6 of {126} must be in R8C8 -> no 6 in R7C8 + R8C7

17. 1 in R7 locked in R7C258
17a. R7C258 (step 1) = {128/137/146}, no 5
17b. 6,7 of {137/146} must be in R7C2 -> no 3,4 in R7C2

18. 45 rule on R12 3 outies R3C258 = 17 = {179/269/278/359/368/467} (cannot be {458} because R3C5 only contains 6,7,9)
18a. 1,2,3,4 only in R3C8 -> R3C8 = {1234}

19. 13(3) cage at R8C4 = {256/346} (cannot be {139/148/157/238/247} because 1,2,7,8,9 only in R9C3), no 1,7,8,9
19a. 2 of {256} must be in R9C3 -> no 5 in R9C3

20. R5C123 = {129/138}, no 5, 1 locked for R5 and N4
20a. R5C789 = {259/358}, 5 locked for N6

21. 1 in C3 locked in R58C3
21a. 45 rule on C12 3 outies R258C3 = 16 = {169/178}, no 2,3,4,5

22. 12(3) cage at R1C3 = {138/147/156} (cannot be {345} because cannot place both 1 and 8 in R3C4) -> R2C4 = 1
[Alternatively cannot be {345} which clashes with R789C4]
22a. R1C34 = [38/65/74/83], no 5 in R1C3

23. 9(3) cage in N3 = {126/135/234}
23a. 3 of {234} must be in R2C78 (R2C78 cannot be [42] which clashes with R2C1), no 3 in R3C8

24. 16(3) cage at R1C6 = {259/349/358/457} (cannot be {268/367} because 6,7,8 only in R1C7), no 6
24a. 7,8,9 only in R1C7 -> R1C7 = {789}

25. 45 rule on N7 3 innies R7C13 + R9C3 = 12 = {237/246/345}, no 8,9

26. 14(3) cage at R6C1 = {257/347/356}
26a. 3 of {347} must be in R7C1 -> no 4 in R7C1

27. R7C13 + R9C3 (step 25) = {237/246/345}
27a. 4 of {246} must be in R9C3 -> no 6 in R9C3

28. 13(3) cage at R8C4 (step 19) = {256/346}
28a. 6 locked in R89C4, locked for C4

29. 15(3) cage in N7 = {159/168/267/357/456} (cannot be {249/258/348} which clash with R7C13 + R9C3)
29a. 1 of {159} must be in R9C2 -> no 9 in R9C2

30. 13(3) cage at R3C6 = {238/247/256/346}, no 9

31. 45 rule on N3 3 innies R1C7 + R3C79 = 17 = {179/269/278/359/458/467} (cannot be {368} which clashes with 9(3) cage in N3)
31a. 1 of {179} must be in R3C9 -> no 9 in R3C9

32. 14(3) cage at R6C3 = {257/347/356}
32a. Killer pair 6,7 in R258C3 and R67C3, locked for C3, clean-up: no 4,5 in R1C4 (step 22a)

33. Naked pair {38} in R1C34, locked for R1

34. 45 rule on N1 3 innies R1C3 + R3C13 = 16 = {358} (only remaining combination), locked for N1
34a. 5 in N1 locked in R3C13, locked for R3
34b. Naked triple {679} in R2C235, locked for R2
34c. 9 in N3 locked in R1C78, locked for R1

35. R2C9 = 8 (hidden single in R2)
35a. R1C89 = 11 = [47/56/65/92], no 2,7 in R1C8

36. 9(3) cage in N3 = {135/234}, 3 locked for R2C78, locked for R2 and N3

37. 5 in N2 locked in R12C6, locked for C6

38. 17(3) cage at R3C3 = {359/458} -> R3C3 = 5, locked for D\
38a. 9 of {359} must be in R4C3 -> no 3 in R4C3
38b. 3 on D\ locked in R7C7 + R8C8 + R9C9, locked for N9

39. 5 in R6 locked in R6C12, locked for 14(3) cage -> no 5 in R7C1
39a. 14(3) cage at R6C1 = {257/356}, no 4
39b. 3 of {356} must be in R7C1 -> no 6 in R7C1

40. 14(3) cage at R6C3 (step 32) = {257/347/356}
40a. 6 of {356} must be in R6C3 -> no 6 in R7C3

41. R7C13 + R9C3 (step 25) = {237} (only remaining combination), locked for N7, 7 locked for R7

42. 18(3) cage in N7 = {189} (only remaining combination) -> R8C2 = 8, R7C2 = 1, R8C3 = 9, clean-up: no 3 in R3C4 (step 38)

43. R5C3 = 1 (hidden single in C3), R2C3 = 6 (step 21a)
43a. Naked pair {79} in R23C2, locked for C2
43b. R5C12 (step 20) = [83/92], no 2,3 in R5C1
43c. 6 on D\ locked in R7C7 + R8C8 + R9C9, locked for N9

44. R7C258 (step 17a) = {128} (only remaining combination) -> R7C58 = [82]
44a. R7C8 = 2 -> R8C78 = 7 = [16/43], no 5 in R8C7
44b. 2 on D/ locked in R1C9 + R3C7, locked for N3

45. Naked pair {37} in R7C13, locked for R7 and N7 -> R9C3 = 2
45a. R9C3 = 2 -> R89C4 = {56} (step 28), locked for C4 -> R7C4 = 4, R13C4 = [38], R14C3 = [84], R67C3 = [73], 3 locked for D/, R7C1 = 7, R7C67 = [96], R7C9 = 5, R8C8 = 3, R8C7 = 4 (step 44a), R89C6 = [73], R8C9 = 1, R2C78 = [35], 5 locked for D/, R89C1 = [56], 6 locked for D/, R9C2 = 4, R1C2 = 2, R5C2 = 3, R5C1 = 8 (step 43b), R1C9 = 7, R9C9 = 9, locked for D\

and the rest is naked singles.


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PostPosted: Wed Apr 27, 2011 11:17 pm 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Assassin 102 by Afmob (May 2008) here
Puzzle Diagram:
Image
Images with "udosuk style Killer Cages" by Børge:
Image     Image
Code: Select, Copy & Paste into solver:
3x3::k:6144:6144:6144:4611:4611:4611:6150:6150:6150:4105:6144:6144:2828:2828:2828:6150:6150:3089:4105:3859:1300:1300:5654:4375:4375:4121:3089:4105:3859:3859:5654:5654:5654:4121:4121:3089:5668:5668:2342:6183:6183:6183:3114:2859:2859:2349:5668:2342:3632:6183:5170:3114:2859:3381:2349:3632:3632:5689:6183:3387:5170:5170:3381:2349:1600:5689:5689:3907:3387:3387:2886:3381:1600:3657:3657:3907:3907:3907:2638:2638:2886:
Solution:
+-------+-------+-------+
| 7 5 1 | 8 4 6 | 2 3 9 |
| 8 9 2 | 3 7 1 | 4 6 5 |
| 6 4 3 | 2 5 9 | 8 7 1 |
+-------+-------+-------+
| 2 3 8 | 1 9 7 | 5 4 6 |
| 9 7 4 | 5 6 2 | 3 1 8 |
| 1 6 5 | 4 3 8 | 9 2 7 |
+-------+-------+-------+
| 3 1 9 | 6 8 4 | 7 5 2 |
| 5 2 7 | 9 1 3 | 6 8 4 |
| 4 8 6 | 7 2 5 | 1 9 3 |
+-------+-------+-------+
Quote:
Afmob: This Assassin offers lots of Innies and Outies to analyze. Use the right ones and together with basic killer techniques you can solve fast.
Note that this Killer was derived from a famous Sudoku. Do you know which one? Hint : This Sudoku is as hard as metal. Hint 2: Ed said a part of its name in his wt post.
SS Score (v3.1): 1.09 Estimated rating: 1.0 - Hard 1.0. It felt nearly (but not quite) as difficult as A101.

gary W: Now to Afmob's puzzle which based on my solving time (2 hours plus) I'ld rate about 1.25

Ed: No idea. Don't know any famous vanilla! Bit one-eyed!
A102 is a really fun puzzle - lots of hidden nuggets. ... agree with gary on the 1.25 rating.
I really enjoyed this puzzle. Thanks very much Afmob!
Mike (mhparker): In the land of the blind, the one-eyed man :pirate: is king :king:. As Børge would say, I'm completely clueless! :viking:

Nasenbaer: A fun puzzle, all right. But it took me a lot longer to solve it on my first go than A101 because I didn't see the killer pair {89} in c1 which sets r2c1 to {89} :oops: . My notes from the second run look like Ed's walkthrough so there will be none by me.
Rating: for me it was a bit harder than A101... I would give it a 1.25

Afmob:
The famous Sudoku is:
The Golden Nugget
.......39.....1..5..3.5.8....8.9...6.7...2...1..4.......9.8..5..2....6..4..7.....

This is one of the hardest Sudokus known so far with an incredible SudokuExplainer (v1.2.1) Rating of 11.9. It was created by Tarek: http://www.sudoku.com/boards/viewtopic.php?t=4212&postdays=0&postorder=asc&start=675.
For more infos, look here: http://www.sudoku.com/boards/viewtopic.php?t=4212&postdays=0&postorder=asc&start=795
Andrew: ... this felt to me like a 1.25 so I'll give it that rating

Solving outline by gary W:
r3c7+r6c9=15 8/9 and 6/7
n6 9 not in c9
c9 9 at r1 or r9
outies c1 -> r9c1=4/5 r8c2=1/2
now easy to see that if
r3c7=9 r9c9=9 r6c9=6 and so cannot place a 1 in n9 so r3c7=8
comes out pretty quickly now
Walkthrough by Ed:
A102 is a really fun puzzle - lots of hidden nuggets. No chains needed, though agree with gary on the 1.25 rating. Did use one complex implied cage block. No real cage-placement/combination work either which was a relief after I kept going wrong in n5 with A101 :scratch: . I don't seem to enjoy 'fiddly' stuff anymore, but try very hard to get the clean-up done on-the-spot. Please let me know if I missed any or need corrections. [edit- I did: Thanks Andrew]

Assassin 102 Walk-through[24 steps]
Prelims
i. n1: 5(2) = {14/23}
ii. n2: 11(3) no 9; 17(2) = {89}
iii. n4: 22(3) no 1..4; 9(2) no 9; 9(3) no 7,8,9
iv. n5: 20(3) no 1,2
v. n6: 12(2) no 1,2,6; 11(3) no 9
vi. n7: 6(2) no 3,6..9; 14(2) no 1..4 nor 7
vii. n8: 22(3) no 1..4
viii. n9: 11(2) no 1; 10(2) no 5

1. 17(2)n2 = {89}: both locked for r3

2. 22(3)n4 = 9{58/67}: 9 locked for n4

3. "45" n1: r4c1 + 5 = r3c23
3a. max. r3c23 = [74] = 11 -> max r4c1 = 6

4. "45" c1: 3 innies r159c1 = h20(3)
4a. = {479/569/578}(no 1,2,3) ({389} blocked by no candidates in r9c1) = [8/9..]
4b. = [4/5] but not both -> no 4 or 5 in r15c1
4c. r8c2 = {12}

5. hidden killer pair {89} in c1. h20(3) has just 1 of 8/9 for c1 (step 4a). The only other place for 8/9 is r2c1
5a. r2c1 = (89)

6. "45" r12: r2c19 = h13(2) = [85/94]
6a. r2c9 = (45)
6b. min. r2c9 = 4 -> max. r34c9 = 8 (cage sum)(no 8,9)

7. "45" n36: 2 innies r3c7 + r6c9 = 15 = [87/96]
7a. r6c9 = (67)
7b. min. r6c9 = 6 -> max. r78c9 = 7 (cage sum) (no 7,8,9)

8. "45" c9: r159c9 = h20(3) and must have 8 & 9 for c9 = {389} only : all locked for c9
8a. 11(3)n6 must have 3/8 = {128/137/236} (no 4,5)
8b. 11(3) = one of 3/8 -> no 3/8 in r56c8
8c. r9c9 = (389) -> r8c8 = (238)

9. complex implied cage block: r9c123 = [4/6] (if 5 in r9c1 -> 14(2)n7 = {68}; if 5 not in r9c1 -> r9c1 = 4)
9a. ->{46} combo blocked from 10(2)n9 = {19/28/37} = [3/8/9]

10. complex hidden single on 9 in n9 in 11(2) & 10(2). (if 9 is not in 11(2)n9 it must be {38} -> 10(2)n9 = {19})
10a. 9 locked for n9 & r9 in r9c789

11. 14(2)n7 = {68}: both locked for n7 & r9
11a. no 2 in 10(2)n9
11b. no 3 in r8c8

12. Killer pair (39) in 10(2)n9 & r9c9: 3 locked for n9 & r9

13. 2 in r9 only in n8: 2 locked for n8
13a. (including!...since I often forget if it's the same cage) no 2 in r8c5
13b. 15(4)n8 must have 2: {1347/1356} blocked

14. Don't know what happened to this step(?)

15. Hidden Killer pair {45} in r9: r9c456 must have one of 4/5 for r9, only other spot is r9c1
15a. ->15(4)n8 must have at least 1 of 4/5 = 2{148/157}(no 3,6,9) ({2346} blocked by 3 & 6 only available in r8c5)
15b. 15(4)n8 = one of 4/5 -> no 4/5 in r8c5
15c. 15(4)n8 = 12{48/57} -> 1 locked for n8

16. "45" r9: r8c258 = h11(3)
16a. only has candidates {1278} which sum to 18
16b. only way to get back to 11 is without the 7
16c. ->h11(3) = {128} only: all locked for r8

17. 13(3)n8 cannot have 1/2 so = {346} only
17a. -> no 6 in r8c4
17b. [missed this one] 3 only in r78c6: 3 locked for n8 & c6

18. 7 & 9 in r8 are only in 22(3)n8 = {679} only
18a. r7c4 = 6
18b. r8c34 = {79}

19. Naked Pair (NP) {34} in r78c6: both locked for n8, c6 & 13(3) cage
19a. ->r8c7 = 6

20. r9c1 = 4 (hsingle r9)
20a. h20(3) r159c1 = {79}[4]: 7 & 9 both locked for c1`

21. r8c2 = 2 (cage sum)
21a. r8c58 = [18]

22. r9c9 = 3 (cage sum)
22a. 10(2)n9 = {19}: 1 locked for n9

23. r7c5 = 8 (hsingle n8)

24. r2c19 = h13(2) = [85]

rest is easy stuff
Afmob's steps which explain why he estimated A102 at Hard 1.0:
After Ed's step 8:

9. 12(3) @ C9 = {147/156/246} -> R34C9 <> 4,5 because R2C9 = (45)

10. Naked quad (1267) locked in R46C9+R56C8 for N6
10a. 12(2) <> 5
10b. Killer pair (38) locked in 12(2) + R5C9 for N6

11. 5 locked in R4C78 @ N6 for R4
11a. 16(3) @ N6 = 5{29/47} -> R3C8 = (27)

12. Killer pair (27) locked in R3C8 + 11(3) for C8
12a. 11(2) = {38} locked for N9
12b. 10(2) <> 2,7
12c. Hidden Single: R1C9 = 9 @ C9, R3C7 = 8, R3C6 = 9
12d. Innies N36 = 15(1+1) = [87] (step 7) -> R6C9 = 7

13. 2,7 locked in R9C456 for N8
13a. 15(4) = {1257} locked for N8
13b. Hidden Single: R9C9 = 3 @ R9, R8C8 = 8, R5C9 = 8

Puzzle is cracked.
Walkthrough by Andrew:
I should have posted this a few days ago but I had to tidy it up before posting it. Several unnecessary steps have been deleted but I've retained step 16 because I originally extended it with a flawed elimination which got me to the correct solution more quickly.

In the re-work, after correcting step 16, I managed to find steps 19 and 20 which are the equivalent of Afmob's alternative solution.

Even with those steps this felt to me like a 1.25 so I'll give it that rating. Maybe Afmob is right but I feel that those who find alternative paths may possibly give slightly too low a rating; that might not apply in this case because Afmob did suggest it when he posted his puzzle.

Here is my walkthrough for A102.

Prelims

a) R3C34 = {14/23}
b) R3C67 = {89}, locked for R3
c) R56C3 = {18/27/36/45}, no 9
d) R56C7 = {39/48/57}, no 1,2,6
e) 6(2) diagonal cage at R8C2 = {15/24}
f) 11(2) diagonal cage at R8C8 = {29/38/47/56}, no 1
g) R9C23 = {59/68}
h) R9C78 = {19/28/37/46}, no 5
i) R2C456 = {128/137/146/236/245}, no 9
j) 22(3) cage in N4 = {589/679}, 9 locked for N4
k) 11(3) cage in N6 = {128/137/146/236/245}, no 9
l) R678C1 = {126/135/234}, no 7,8,9
m) 20(3) part-diagonal cage at R6C6 = {389/479/569/578}, no 1,2
n) 22(3) cage at R7C4 = {589/679}, CPE no 9 in R8C56

1. 45 rule on R12 2 innies R2C19 = 13 = {49/58/67}, no 1,2,3
1a. Min R2C9 = 4 -> max R34C9 = 8, no 8,9 in R4C9

2. 45 rule on N14 2 innies R3C3 + R6C1 = 4 = [13/22/31], clean-up: no 1 in R3C4

3. 45 rule on N36 2 innies R3C7 + R6C9 = 15 = [87/96], R6C9 = {67}
3a. R678C9 = {157/247/256/346} (cannot be {139/148/238} because R6C9 only contains 6,7), no 8,9
3b. R6C9 = {67} -> no 6,7 in R78C9

4. 45 rule on C1 3 innies R159C1 = 20 = {479/569/578} (cannot be {389} because R9C1 only contains 1,2,4,5), no 1,2,3, clean-up: no 4,5 in R8C2
4a. R9C1 = {45} -> no 4,5 in R15C1

5. 45 rule on C9 3 innies R159C9 = 20 = {389/479/569/578}, no 1,2, clean-up: no 9 in R8C8

6. 45 rule on N7 1 innie R8C3 = 2 outies R6C14 + 2, max R8C3 = 9 -> max R6C14 = 7, no 7,8,9 in R6C4

7. 45 rule on C789 2 outies R36C6 = 1 innie R8C7 + 11, max R36C6 = 17 -> max R8C7 = 6
7a. 9 in R8 locked in R8C34, locked for 22(3) cage -> no 9 in R7C4

8. R1C456 = {279/369/378/459/468/567} (cannot be {189} which clashes with R3C6), no 1

9. 45 rule on N2 3 innies R3C456 = 16 = {259/268/349/358} (cannot be {169/178} because R3C4 only contains 2,3,4, cannot be {367/457} because R3C6 only contains 8,9), no 1,7
9a. 5,6 of {259/268} must be in R3C5 -> no 2 in R3C5

10. 1 in N2 locked in R2C456, locked for R2
10a. R2C456 = {128/137/146}, no 5

11. 45 rule on N1 2 innies R3C23 = 1 outie R4C1 + 5, max R3C23 = 10 -> max R4C1 = 5

12. R234C1 = {169/178/268/349/358} (cannot be {259/367} which clash with R678C1, cannot be {457} which clashes with R9C1)
12a. 1,2 of {169/178/268} must be in R4C1 -> no 1,2 in R3C1
12b. 8,9 must be in R2C1 -> R2C1 = {89}, R2C9 = {45} (step 1)

13. R234C9 = {147/156/246} (cannot be {237} because R2C9 only contains 4,5, cannot be {345} which clashes with R159C9), no 3
13a. R2C9 = {45} -> no 4,5 in R34C9

14. Killer pair 6,7 in R34C9 and R6C9, locked for C9, clean-up: no 4,5 in R8C8

15. R159C9 (step 5) = {389} (only remaining combination), locked for C9, clean-up: no 6,7 in R8C8

16. 20(3) part-diagonal cage at R6C6 = {389/479/569/578}
16a. 9 of {389} must be in R6C6 (R7C78 = {39/89} clash with 11(2) diagonal cage at R8C8) -> no 3 in R6C6

17. 45 rule on R9 3 outies R8C258 = 11 = {128/137/236} (cannot be {146/245} because 4,5,6 only in R8C5), no 4,5
17a. 7 of {137} must be in R8C5 -> no 3 in R8C5

[At this stage I spotted Killer Pair 5,6 in R789C1 (if R678C1 = {234}, R9C1 = 5) and R9C23, locked for N7. However this proved unnecessary so I omitted it and used simpler steps.]

18. 11(3) cage in N6 = {128/137/236} (cannot be {146/245} because R5C9 only contains 3,8), no 4,5
18a. R5C9 = {38} -> no 3,8 in R56C8

19. Hidden killer triple 4,5,9 in R4C78 and R56C7 for N6 -> R4C78 must contain two of 4,5,9 -> R4C78 = {459}
19a. R4C78 = 9,13,14 -> R3C8 = {237}
[Strange that I spotted step 19 rather than the possibly more obvious naked quad {1267}!]

20. Hidden killer pair 3,8 in R56C7 and R5C9 for N6 -> R56C7 must contain 3 or 8 -> R56C7 = {39/48}, no 5,7
20a. Killer pair 8,9 in R3C7 and R56C7, locked for C7, clean-up: no 1,2 in R9C8

21. 5 in N6 locked in R4C78, locked for R4
21a. R4C78 = {45}/[59] = 9,14 -> R3C8 = {27}

22. Killer pair 2,7 in R3C8 and R56C8, locked for C8, clean-up: no 3 in R9C7, no 9 in R9C9

23. Naked pair {38} in 11(2) diagonal cage in N9, locked for N9, clean-up: no 2,7 in R9C7

24. R7C7 = 7 (hidden single in N9)
24a. R6C6 + R7C8 (step 16) = {49}/[85], no 6, no 5 in R6C6

25. R8C3 = 7 (hidden single in N7), R78C4 = 15 = [69], clean-up: no 2 in R56C3

26. R8C258 (step 17) = {128} (only remaining combination) -> R8C8 = 8, R9C9 = 3, R5C9 = 8, R1C9 = 9, R3C67 = [98], R6C9 = 7 (step 3), clean-up: no 4 in R56C7, no 1 in R6C3, no 4 in R7C8 (step 24a)
26a. Naked pair {12} in R8C25, locked for R8
26b. Naked pair {39} in R56C7, locked for C7 and N6
26c. Naked pair {45} in R4C78, locked for R4, R3C8 = 7 (step 21a)
26d. Naked pair {45} in R28C9, locked for C9
26e. 8 in C1 locked in R12C1, locked for N1

27. R5C9 = 8 -> R56C8 = {12} (step 18), locked for C8 and N6 -> R4C9 = 6
27a. Killer pair 1,2 in R3C34 and R3C9, locked for R3

28. 45 rule on C123 2 outies R36C4 = 6 = {24}, locked for C4, clean-up: no 2 in R3C3, no 2 in R6C1 (step 2)

29. R3C6 = 9 -> R3C45 = [25/43] (step 9), no 4,6 in R3C5
29a. 6 in R3 locked in R3C12, locked for N1

30. R159C1 (step 4) = {479/578} (cannot be {569} because R1C1 only contains 7,8), no 6

31. R678C1 = {126/135/234}
31a. 2 of {234} must be in R7C1 -> no 4 in R7C1

32. 7 in R9 locked in R9C456
32a. 15(4) cage in N8 = {1257}, locked for N8, 5 locked for R9 -> R9C1 = 4, R8C2 = 2, R8C5 = 1, clean-up: no 9 in R9C23, no 6 in R9C78
[I’d have done this a few moves earlier if I’d realised how powerful it would be.]

33. R9C78 = [19] (naked singles), R7C89 = [52], R8C79 = [64], R4C78 = [54], R23C9 = [51], R2C1 = 8 (step 1), R3C34 = [32], R6C4 = 4, R6C1 = 1 (step 2)

and the rest is naked singles.


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PostPosted: Wed Apr 27, 2011 11:41 pm 
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Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Assassin 102X by Mike (mhparker) (May 2008) here
Puzzle Diagram:
Image
Note: It's a Killer-X, where no repeated digits are allowed on either diagonal.
Images with "udosuk style Killer Cages" by Børge:
Image     Image
Code: Select, Copy & Paste into solver:
3x3:d:k:2304:3329:3329:5891:5891:5891:1030:1030:3592:3849:2304:4875:4875:5891:2318:2318:3592:3089:3849:3859:3859:4875:2326:2318:4632:4632:3089:3849:7708:2077:3859:2326:4632:3361:5666:3089:7708:7708:2077:3367:3367:3367:3361:5666:5666:3885:7708:2077:3632:2865:3378:3361:5666:4149:3885:3632:3632:3129:2865:5691:3378:3378:4149:3885:1600:3129:3129:4931:5691:5691:3398:4149:1600:2121:2121:4931:4931:4931:2638:2638:3398:
Solution:
+-------+-------+-------+
| 8 4 9 | 2 7 5 | 3 1 6 |
| 7 1 5 | 6 9 3 | 2 8 4 |
| 3 6 2 | 8 1 4 | 9 7 5 |
+-------+-------+-------+
| 5 9 1 | 7 8 2 | 4 6 3 |
| 6 7 4 | 9 3 1 | 8 5 2 |
| 2 8 3 | 4 5 6 | 1 9 7 |
+-------+-------+-------+
| 4 3 7 | 1 6 9 | 5 2 8 |
| 9 5 8 | 3 2 7 | 6 4 1 |
| 1 2 6 | 5 4 8 | 7 3 9 |
+-------+-------+-------+
Quote:
Mike (mhparker): Nasenbaer's A101 broke the mould by being the first original Killer-X Assassin. Afmob's A102 did likewise by being the first Assassin to contain mulitple diagonal cages. The puzzle below continues both themes by simply combining them. Unless I'm very much mistaken, it should make a refreshing change from the usual "fiddly" V2... :-)
SudokuSolver v3.1 scores this at 1.06, which is probably not far off the mark.
Happy manual solving!

Afmob: There is nothing like coming back from a sunny (and nearly killer-free) week and writing your shortest walkthrough (good bye, uA 99) so far. :dance:
Though my walkthrough is very short this assassin is not a push-over.
Rating: 1.0.

Andrew: Thanks Mike for a fun variant! Quite a bit different from A102 but clearly still a variant.
In the introduction to Messy One #2, Afmob wrote:
If you don't find the cracking move which is available right from the start, then you'll have a harder time than SS suggests.
That also applies to A102X.
I'll rate A102X as Hard 1.0.

Walkthrough by Afmob:
A102X Walkthrough:

1. C123 !
a) 8(3) = 1{25/34} -> 1 locked for C3+N4
b) Innies N4 = 7(2) = {25/34}
c) Outies N7 = 10(3+1): R6C1 <> 5 and R678C4 <> 6,7,8,9 because R6C1 >= 2
e) Innies N4 = 7(2): R4C1 <> 2
f) ! 15(3) @ R6C1 <> 1,8 because R6C1 = (234) and Innies N4 block 8{25/34}
g) ! 15(3) @ R2C1 <> 8 because R4C1 = (345) and Innies N4 block 8{25/34}
h) ! Killer pair (25) locked in both 15(3) @ C1 for C1
i) 8 locked in Innies C1 = 15(3) = 8{16/34}
j) 30(4) = {6789} -> 7,9 locked for C2

2. R1
a) 4(2) = {13} locked for R1+N3
b) 9(2) = [45/63/81]
c) 2 locked in R1C456 for N2 -> 23(4) = 2{489/579/678} <> 1,3

3. C123
a) Innies C1 = 15(3) = {168} -> R9C1 = 1, {68} locked for C1
b) 6(2) = {15} -> R8C2 = 5
c) 8(2) = {26} locked for R9+N7
d) 15(3) @ R6C1 = {249} -> R6C1 = 2; {49} locked for C1+N7
e) 14(3) = {347} -> R7C2 = 3, R7C3 = 7, R6C4 = 4
f) 12(3) = {138} -> R7C4 = 1, R8C4 = 3, R8C3 = 8
g) 9(2) = {18} -> R1C1 = 8, R2C2 = 1
h) 13(2) = {49} -> R1C2 = 4, R1C3 = 9
i) 15(3) @ R3C2 = {267} because R3C2 = (26) -> R4C4 = 7; {26} locked for R3+N1
j) 19(3) = {568} -> R2C3 = 5, R3C4 = 8, R2C4 = 6

4. R789
a) Outies R9 = 11(3) = {245} -> R8C8 = 4, R8C5 = 2
b) 13(2) = {49} -> R9C9 = 9
c) 10(2) = {37} locked for R9+N9
d) R8C7 = 6, R8C9 = 1
e) 16(3) = {178} -> R7C9 = 8, R6C9 = 7
f) 13(3) = {256} -> R6C6 = 6, {25} locked for R7

5. C5
a) 11(2) = {56} -> R6C5 = 5, R7C5 = 6
b) 9(2) = {18} -> R3C5 = 1, R4C5 = 8

6. Rest is singles without considering diagonals.

Rating: 1.0. I used Killer pairs and combo conflicts with 2-cell Innies.
Walkthrough by Andrew:
In the introduction to Messy One #2, Afmob wrote:
If you don't find the cracking move which is available right from the start, then you'll have a harder time than SS suggests.
That also applies to A102X, see my comment after step 17. As you will see in my walkthrough below, it took me some time to find the breakthrough. I was thinking of reworking my walkthrough today but Afmob beat me to it with a very short walkthrough so I've stuck with my original path.

I missed Afmob's step 1c, although I think the combinations in C1 can be worked easily without it. It's surprising to see a step like that so early in a walkthrough. I don't normally think of looking for multiple outies that can't all see each other until I've done more normal steps.

I'll rate A102X as Hard 1.0. I think Hard is justified by steps 17 and 18, which are fairly similar to Afmob's steps 1f and 1g.

Here is my walkthrough. This is a Killer-X. I've included eliminations on the diagonals for those who do their own eliminations.

Prelims

a) 9(2) diagonal cage in N1 = {18/27/36/45}, no 9
b) R1C23 = {49/58/67}, no 1,2,3
c) R1C78 = {13}, locked for R1 and N3, clean-up: no 6,8 in R2C2
d) 14(2) diagonal cage in N3 = {59/68}
e) R34C5 = {18/27/36/45}, no 9
f) R67C5 = {29/38/47/56}, no 1
g) 6(2) diagonal cage in N7 = {15/24}
h) 13(2) diagonal cage in N9 = {49/58/67}, no 1,2,3
i) R9C23 = {17/26/35}, no 4,8,9
j) R9C78 = {19/28/37/46}, no 5
k) 19(3) cage at R2C3 = {289/379/469/478/568}, no 1
l) 9(3) cage at R2C6 = {126/135/234}, no 7,8,9
m) R456C3 = {125/134}, 1 locked for C3 and N4, clean-up: no 7 in R9C2
n) 22(3) cage at R7C6 = {589/679}, CPE no 9 in R8C45
o) 30(4) cage in N4 = {6789}, locked for N4

1. 9(3) cage at R2C6 = {126/135/234}
1a. 5 of {135} must be in R2C7 -> no 5 in R23C6

2. 45 rule on N1 2 outies R4C14 = 1 innie R2C3 + 7
2a. Min R2C3 = 2 -> min R4C14 = 9, min R4C4 = 4
2b. Max R4C14 = 14 -> max R2C3 = 7
2c. Max R2C3 = 7 -> min R23C4 = 12, no 2 in R23C4

3. 45 rule on N3 2 outies R4C69 = 1 innie R2C7 + 3
3a. Max R2C7 = 6 -> max R4C69 = 9, no 9 in R4C69

4. 45 rule on N7 1 innie R8C3 = 2 outies R6C14 + 2
4a. Min R6C14 = 3 -> min R8C3 = 5
4b. Max R8C3 = 9 -> max R6C14 = 7, no 6,7,8,9 in R6C4

5. 45 rule on N9 2 outies R6C69 = 1 innie R8C7 + 7
5a. Min R8C7 = 5 -> min R6C69 = 12, no 1,2 in R6C69

6. 45 rule on N6 2 innies R46C9 = 10 = [19/28]/{37/46}, no 5, no 8 in R4C9

7. 45 rule on R9 3 outies R8C258 = 11 = {128/137/146/236/245}, no 9, clean-up: no 4 in R9C9
7a. 7,8 of {128/137} must be in R8C8 -> no 7,8 in R8C5

8. R234C9 = {129/147/237/246/345} (cannot be {138} because 1,3 only in R4C9, cannot be {156} which clashes with 14(2) diagonal cage), no 8
8a. 1,3 of {147/237} must be in R4C9 -> no 7 in R4C9, clean-up: no 3 in R6C9 (step 6)

9. 45 rule on C9 3 innies R159C9 = 17 = {179/269/278/359/368/458/467}
9a. 1,2,3,4 only in R5C9 -> R5C9 = {1234}

10. R456C7 = {148/157/238/247/256/346} (cannot be {139} which clashes with R1C7), no 9

11. 45 rule on N4 2 innies R46C1 = 7 = {25/34}

12. 45 rule on C1 3 innies R159C1 = 15 = {159/168/258/267} (cannot be {249/456} which clash with R46C1), no 4, clean-up: no 5 in R2C2, no 2 in R8C2

13. 45 rule on R1 3 outies R2C258 = 18 = {189/279/369/378/459/468/567}
13a. 1 of {189} must be in R2C2 -> no 1 in R2C5
13b. 4 of {459/468} must be in R2C2 -> no 4 in R2C5

14. 12(3) cage at R7C4 = {129/138/147/156/237/246/345}
14a. 7,8,9 of {129/138/147/237} must be in R8C3 -> no 7,8,9 in R78C4

15. 45 rule on N2 2 outies R2C37 = 1 innie R3C5 + 6
15a. Max R2C37 = 13 -> max R3C5 = 7, clean-up: no 1 in R4C5

16. 45 rule on N8 2 outies R8C37 = 1 innie R7C5 + 8
16a. Min R8C37 = 11 -> min R7C5 = 3, clean-up: no 9 in R6C5

17. 15(3) cage at R2C1 = {159/249/267/357/456} (cannot be {168} because R4C1 only contains 2,3,4,5, cannot be {258/348} because of overlap clash with R46C1), no 8
[Steps 17 to 21 have been possible since the final Prelim and steps 11,12 but I only spotted them here]

18. 15(3) cage at R6C1 = {159/249/267/357/456} (cannot be {168} because R6C1 only contains 2,3,4,5, cannot be {258/348} because of overlap clash with R46C1), no 8

19. 8 in C1 locked in R15C1 -> R159C1 (step 12) = {168/258}, no 7,9, clean-up: no 2 in R2C2
[I missed the fact that the two 15(3) cages contain killer pair 2,5, which would have got me straight to step 21.]
19a. 7,9 in N4 locked in R456C2, locked for C2, clean-up: no 4,6 in R1C3, no 2 in R1C1

20. 15(3) cage at R2C1 (step 17) = {249/357} (cannot be {159/267/456} which clash with R159C1), no 1,6
20a. 15(3) cage at R6C1 (step 18) = {249/357} (cannot be {159/267/456} which clash with R159C1), no 1,6

21. R159C1 (step 12) = {168} (hidden triple in C1) -> R9C1 = 1, R8C2 = 5, both locked for D/, clean-up: no 8 in R1C3, no 4 in R2C2, no 9 in 14(2) diagonal cage in N3, no 3 in R9C23, no 7 in R9C3, no 9 in R9C78, no 8 in R9C9

22. Naked pair {68} in R1C9 + R2C8, locked for D/ and N3

23. Naked pair {26} in R9C23, locked for R9 and N7, clean-up: no 7 in R8C8, no 4,8 in R9C78

24. Naked pair {37} in R9C78, clean-up: no 6 in R8C8

25. R8C258 (step 7) = {245} (only remaining combination) -> R8C58 = [24], R9C9 = 9, 4,9 locked for D\, clean-up: no 7 in R34C5, no 9 in R7C5

26. Naked triple {458} in R9C456, locked for N8, clean-up: no 3,6,7 in R6C5

27. R3C5 = 1 (hidden single in C5), R4C5 = 8, clean-up: no 3 in R7C5

28. 9(3) cage at R2C6 = {234} (only remaining combination) -> 3 locked in R23C6, locked for C6 and N2

29. 22(3) cage at R7C6 = {679} (only remaining combination) -> R8C7 = 6, R78C6 = {79}, locked for C6 and N8 -> R7C5 = 6, R6C5 = 5, R6C6 = 6, locked for D\, R1C1 = 8, R2C2 = 1, both locked for D\, R1C9 = 6, R2C8 = 8, R4C4 = 7, locked for D\, R5C5 = 3, locked for both diagonals, R5C1 = 6, R4C2 = 9, R9C5 = 4, R2C5 = 9 (step 13), R1C5 = 7, R5C9 = 2 (step 9), R1C2 = 4, R1C3 = 9, clean-up: no 2 in R4C1 (step 11)

30. R4C6 + R6C4 = {24}, locked for N5 and D/ -> R5C46 = [91], R7C3 = 7, locked for D/, R3C7 = 9, R8C3 = 8, R7C2 = 3, R78C4 = [13], R78C1 = [49], R78C6 = [97], R8C9 = 1, R6C1 = 2 (step 20a), R4C1 = 5 (step 11), R5C3 = 4, R6C4 = 4, R4C6 = 2, R1C46 = [25], R23C4 = [68], R9C46 = [58]

31. R7C9 = 8 (hidden single in R7)

and the rest is naked singles.


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PostPosted: Thu Apr 28, 2011 1:04 am 
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Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Assassin 103 by Mike (mhparker) (May 2008) here
Puzzle Diagram:
Image
Images with "udosuk style Killer Cages" by Børge:
Image     Image
Code: Select, Copy & Paste into solver:
3x3::k:5632:5632:3074:3843:3843:3843:5126:3591:3591:5632:3074:1547:1547:3085:1038:1038:5126:3591:3074:2835:2835:3605:3085:5143:2840:2840:5126:5147:2835:3605:3605:5663:5143:5143:2840:4131:5147:1061:1061:5663:5663:5663:3114:3114:4131:5147:3374:3887:3887:5663:2610:2610:6196:4131:4918:3374:3374:3887:3386:2610:6196:6196:2622:3135:4918:3137:3137:3386:3908:3908:2622:2887:3135:3135:4918:4171:4171:4171:2622:2887:2887:
Solution:
+-------+-------+-------+
| 9 7 4 | 6 8 1 | 5 2 3 |
| 6 5 2 | 4 7 3 | 1 8 9 |
| 3 1 8 | 2 5 9 | 6 4 7 |
+-------+-------+-------+
| 5 2 9 | 3 6 7 | 4 1 8 |
| 8 3 1 | 9 2 4 | 7 5 6 |
| 7 4 6 | 8 1 5 | 3 9 2 |
+-------+-------+-------+
| 4 6 3 | 1 9 2 | 8 7 5 |
| 2 8 5 | 7 4 6 | 9 3 1 |
| 1 9 7 | 5 3 8 | 2 6 4 |
+-------+-------+-------+
Quote:
Mike (mhparker): The cage pattern for this Assassin reminded me of a mounted photo, so I decided to stick with this analogy whilst coloring it.
A picture may be proverbally worth a thousand words, but this one sure ain't givin' anything away!
Est. rating: 1.25. SudokuSolver v3.1 scores this at 1.24, which seems pretty accurate again.

Ed: Good luck!
I get an SS(v3.1) score of 1.74. Might need that good luck and 2 weeks!

Mike replied: Hmm. You're right. On my Windows Vista installation, I get 1.75. However, I've just repeated the same test on my Windows XP installation, and got the published score of 1.24 again. Looked at the solver list and found that the default scoring options were not set. For some reason, SS did not alert me to this fact like it normally does. :?
Despite this, I do quite a bit of analysis before posting a puzzle, and would not have published it as a V1 if I had felt that it was a genuine 1.75. The moral of this story is that we shouldn't always take what the automated solvers say for granted, even though they have an invaluable role to play in the puzzle evaluation process these days.

HATMAN: Interesting puzzle - I managed to do it with a bit of T&E and I think I can now see how to do it without.
Afmob: This was an interesting Killer where the hardest move (step 4b) was available right from the start. Thanks Mike! :applause:
I'm not sure about the rating. My walkthrough could also justify a 1.25 depending on how you rate step 4b. My first gut feeling went for 1.5, so I'll stay with that.

Andrew: Thanks Mike for a challenging puzzle.
Yes, it (the key breakthrough step) was there right after the Prelims. It took me a very long time to find this key move. Then I just came across it after I found that the other moves I was working with didn't seem to be making any more progress. With hindsight I feel that I ought at least to have got it after step 19 but I didn't find it until step 54!

Solving comment by HATMAN:
Main point:
C1: conflict between 22(3) 20(3) reduces posibilities which together with the outies minus innies of C1 allows decision on the 19(3) in N7.
Walkthrough by Afmob:
I'm not sure about the rating. My walkthrough could also justify a 1.25 depending on how you rate step 4b. My first gut feeling went for 1.5, so I'll stay with that. But it's definitely overrated by SudokuSolver and JSudoku (which used XY-Chains).

A103 Walkthrough:

1. R123
a) 4(2) = {13} locked for R2
b) 6(2) = {24} locked for R2
c) Outies N1 = 6(1+1) = {24}
d) Outies N3 = 4(1+1) = {13}
e) 12(2): R3C5 <> 8,9
f) 11(3) @ N1 <> 7 because R4C2 = (24)
g) 12(3) <> 6 because R2C3 = (24) blocks {246} and {156} blocked by Killer pair (56) of 22(3)
h) 22(3) = 9{58/67} -> 9 locked for N1
i) 12(3) can only have one of (578) and R2C2 = (578) -> R1C3+R3C1 <> 5,7,8

2. R6789
a) Innies N9 = 24(3) = {789} locked for N9
b) 15(2): R8C6 <> 9
c) Innies N8 = 16(4): R78C4 <> 8,9 because R8C6 >= 6
d) 12(2): R8C3 <> 3,4
e) Outies N7 = 11(1+1) -> R6C2 = (4678)
f) Outies R89 = 18(3) <> 1,2 because R7C78 = (789) blocks 9{18/27}
g) Killer triple (789) locked in Outies R89 + R7C78 for R7

3. R456 !
a) 4(2) = {13} locked for R5+N4
b) 12(2) <> 9
c) ! Killer triple (789) locked in 16(3) + 12(2) + R6C8 for N6
d) 20(3) @ N5: R34C6 <> 3,4 because R4C7 <> 7,8,9

4. C123 !
a) 22(3) = 9{58/67} must have exactly two of (569)
b) ! 20(3) = 7{49/58} because 20(3) <> {569} since 22(3) could have only one of (569)
-> 7 locked for C1+N4
c) 7 locked in R89C3 for N7
d) 22(3): R1C2 <> 6 because 7 only possible there
e) 22(3): R1C2 <> 5,8 because {589} blocked by Killer pairs (59,89) of 20(3)
f) Innies+Outies C1: 9 = R19C2 - R37C1 -> R7C1 <> 8,9

5. R789
a) Outies R89 = 18(3): R7C5 <> 4,5,6 because R7C19 <= 11
b) 13(2): R8C5 <> 7,8,9
c) Outies N7 = 11(1+1): R8C4 <> 4
d) 12(2) <> 8
e) Killer pair (79) locked in 12(2) + 15(2) for R8
f) 19(3) <> 3 because 7,9 only possible @ R9C3

6. C123 !
a) ! Hidden triple (123) locked in R389C1 for C1
b) 12(3) @ N7: R9C2 = (89) because R89C1 <= 5
c) 12(2) = 1{29/38} -> 1 locked for C1+N7
d) Killer pair (89) locked in R9C2 + 19(3) for N7
e) 12(2) = {57} locked for R8
f) Hidden Single: R8C7 = 9 @ R8 -> R8C6 = 6
g) R8C5 = 4 -> R7C5 = 9,
h) Hidden Single: R8C2 = 8 @ R8, R9C2 = 9, R1C2 = 7, R2C2 = 5
i) 22(3) = {679} -> {69} locked for C1+N1
j) 11(3) = {128} -> R4C2 = 2, R3C2 = 1, R3C3 = 8
k) 20(3) = {578} locked for C1+N4
l) R5C2 = 3

7. R789
a) R7C1 = 4 -> R9C3 = 7
b) 24(3) = {789} -> R6C8 = 9
c) R7C2 = 6, R6C2 = 4, R6C3 = 6, R8C3 = 5, R8C4 = 7
d) 15(3) = {168} -> R7C4 = 1, R6C4 = 8

8. R456
a) R4C3 = 9
b) 14(3) = {239} -> R4C4 = 3, R3C4 = 2
c) R3C1 = 3
d) 11(3) = {146} -> R4C8 = 1, {46} locked for N3
e) 22(5) = {12469} -> R4C5 = 6, R5C5 = 2, R6C5 = 1; {49} locked for R5
f) 12(2) = {57} locked for R5+N6
g) R4C7 = 4
h) 20(3) @ N5 = {479} -> R4C6 = 7, R3C6 = 9
i) R4C9 = 8, R5C9 = 6 -> R6C9 = 2

9. Rest is singles.

Rating: (Easy) 1.5. I used Killer triples and combo conflicts to solve it.
Walkthrough by Andrew:
I'll rate this puzzle as a solid 1.5 the way I did it. However if one got that key move right after the Prelims I'm guessing that it might be a normal or hard 1.25.

Here is my walkthrough. I got into some interesting stuff because I didn't find the key move early enough.

Thanks Afmob for pointing out that step 17a was invalid. I must have seen 3 in R7C9 but not noticed that it also contained 6. Later steps that depended on step 17a are coloured red; consider them to be deleted but I've left them in so that the effect of one incorrect elimination can be seen, some of them have been used later. Other editing, plus the re-use of earlier steps when they became valid, is in blue.

Prelims

a) R2C67 = {13}, locked for R2
b) R2C34 = {24}, locked for R2
c) R23C5 = {57}/[84/93], no 1,2,6, no 8,9 in R3C5
d) R5C78 = {39/48/57}, no 1,2,6
e) R5C23 = {13}, locked for R5 and N4, clean-up: no 9 in R5C78
f) R78C5 = {49/58/67}, no 1,2,3
g) R8C34 = {39/48/57}, no 1,2,6
h) R8C67 = {69/78}
i) 22(3) cage in N1 = {589/679}, 9 locked for N1
j) 20(3) diagonal cage in N3 = {389/479/569/578}, no 1,2
k) 11(3) cage at R3C2 = {128/137/146/236/245}, no 9
l) 11(3) cage at R3C7 = {128/137/146/236/245}, no 9
m) 20(3) cage at R3C6 = {389/479/569/578}, no 1,2
n) R456C1 = {479/569/578}, no 2
o) 10(3) cage at R6C6 = {127/136/145/235}, no 8,9
p) 24(3) cage at R6C8 = {789}, CPE no 7,8,9 in R89C8
q) 19(3) diagonal cage in N7 = {289/379/469/478/568}, no 1
r) 10(3) diagonal cage in N9 = {127/136/145/235}, no 8,9
s) 11(3) cage in N9 = {128/137/146/236/245}, no 9

1. 45 rule on N1 1 outie R4C2 = 1 innie R2C3 -> R4C2 = {24}

2. 45 rule on N3 1 outie R4C8 = 1 innies R2C7 -> R4C8 = {13}

3. 45 rule on N7 1 innie R8C3 = 1 outie R6C2 + 1, no 5,9 in R6C2, no 4 in R8C3, clean-up: no 8 in R8C4

4. 45 rule on N9 1 outie R6C8 = 1 innie R8C7, no 6 in R8C7, clean-up: no 9 in R8C6

5. Naked triple {789} in R7C78 + R8C7, locked for N9

6. 45 rule on R1234 3 innies R4C159 = 19 = {289/379/469/478/568}, no 1

7. 45 rule on R6789 3 innies R6C159 = 10 = {127/136/145/235}, no 8,9
7a. 6,7 of {127/136} must be in R6C1 -> no 6,7 in R6C59

8. 45 rule on C1234 3 innies R159C4 = 20 = {389/479/569/578}, no 1,2

9. 45 rule on C6789 3 innies R159C6 = 13 = {148/157/238/247/256/346} (cannot be {139} which clashes with R2C6), no 9

10. 9 in C6 locked in R34C6 for 20(3) cage -> no 9 in R4C7
10a. 20(3) cage at R3C6 = {389/479/569}

11. 11(3) cage at R3C2 = {128/146/236/245} (cannot be {137} because R4C2 only contains 2,4), no 7

12. 12(3) diagonal cage in N1 = {138/147/237/345} (cannot be {156} which clashes with 22(3) cage, cannot be {246} which clashes with R2C3), no 6
12a. R2C2 = {578} -> no 5,7,8 in R1C3 + R3C1

13. 11(3) cage at R3C7 = {128/137/146/236} (cannot be {245} because R4C7 only contains 1,3), no 5
13a. R2C7 = R4C8 (step 2) -> R2C7 + R3C78 = {128/137/146/236}

14. 45 rule on N2 4 innies R23C46 = 18 = {1269/1278/1458/1467/2349/2367} (cannot be {1359/1368} because R2C4 only contains 2,4, cannot be {2457} because R2C6 only contains 1,3, cannot be {2358/3456} which clash with R23C5)
14a. 1,3 must be in R2C6 -> no 1,3 in R3C46

15. Combined cage R8C3467 = 27 = {3789/4689/5679}, 9 locked for R8, clean-up: no 4 in R7C5

16. 45 rule on R12 3 outies R3C159 = 15 = {159/249/258/267/348/357/456} (cannot be {168} because R3C5 only contains 3,4,5,7}
16a. 6,8,9 of {249/348/456} must be in R3C9 and 3 of {357} must be in R3C1 -> no 3,4 in R3C9

17. 45 rule on R89 3 outies R7C159 = 18 = {369/459/468/567} (cannot be {189/279/378} which clash with R7C78), no 1,2
17a. 3 of {369} must be in R7C9 -> no 3 in R7C1

18. Killer triple 7,8,9 in R7C159 and R7C78, locked for R7

19. R389C1 = {123} (hidden triple in C1)

20. 12(3) cage in N7 = {129/138/237} (cannot be {147/156/246/345} because R89C1 only contain 1,2,3)
20a. 7,8,9 can only be in R9C2 -> R9C2 = {789}


21. 45 rule on N8 4 innies R78C46 = 16 = {1258/1267/1348/1357/2347/2356} (cannot be {1249} because R8C6 only contains 6,7,8, cannot be {1456} which clashes with R78C5), no 9, clean-up: no 3 in R8C3, no 2 in R6C2 (step 3)
21a. 1,2 of {1267} must be in R7C46, 6 of {2356} must be in R8C6 -> no 6 in R7C46

22. 45 rule on C789 4 innies R2468C7 = 17 = {1259/1268/1349/1358/1367/2348/2357} (cannot be {1457} which clashes with R5C78, cannot be {2456} because R8C7 only contains 7,8,9)
22a. R8C7 = {789} -> no 7,8 in R46C7

23. 45 rule on C1 2 outies R19C2 = 2 innies R37C1 + 9
23a. Max R19C2 = 17 -> max R37C1 = 8, no 8,9 in R7C1

24. 20(3) cage at R3C6 (step 10a) = {389/479/569}
24a. 3,4 of {389/479} must be in R4C7 -> no 3,4 in R34C6

25. 10(3) cage at R6C6 = {127/136/145/235}
25a. 6 of {136} must be in R6C6 (R67C6 cannot be {13} which clashes with R2C6) -> no 6 in R6C7

26. 14(3) cage in N3 = {149/158/239/248/257/347/356} (cannot be {167} which clashes with R2C7 + R3C78)
26a. 9 of {149/239} must be in R2C9 -> no 9 in R1C89

27. 14(3) cage at R3C4 = {149/158/167/239/248/257/347/356}
27a. 1,3 of {149/167/239/356} must be in R4C4 -> no 6,9 in R4C4

28. R8C3 = R6C2 + 1 (step 3)
28a. 45 rule on C123 4 innies R2468C3 = 22 = {2479/2569/2578/4567}
28b. 8 of {2578} must be in R46C3 (R8C3 cannot be 8 when R46C3 = {57} clashes with R6C2 = 7), no 8 in R8C3, clean-up: no 7 in R6C2 (step 3), no 4 in R8C4

29. Combined cage R8C3467 (step 15) = {3789/5679}, 7 locked for R8, clean-up: no 6 in R7C5

30. 13(3) cage at R6C2 = {148/256/346} (cannot be {238} which clashes with R89C1)
30a. Killer triple 1,2,3 in R7C23 and R89C1, locked for N7

31. R3C159 (step 16) = {159/249/258/267/348/357} (cannot be {456} because R3C1 only contains 1,2,3)
31a. 3 of {348/357} must be in R3C1 -> no 3 in R3C5, clean-up: no 9 in R2C5

32. R78C5 = [76/94] (cannot be {58} which clashes with R23C5), no 5,8
32a. Combined cage R2378C5 = {4579/4678}, 4,7 locked for C5

33. Naked triple {789} in R7C578, locked for R7
33a. 8 in R7 locked in R7C89, locked for N9 and 24(3) cage -> no 8 in R6C8, clean-up: no 7 in R8C6

34. Hidden killer pair 1,3 in R1C456 and R2C6 for N2 -> R1C456 must contain 1 or 3
34a. R1C456 = {159/168/348/357} (cannot be {249/258/267/456} which don’t contain 1 or 3), no 2

35. 2 in N2 locked in R23C4, locked for C4 and locked in R23C46
35a. R23C46 (step 14) = {1269/2349/2367} (cannot be {1278} which clashes with R23C5, cannot be {1458/1467} which don’t contain 2), no 5,8


36. 19(3) diagonal cage in N7 = {379/469/478/568} (cannot be {289} because 2,8,9 only in R8C2 + R9C3), no 2
36a. 7,9 of {469/478} can only be in R9C3 -> no 4 in R9C3
[Afmob pointed out that I could have eliminated 3 from R7C1 + R9C3, because no 7,9 in R8C2, and then inserted the deleted important step 19 instead of putting it as step 56. I missed that because while editing for the effects of deleting step 17a, I was only looking for which other steps before step 54 were still valid and avoiding any re-work until after that step.]

37. R456C9 = {169/259/268/349/367} (cannot be {178/358/457} which clash with R5C78)

38. Hidden killer triple 7,8,9 in R12C9, R3C9 and R45C9 for C9 -> R12C9 must contain one of 7,8,9 (cannot have two of them in 14(3) cage) -> R3C9 = {789}
38a. 14(3) cage in N3 (step 26) = {149/158/239/248/257/347} (cannot be {356} which doesn’t contain 7,8,9), no 6
38b. 7,8,9 in R12C9 -> no 7,8 in R1C8

39. 20(3) diagonal cage in N3 = {389/479/569/578}
39a. 3,4 can only be in R1C7 -> no 9 in R1C7
39b. 9 in C7 locked in R78C7, locked for N9

40. R3C159 (step 16) = {159/249/258/348/357}
40a. R3C9 = {789} -> no 7 in R3C5, clean-up: no 5 in R2C5

41. 11(3) cage at R3C2 (step 11) = {128/146/236/245}
41a. 4 of {146/245} must be in R4C2 (R3C23 cannot be {45} which clashes with R3C5) -> no 4 in R3C23

42. 4 in N1 locked in R12C3, locked for C3

43. 13(3) cage at R6C2 (step 30) = {148/256/346}
43a. 1 of {148} must be in R7C3 -> no 1 in R7C2

44. R78C46 (step 21) = {1267/1348/2356} (cannot be {1258} which clashes with combined cage R8C3467, cannot be {1357/2347} because R8C6 only contains 6,8)
44a. 5 of {2356} must be in R8C4 (R8C46 cannot be {36} which clashes with combined cage R8C3467) -> no 5 in R7C46
44b. 3 of {1348} must be in R8C4, 2 of {2356} must be in R7C6 -> no 3 in R7C6

45. Combined cage R78C456 = {124679/134678/234569}, 4,6 locked for N8

46. 4 in R9 locked in R9C789, locked for N9

47. R2468C7 (step 22) = {1259/1349/1367/2357} (cannot be {1268/1358/2348} because R8C7 only contains 7,9)
[These combinations also apply for R46C78 because R2C7 = R4C8 and R6C8 = R8C7]
47a. 2 of {1259/2357} must be in R6C7 -> no 5 in R6C7

48. R46C78 (step 47) = {1259/1349/1367/2357}
48a. Combined cage R456C78 = {124589/134579/134678/234578}, 4 locked for N6

49. 10(3) cage at R6C6 = {127/136/145/235}
49a. 5,6,7 can only be in R6C6 -> R6C6 = {567}

50. R456C9 (step 37) = {169/259/268/367}
50a. 3 of {367} must be in R6C9 -> no 3 in R4C9

51. Hidden killer quint 5,6,7,8,9 in R159C6 and R3468C6 for C6 -> R159C6 must contain one of 5,6,7,8
51a. R159C6 (step 9) = {148/238/247/256/346} (cannot be {157} which contains both 5 and 7)

52. 15(3) cage at R6C3 = {159/168/249/348/357/456} (cannot be {258/267} because R7C4 only contains 1,3,4)
52a. 1 of {159/168} must be in R7C4 -> no 1 in R6C4

53. 2 in N5 locked in 22(5) cage = {12379/12469/12568/23458} (cannot be {12478/23467} which clash with R5C78)
53a. 2 of {23458} must be in R5C456 (R5C456 cannot be {458} which clashes with R5C78) -> no 2 in R6C5


54. 22(3) cage in N1 = {589/679}
54a. R12C1 = {58/69} (cannot be {59/67/79/89} which clash with R456C1), no 7, R1C2 = {79}
54b. R456C1 = {479/578} (cannot be {569} which clashes with R12C1), no 6, 7 locked for C1 and N4
54c. 7 in N1 locked in R12C2, locked for C2

55. 19(3) diagonal cage in N7 (step 36) = {469/478/568} (cannot be {379} because 7,9 only in R9C3), no 3
55a. 7,9 of {469/478} can only be in R9C3 -> no 4 in R9C3
[That has at last made the elimination that I tried to do in step 17a! I can now use some of the steps that I had to delete earlier.]

56. R389C1 = {123} (hidden triple in C1)

57. 12(3) cage in N7 = {129/138} (cannot be {156/246/345} because R89C1 only contain 1,2,3)
57a. 8,9 can only be in R9C2 -> R9C2 = {89}
57b. 1 locked in R89C1, locked for C1 and N7

58. R3C159 (step 40) = {249/258/348/357}
58a. 3 of {348/357} must be in R3C1 -> no 3 in R3C5, clean-up: no 9 in R2C5

59. R78C5 = [76/94] (cannot be {58} which clashes with R23C5), no 5,8
59a. Combined cage R2378C5 = {4579/4678}, 4,7 locked for C5

60. 11(3) cage at R3C2 (step 11) = {128/146/236/245}
60a. 4 of {146/245} must be in R4C2 (R3C23 cannot be {45} which clashes with R3C5) -> no 4 in R3C23

61. 4 in N1 locked in R12C3, locked for C3

62. 13(3) cage at R6C2 = {256/346} (cannot be {238} which clashes with R89C1), no 8, clean-up: no 9 in R8C3 (step 3), no 3 in R8C4


[At this stage I was going to use 45 rule on R789 4 innies R7C2346 = 1 outie R6C8 + 3 which I’d seen a long time ago but was only useful now that 1 was locked in R7C46. However the naked pairs and naked triple in the next steps are more direct.]

63. Naked pair {57} in R8C34, locked for R8, clean-up: no 8 in R8C67
63a. R8C67 = [69]
, R8C5 = 4, R7C5 = 9, R8C2 = 8, R9C2 = 9, R12C2 = [75], R3C5 = 5, R2C5 = 7, R6C8 = 9 (step 4), R3C6 = 9, clean-up: no 8 in R12C1 (step 54a)

64. Naked pair {69} in R12C1, locked for C1 and N1, clean-up: no 4 in R456C1 (step 54b)
64a. Naked triple {578} in R456C1, locked for C1 and N1 -> R7C1 = 4, R9C3 = 7 (step 36), R8C34 = [57]

65. 45 rule on R789 2 outies R6C28 = 2 outies R7C46 + 10
65a. 1 in R7 locked in R7C46, locked for N8
65b
. R6C28 must be odd -> R7C46 must be odd = {12}, locked for R7 and N8, R7C23 = {36}, locked for R7, N7 and 13(3) cage -> R7C9 = 5, R6C2 = 4, R4C2 = 2
[I missed R6C2 = 4 (step 3) after step 62a but if I’d done it then I might not have used this interesting step.]

66. R46C3 = [96] (naked pair), R7C23 = [63], R5C23 = [31], R3C23 = [18], R3C6 = 9, R3C9 = 7

67. Naked pair {12} in R89C1, locked for C1 -> R3C1 = 3, R1C3 = 4 (step 12), R2C34 = [24]

68. R4C3 = 9 -> R34C4 = 5 = [23], R4C8 = 1

69. Naked pair {46} in R3C78, locked for N3 -> R2C89 = [89], R12C1 = [96], R7C78 = [87], R1C7 = 5 (step 39)

70. Naked pair {46} in R34C7, locked for C7 -> R5C78 = [75], R5C1 = 8

71. Naked pair {23} in R6C79, locked for R6 and N6 -> R6C5 = 1

72. R4C9 = 8 (hidden single in C9), R56C9 = 8 = [62]


and the rest is naked singles and a hidden single (or cage sum).


Last edited by Andrew on Fri Apr 29, 2011 9:14 pm, edited 1 time in total.

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PostPosted: Thu Apr 28, 2011 2:50 am 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Human Solvable 1 by HATMAN (May 2008) here
Puzzle Diagram:
Image
Images with "udosuk style Killer Cages" by Børge:
Image     Image
A much easier version (not within the Human Solvable classification) without r5c5 being part of a cage, i.e. r5c5 is a Zero Killer cell
Warning: Viewing these diagrams may be a spoiler for the full puzzle:
Image     Image
Code: Select, Copy & Paste into solver:
3x3:d:k:6401:1808:6401:4372:4372:4372:6404:2567:6404:1808:6401:3343:3343:3350:3078:3078:6404:2567:6401:3342:6401:25:3350:26:6404:3077:6404:27:3342:28:4373:3350:2584:29:3077:30:3601:3601:3601:31:4373:32:2578:2578:2578:33:3596:34:2584:3863:4373:35:3336:36:6403:3596:6403:37:3863:38:6402:3336:6402:1549:6403:3595:3595:3863:3337:3337:6402:1290:6403:1549:6403:4115:4115:4115:6402:1290:6402:
Also Afmob posted Here is the PS Code for people using SumoCue: 3x3:d:k:6400:1793:6400:4355:4355:4355:6406:2567:6406:1793:6400:3339:3339:3341:3086:3086:6406:2567:6400:3347:6400:21:3341:23:6406:3097:6406:27:3347:29:30:3341:2592:33:3097:35:3620:3620:3620:39:2592:41:2602:2602:2602:45:3630:47:2592:3889:50:51:3380:53:6454:3630:6454:57:3889:59:6460:3380:6460:1599:6454:3649:3649:3889:3396:3396:6460:1351:6454:1599:6454:4171:4171:4171:6460:1351:6460:
Note that it doesn't include the 17(3) cage in N5.

Code string for the much easier version
3x3:d:k:6400:1793:6400:4355:4355:4355:6406:2567:6406:1793:6400:3339:3339:3341:3086:3086:6406:2567:6400:3347:6400:21:3341:23:6406:3097:6406:27:3347:29:2846:3341:1056:33:3097:35:3620:3620:3620:39:40:41:2602:2602:2602:45:3630:47:1056:3889:2846:51:3380:53:6454:3630:6454:57:3889:59:6460:3380:6460:1599:6454:3649:3649:3889:3396:3396:6460:1351:6454:1599:6454:4171:4171:4171:6460:1351:6460:
Solution:
+-------+-------+-------+
| 7 5 1 | 3 8 6 | 2 4 9 |
| 2 3 4 | 9 1 5 | 7 8 6 |
| 6 9 8 | 4 7 2 | 5 3 1 |
+-------+-------+-------+
| 1 4 7 | 2 5 3 | 6 9 8 |
| 9 2 3 | 7 6 8 | 1 5 4 |
| 8 6 5 | 1 4 9 | 3 7 2 |
+-------+-------+-------+
| 3 8 2 | 5 9 1 | 4 6 7 |
| 5 7 6 | 8 2 4 | 9 1 3 |
| 4 1 9 | 6 3 7 | 8 2 5 |
+-------+-------+-------+
Quote:
HATMAN: One of my interests (and I think Matt's) is creating human solvable puzzles that the programs have difficulty with.
HATMAN's full introduction and various discussions are included in the first hidden section below, so that any "spoilers" are hidden.

Afmob: Finally a long walkthrough :cheesey: because my present wts kept getting shorter and shorter. But this difficult Killer deserves a long walkthrough.

udosuk: after studying Afmob's step 11 I realise there is a easy way to solve this puzzle.
Kudos to Afmob for spotting the breakthrough point. :ugeek:

Andrew (in 2012): I tried Human Solvable 1 for the first time a few days ago and managed to finish it a couple of days later. Thanks HATMAN for a challenging puzzle!
I enjoyed some of the steps in the other walkthroughs, breakthroughs and outlines…
Rating 1.75.


HATMAN's full introduction and various discussions:
HATMAN
One of my interests (and I think Matt's) is creating human solvable puzzles that the programs have difficulty with. It is relatively easy with the exotic versions - JC has to work hard to keep up. However the challenge is with plain Killers.

This one is just an X. JSudoku uses about 25 fishes. SudokuSolver has difficulties with the centre crossover and putting the 10(3) as a hidden cage gives it a 2.8 using Bowman's Bingo (which I have not come across before and do not quite understand).

I've solved it without any fishes. The ring and then N5

Now you can argue whether the human approach is T&E or "short consequential analysis" (SCA) {I've been looking for an appropriate phrase for a while) and this is probably the right forum to have the argument.

udosuk
I did use a grouped turbot fishto crack this one (see next hidden window for details of this)
Interested to know how you got around that move in your "no-fish" solving route. :geek:

Para
I think there's also this. Step 1,2,3 are okay. Don't know if step 4 qualifies as the nicest logic, but it sounds a bit like the "short sequence analysis" mentioned.
1. 9 locked for R2 and N2 in R2C46
2. R46C5 = {45/38}: only options left with your 17(3), 10(3) and hidden 21(3) options, so R456C5 = {4[6]5} or {3[7]8}
3. R456C5 = [873] blocked by 15(3) R6C5: R78C5 can't equal 12, as 3, 7 and 8 are already used in C5.
4. R456C5 = [378] -> R5C4 = 9 -> R2C4 = 6: which leave no options for 13(3) at R2C5 as 6, is used in N2 and 7,8 in C5 and 9 was locked in step 1 and R23C5 can't equal 10 anymore.
5. This leaves: R456C5 = {4[6]5}
This is how i broke N5 at least.

Two posts omitted, then

HATMAN
Matt my previous message was was not just cryptic but wrong. I had been working and I checked in quickly, but my mind was on Chelski versus the Manx.
I used minimal T&E to clear 4,5 from r5c5 and was simliar to Para on clearing the 7. (Udosuk's walkthrough with my stuff in italics)

With the Ring in place
R2c6r4c8 = {59} -> r2c8r4c6 <> 59
62c8r8c6 = {47} -> r6c6r8c8 <> 47


Innies @ r5: r5c456 = 21 = {489|579|678}
10/3 @ /456 = {127|136|145|235}

=> 17/3 @ \456 = [746|458|269|962|476]

r2c3467 = [ 4957 | 7693 ] =79..
r3467c2 = [ 9468 | 6795 ] =69..
r3467c8 = [ 3976 | 7549 ] =79..
r8c3467 = [ 6849 | 9576 ] =69.. r8c46 = 12(2)

r46c2=[46|79] => \456 can't be [746] and <> [647] r6c6<>7
r28c6+r4c2=[544|977] => r4c4+r5c456 can't be [4759|4957] => \456 can't be [458]
and <> [854] r6c6<>4

=> 17/3 @ \456 = [269|962|476] with 6 locked r5c5 = 6|7
=> 10/3 @ /456 = {127|136} with 1 locked
=> r5c456 = 21 = {579|678} with 7 locked
=> r46c46 = {2913|4612} with 2 locked
At this stage Matt has reduced to r5c5 to 6/7 without any hint of T&E (mine was sort of T&E)
innies on C5 -> r159c5 = 17/3
If r5c5 =6 r46c5 = {46} r5c46 = {78} r4c6r6c4 = {13} r4c4r6c6 = {29}
If r5c5 =7 r46c5 = {38} r5c46 = {59} r4c6r6c4 = {12} r4c4r6c6 = [46]
-> c5 <>38 r19c5 = {46}|[19] but r1c456 <>9 hence <> {179} -> r1c5<>1 -> {46} but r234c5 = {23}8 | {14}8 | {46}3 | {28}3 | {19}3 all these conflict with the {46} in r19 or the 3|8 in r6 so fail-> r5c5 =6
This is the same as Para’s approach so is it SCA or T&E?
Simple from here


corrected and clarified given Matt's comment

udosuk
That makes 2 of us! :mrgreen:

HATMAN had written
At this stage Matt has reduced to r5c5 to 6/7 without any hint of T&E (mine was sort of T&E)
If r5c5 =6 r46c5 = {46} r5c46 = {78} r4c6r6c4 = {13} r4c4r6c6 = {29}
If r5c5 =7 r46c5 = {38} r5c46 = {59} r4c6r6c4 = {12} r4c4r6c6 = [46]
-> c5 <>38 r19c5 = {46}|[19] but r1c456 <>9 -> r1c5<>1 ->{46} but r234c5 = {46}5
-> r5c5 =6
This is the same as Para’s approach so is it SCA or T&E?
Simple from here


Now that you've locked the 9 @ r2,n2 @ r2c46,
if r5c5=7 => r46c5={38}, r19c5=17-7=10 (=> 13/3 @ r234c5=[463|643|148|418])
But 9 @ n2 locked @ r2c46 so r1c5 can't be 9
Also 17/3 @ r1c456 can't be {179} so r1c5 can't be 1
=> r19c5={46} => 13/3 @ r234c5 must be from {12358}={238} => contradicts r46c5={38}
Therefore r5c5 can't be 7, must be 6.

Your "but r234c5 = {46}5" looks completely non-understandable to me. :scratch:
Still recovering from the booze? :drunk:

udosuk
Commenting on Afmob's walkthrough
I like your step 11. Longer than my grouped turbot fish but I guess it's more to HATMAN's taste of "no fish". :ugeek:

HATMAN
Excellent walkthroughs - I particularly liked the diagonal work and the extra pointing pairs.

Richard (rcbroughton)
Maybe I fixed something . . . SudokuSolver does solve this without T&E but does use 2 Y-Wings and an ALS in the solution. It also needs to have boh the 17(3) and the 10(3) defined in n5. But it takes a long time to get there . . .

Maybe I need to teach it some new tricks . . .
udosuk's original breakthrough steps:
After easy moves to set up the ring and n5 (using innies @ r5 & 10/3 @ /456):
Code:
     .         .         .     |     .         .         .     |     .         .         .
     .         .         47    |     69        .         59    |     37        .         .
     .         69        .     |     .         .         .     |     .         37        .
-------------------------------+-------------------------------+-------------------------------
     .         47        .     | 123456789     .        1234   |     .         59        .
     .         .         .     |   56789      4567     56789   |     .         .         .
     .         69        .     |   12345       .      1235689  |     .         47        .
-------------------------------+-------------------------------+-------------------------------
     .         58        .     |     .         .         .     |     .         69        .
     .         .         69    |     58        .         47    |     69        .         .
     .         .         .     |     .         .         .     |     .         .         .

Innies @ r5: r5c456 = 21 = {489|579|678}
10/3 @ /456 = {127|136|145|235}

=> 17/3 @ \456 = [746|458|269|962|476]

r2c3467 = [ 4957 | 7693 ]
r3467c2 = [ 9468 | 6795 ]
r3467c8 = [ 3976 | 7549 ]
r8c3467 = [ 6849 | 9576 ]

r46c2=[46|79] => \456 can't be [746]
r28c6+r4c2=[544|977] => r4c4+r5c456 can't be [4759|4957] => \456 can't be [458]

=> 17/3 @ \456 = [269|962|476] with 6 locked
=> 10/3 @ /456 = {127|136} with 1 locked
=> r5c456 = 21 = {579|678} with 7 locked
=> r46c46 = {2913|4612} with 2 locked

Innies @ c5: r159c5=17 => r19c5 can't have 5
13/3 @ r234c5: r4c5 from {34589} => r23c5 can't have 5
r28c6+r4c2=[544|977] => r4c4+r5c456 can't be [4579] => r5c456 can't be [579]
Code:
     .         .         .     |     .      12346789     .     |     .         .         .
     .         .         47    |     69     12346789     59    |     37        .         .
     .         69        .     |     .      12346789     .     |     .         37        .
-------------------------------+-------------------------------+-------------------------------
     .         47        .     |    249      34589      123    |     .         59        .
     .         .         .     |    789        67       578    |     .         .         .
     .         69        .     |    123      34589      269    |     .         47        .
-------------------------------+-------------------------------+-------------------------------
     .         58        .     |     .         .         .     |     .         69        .
     .         .         69    |     58        .         47    |     69        .         .
     .         .         .     |     .      12346789     .     |     .         .         .

5 @ c5 locked @ r4678c5

r2c6+r8c46=[584|957] => exactly one of r2c6+r8c4 must be 5

Grouped turbot fish:
n8: either r78c5 or r8c4 must not be 5 => either r46c5 or r2c6 must be 5 => r5c6 can't be 5

=> r5c456=[768|867]

The rest is trivial stuff.
Walkthrough by Afmob:
Finally a long walkthrough :cheesey: because my present wts kept getting shorter and shorter. But this difficult Killer deserves a long walkthrough.

Like the other guys I started with setting up the ring and then worked on N5 but after that I took a different path which is longer but I think technically easier: Hidden Killer Pairs in D/ and Outies of D/ to fix 10(2) in N3.

I also used many chains so my walkthrough might deserve a 2.0 rating but those chains were established between 2-valued cells or cages with 2 combos so you kinda get drawn to them.

Human Solvable 1 (HS 1) Walkthrough:

1. N39
a) Innies N3 = 10(2) = {37} locked
b) Outies N3 = 14(2) = {59} -> CPE: R2C8+R4C6 <> 5,9
c) Innies N9 = 15(2) <> 4,5
d) Outies N9 = 11(2) <> 8,9

2. R58+N5
a) Innies R5 = 21(3) <> 1,2,3; R5C46 <> 4 because R5C5 <> 8,9
b) 10(3) @ N5: R4C6+R6C4 <> 6,7 because R5C5 >= 4
c) Killer pair (58) of 14(2) blocks {58} of 13(2)
d) Killer pair (69) locked in 14(2)+13(2) for R8

3. N1+R2+C2
a) Killer pair (58) of 14(2) blocks {58} of 13(2) @ C2
b) Killer pair (69) locked in 13(2) + 14(2) for C2
c) 7(2): R2C1 <> 1
d) Innies N1 = 13(2) <> 5,8
e) 13(2) @ R2 <> 5,8
f) Killer pair (79) locked in 13(2) + 12(2) for R2

4. C789 !
a) Innies N9 = 15(2): R7C8 <> 7
b) ! Innies+Outies N39: R28C7 = R46C8 -> R6C8 <> 5 since R28C7 cannot be 14(2)
c) 13(2) @ C8 <> 8
d) Innies N9 = 15(2) = {69} locked for N9
e) Outies N9 = 11(2) = {47} -> CPE: R6C6+R8C8 <> 4,7
f) Killer pair (79) locked in 12(2) + 13(2) for C8
g) 10(2) = {28/46}

5. R789 !
a) ! Innies+Outies N79: -2 = R8C46 - R7C28 -> R7C2 <> 6,9 because:
- R8C46 = 13(2) clashes with 13(2) @ R8
b) 14(2) @ R6C2: R6C2 <> 5,8
c) Outies N9 = 14(2): R8C4 <> 6,9
d) 14(2) @ R8: R8C3 <> 5,8

6. N5
a) 17(3) <> 1 because 7 in R5C5 forces 10(3) = {127}
b) 17(3) <> 3 because {359} forces Innies R5 = {579} and {368} forces Innies R5 = {678}
with 5/6 in R5C5
c) 17(3) <> {278} since 7 in R5C5 forces 10(3) = {127} -> 17(3) = {269/458/467}
d) 17(3): R4C4+R6C6 <> 5 because 4 of {458} would be in R5C5 which forces 10(3) = {145}
e) 10(3): R4C6+R6C4 <> 4 because 5 of {145} would be in R5C5 which forces 17(3) = {458}
f) 17(3): R4C4 <> 8 because R6C6 <> 4,5
g) 17(3): R4C4 <> 6 because R5C5 <> 2,9 and R6C6 <> 4,7

7. R123 !
a) Innies+Outies N13: 2 = R2C46 - R3C28 -> R2C3 <> 6 because
- R2C3 = 6 forces R2C46 = [79] -> not possible since R3C28 cannot be 14(2)
b) ! Innies+Outies N13: 2 = R46 - R3C28 -> R2C3 <> 9 because
- R2C3 = 9 forces R2C46 = [45] = 9(2) so that R3C28 = 7(2) = [43]
-> not possible since R4C2 = R4C8 = 9
c) 13(2) @ R2: R2C4 <> 4,7
d) Innies N1 = 13(2): R3C2 <> 4,7
e) 13(2) @ C2: R4C2 <> 6,9
f) 9 locked in R2C46 @ R2 for N2
g) 17(3) <> 1

8. R456 !
a) 13(2)+14(2) @ C2 = [6795/9468] -> R46C2 = [46/79]
b) ! 17(3): R5C5 <> 4 because R4C4+R6C6 = [76] is blocked by Killer pair (67) of R46C2
c) Innies R5 = 21(3) = 7{59/68} -> 7 locked for R5+N5
d) 10(3) @ N5 must have 5,6 xor 7 and R5C5 = (567) -> R6C4 <> 5
e) 14(3) <> 6 because {356} blocked by Killer pair (35) of 10(2) @ N6
f) ! 14(3) <> 1,5 because {149} blocked by Killer pair (49) of R46C2 and
{158} blocked by Killer pair (58) of Innies R5
-> 14(3) = 2{39/48} -> 2 locked for R5+N4
g) 10(3) @ N6 = 1{36/45} -> 1 locked for N6
h) Killer pair (49) locked in 14(3) + R46C2 for N4
i) ! Consider combos of 10(3) @ N6 -> R4C45 <> 9: (Grouped XY-Wing)
- i) 10(3) = {136} -> Innies R5 = {579} -> R4C45 <> 9
- ii) 10(3) = {145} -> R4C8 = 9 -> R4C45 <> 9
j) 9 locked in R4C789 for N6
k) 17(3): R6C6 <> 2 because R4C4 = (24)

9. N5+R28C28 !
a) Possible placements of 2-cell cages in R28C28 (R2-C8-R8-C2):
[4957]-[3976]-[6849]-[9468] / [7693]-[7549]-[9576]-[6795]
b) ! 17(3) <> 5,8 because [458] forces Innies R5 = {579} but at the same time
R4C2 = 7 -> so R28C6 = [97] (step 9a) -> Innies R5 not placeable
c) 17(3) = 6{29/47} -> 6 locked for N5+D\
d) 10(3) = 1{27/36} -> 1 locked for N5+D/

10. R6+N8
a) Naked pair (69) locked in R6C26 for R6
b) 9 locked R79C5 for N8

11. D/ !
a) 25(5) @ N7 = 37{159/168/249} since other combos blocked by 6(2)
b) 25(5) @ N3 can only have one of (48) because it's a Killer pair of 10(2)
c) ! Hidden Killer pair (48) in both 25(5) for D/ since neither of them can have both
-> 25(5) @ N7 = 37{168/249}
d) 5 locked in R1C9+R2C8+R3C7 @ D/ for N3
e) Both 25(5) must have (48) @ D/ -> R1C7+R3C9+R7C1+R9C7 <> 4,8
f) Hidden Killer pair (37) in R7C3+R8C2+R9C1 for D/ since 10(3) can only have one of (37)
-> R7C1+R9C3 must have one of (37) since 25(5) @ N7 has 3 and 7
g) Outies D/ = 15(2+2): 1 locked in R1C7+R3C9 @ N3 = 1{2/6/9}
-> R7C1+R9C3 = 5/8/12(2) = {23/17/39} <> 6
h) 25(5) @ N7: R7C3+R8C2+R9C1 = {247/368/479}
-> 6 in D/ must be in 10(3) or 25(5) @ N7 -> R1C9+R2C8+R3C7 <> 6
i) ! Using step 9a) R2C3+R6C8 = 11(2) = {47} -> CPE: R2C8 <> 4 and R6C3 <> 7

12. N3+N7+D/
a) 10(2) = {46} locked for N3 because R2C8 = (28) blocks {28}
b) 25(5) @ N3 = {12589} -> 8 locked for D/
c) Hidden Single: R7C2 = 8 @ N7 -> Now using step 9a:
d) R6C2 = 6, R4C2 = 4, R3C2 = 9, R2C3 = 4, R2C4 = 9, R2C6 = 5, R2C7 = 7, R3C8 = 3,
R4C8 = 9, R6C8 = 7, R7C8 = 6, R8C7 = 9, R8C6 = 4, R8C4 = 8, R8C3 = 6

13. N58
a) 17(3) = [269] -> R4C4 = 2, R5C5 = 6, R6C6 = 9
b) Innies R5 = 21(3) = {678} -> R5C4 = 7, R5C6 = 8
c) 10(3) = {136} locked for N5+D/
d) R4C5 = 5 -> R23C5 = 8(2) = [17] -> R2C5 = 1, R3C5 = 7
e) 15(3) = {249} -> R6C5 = 4, R7C5 = 9, R8C5 = 2
f) 16(3) = {367} -> R9C5 = 3, R9C4 = 6, R9C6 = 7

14. N9
a) Hidden Single: R8C9 = 3 @ R8 -> R9C8 = 2
b) R2C9 = 6, R4C9 = 8
c) 25(5) = {14578} -> R7C9 = 7, R9C7 = 8; {145} locked for D\

15. Rest is singles without considering diagonals.

Rating: 1.75. I used lots of chains and some Hidden Killer pairs.
udosuk's easier breakthrough, after studying Afmob's step 11:
My holiness, after studying Afmob's step 11 I realise there is a easy way to solve this puzzle. No fish, no analysis on big cages, only elegant logic. Can't believe I missed it earlier! :rambo:
After easy moves to set up the ring and n5 (using innies @ r5 & 10/3 @ /456):
Code:
     .         .         .     |     .         .         .     |     .         .         .
     .         .         47    |     69        .         59    |     37        .         .
     .         69        .     |     .         .         .     |     .         37        .
-------------------------------+-------------------------------+-------------------------------
     .         47        .     | 123456789     .        1234   |     .         59        .
     .         .         .     |   56789      4567     56789   |     .         .         .
     .         69        .     |   12345       .      1235689  |     .         47        .
-------------------------------+-------------------------------+-------------------------------
     .         58        .     |     .         .         .     |     .         69        .
     .         .         69    |     58        .         47    |     69        .         .
     .         .         .     |     .         .         .     |     .         .         .

Innies @ r5: r5c456 = 21 = {489|579|678}
10/3 @ /456 = {127|136|145|235}

=> 17/3 @ \456 = [746|458|269|962|476]

r2c3467 = [ 4957 | 7693 ]
r3467c2 = [ 9468 | 6795 ]
r3467c8 = [ 3976 | 7549 ]
r8c3467 = [ 6849 | 9576 ]

r46c2=[46|79] => \456 can't be [746]
r28c6+r4c2=[544|977] => r4c4+r5c456 can't be [4759|4957] => \456 can't be [458]

=> 17/3 @ \456 = [269|962|476] with 6 @ n5,d\ locked
=> 10/3 @ /456 = {127|136} with 1 @ n5,d/ locked

{79} @ r2 locked @ r2c3467, {79} @ c8 locked @ r3467c8
=> 10/2 @ r1c8+r2c9 = {28|46}
Code:
     .         .         .     |     .         .         .     |     .        2468       .
     .         .        *47    |    #69        .         59    |     37      -2468      2468
     .         69        .     |     .         .         .     |     .         37        .
-------------------------------+-------------------------------+-------------------------------
     .         47        .     |    249        .        123    |     .         59        .
     .         .         .     |    5789       67       5789   |     .         .         .
     .         69        .     |    123        .        269    |     .        *47        .
-------------------------------+-------------------------------+-------------------------------
     .         58        .     |     .         .         .     |     .        #69        .
     .         .         69    |     58        .         47    |     69        .         .
     .         .         .     |     .         .         .     |     .         .         .

r2c3+r6c8 = [47|74] => r2c8+r6c3 can't have {47} (pointing pair)
r2c4+r7c8 = [96|69] => r2c8+r7c4 can't have {69} (pointing pair)

r2c8 from {28} => 10/2 @ r1c8+r2c9 = {46} (NP @ n3)
4 @ n7,d/ locked @ /789 => 6/2 @ r8c1+r9c2 = {15} (NP @ n7)

The rest is trivial stuff.

Kudos to Afmob for spotting the breakthrough point. :ugeek:
Walkthrough by Andrew (in 2012):
I tried Human Solvable 1 for the first time a few days ago and managed to finish it a couple of days later. Thanks HATMAN for a challenging puzzle!

I enjoyed some of the steps]in the other walkthroughs, breakthroughs and outlines. This puzzle required a lot of chains, either written as such or written as permutation analysis; they even seem necessary to reduce the upper-left corner of the R28C28 "ring" to pairs of combinations. After working through how others solved this puzzle, I've realised that I didn't get enough out of the "ring"; particularly the use of chains in that "ring" to reduce the 17(3) and 10(3) cages in N5 to two combinations each. I think Para must also have used that "ring" for his step 2; it's a pity that Para is no longer active on this site so I can't ask him.

My solving path was more like Afmob's than the other ones.

Prelims

a) 7(2) cage at R1C2 = {16/25/34}, no 7,8,9
b) 10(2) cage at R1C8 = {19/28/37/46}, no 5
c) R2C34 = {49/58/67}, no 1,2,3
d) R2C67 = {39/48/57}, no 1,2,6
e) R34C2 = {49/58/67}, no 1,2,3
f) R34C8 = {39/48/57}, no 1,2,6
g) R67C2 = {59/68}
h) R67C8 = {49/58/67}, no 1,2,3
i) 6(2) cage at R8C1 = {15/24}
j) R8C34 = {59/68}
k) R8C67 = {49/58/67}, no 1,2,3
l) 5(2) cage at R8C9 = {14/23}
m) 10(3) cage at R4C6 = {127/136/145/235}, no 8,9
n) 10(3) cage at R5C7 = {127/136/145/235}, no 8,9

1. R34C2 = {49/67} (cannot be {58} which clashes with R67C2), no 5,8
1a. Killer pair 6,9 in R34C2 and R67C2, locked for C2, clean-up: no 1 in R2C1

2. R8C67 = {49/67} (cannot be {58} which clashes with R8C34), no 5,8
2a. Killer pair 6,9 in R8C34 and R8C67, locked for R8

3. 45 rule on N1 2 innies R2C3 + R3C2 = 13 = {49/67}, no 5,8 in R2C3, clean-up: no 5,8 in R2C4

4. 45 rule on N3 2 innies R2C7 + R3C8 = 10 = {37} (only remaining combination), locked for N3, clean-up: R2C6 = {59}, R4C8 = {59}
4a. 45 rule on N3 2 outies R2C6 + R4C8 = 14 = {59}, CPE no 5,9 in R2C8 + R4C6
4b. Killer pair 7,9 in R2C34 and R2C67, locked for R2, clean-up: no 1 in R1C8

5. 45 rule on N9 2 innies R7C8 + R8C7 = 15 = [69/87/96], R7C8 = {689}, R8C7 = {679}, clean-up: R6C2 = {457}, R8C6 = {467}

6. 45 rule on N7 2 innies R7C2 = R8C3 = 14 = {59/68}
[This is currently just for use with the next step.]

7. Chaining round the R28C28 ring of 2-cell cages, using innies for N1, N3 and N7
R2C34 = {49} => R34C2 (step 3) = {49} => R67C2 = {68} => R8C34 (step 6) = {68} => R8C67 = [49], R67C8 (step 5) = [76]
or R2C34 = {67} => R2C67 = [93] => R34C8 = [75] => R67C8 not [58], R34C2 (step 3) = {67} => R67C2 = {59} => R8C34 (step 6) = {59} => R8C67 = {67} => R67C8 not [76] => R67C8 = [49]
-> R67C8 = [49/76], no 5,8, clean-up: no 7 in R8C7 (step 5), no 6 in R8C6
Also from the chains, no 7 in R3C2, no 6 in R4C2, no 6 in R2C3 (step 3), no 7 in R2C4, no 6,9 in R7C2, no 5,8 in R6C2, no 5,8 in R8C3 (step 6), no 6,9 in R8C4
7a. Naked pair {69} in R7C8 + R8C7, locked for N9
7b. Killer pair 7,9 in R34C8 and R67C8, locked for C8, clean-up: no 1 in R2C9
7c. 45 rule on N9 2 outies R6C8 + R8C6 = 11 = {47}, CPE no 4,7 in R6C6 + R8C8

8. 45 rule on R5 3 innies R5C456 = 21 = {489/579/678}, no 1,2,3
8a. 4 of {489} must be in R5C5 -> no 4 in R5C46

9. 10(3) cage at R4C6 = {127/136/145/235}
9a. 6,7 of {127/136} must be in R5C5 -> no 6,7 in R4C6 + R6C4

10. 17(3) cage at R4C1 = {269/458/467} (cannot be {179/278} which clash with 10(3) cage at R4C6 because of the shared 7 in R5C5, cannot be {368} which clashes with 10(3) cage because of the shared 6 in R5C5, cannot be {359} which clashes with R5C456 because of the shared 5 in R5C5), no 1,3
10a. 5 of {458} must be in R5C5 (cannot be [548/845] which clash with R5C456 because of shared 4 in R5C5), no 5 in R4C4 + R6C6
10b. 8 of {458} must be in R6C6 -> no 8 in R4C4
10c. 6 of {269) must be in R5C5, 6 of {467} must be in R6C6 -> no 6 in R4C4
10d. 6 of {467} must be in R6C6 => R6C2 = 9, R34C2 = [67] => {467} can only be [476]
10e. 17(3) cage = {269/458/467} = [269/458/476/962] -> R4C4 = {249}, R5C5 = {567}

11. R5C456 (step 8) = {579/678}, 7 locked for R5 and N5
11a. 6 of {678} must be in R5C5 (cannot be [678/876] which clashes with 17(3) cage at R4C4 because of shared 7 in R5C5), no 6 in R5C46
11b. 10(3) cage at R5C7 = {136/145/235}
11c. Killer pair 5,6 in R5C456 and 10(3) cage at R5C7, locked for R5

12. 10(3) cage at R4C6 = {127/136/235} (cannot be {145} which clashes with 17(3) cage at R4C4 because of shared 5 in R5C5), no 4 in R4C6 + R6C4
12a. R5C5 = {567} -> no 5 in R6C4

13. R34C2 = {49}/[67], R67C2 = [68/95] -> combined cage R3467C2 = {49}[68]/[67][96] -> R46C2 = [46/79/96]
13a. 14(3) cage at R4C1 = {239/248} (cannot be {149} which clashes with R46C2), no 1, 2 locked for R5 and N4
13b. Killer pair 4,9 in R46C2 and 14(3) cage, locked for N4

14. 1 in R5 only in 10(3) cage at R5C7, locked for N6
14a. 10(3) cage (step 11b) = {136/145}

[Looking a bit more at interactions between cages in N5]
15. Consider permutations for 17(3) cage at R4C1 (step 10e) = {269/458/467} = [269/458/476/962]
17(3) cage = [269/962]
or 17(3) cage = [458] => 10(3) cage at R4C6 = {235}, R5C456 = {579}
or 17(3) cage = [476] => 10(3) cage at R4C6 = {127}, R5C456 = {579}
-> killer pair 2,9 in 17(3) cage, 10(3) cage and R5C456, locked for N5

16. Consider combinations for 14(3) cage at R5C1 (step 13a) = {239/248}
14(3) cage = {239}, locked for N4 => R6C2 = 6, R34C2 = [94], R2C3 = 4, R2C4 = 9
or 14(3) cage = {248}, locked for R5 => R5C456 = {579}, locked for N5 => 17(3) cage at R4C4 (step 10e) = [458/476]
-> no 9 in R4C4
16a. 4 must be in R4C2 or R4C4, locked for R4, CPE no 4 in R2C2 using D\
16b. 17(3) cage at R4C1 (step 10e) = {269/458/467} = [269/458/476], no 2 in R6C6

17. Consider combinations for 14(3) cage at R5C1 (step 13a) = {239/248}
14(3) cage = {239}, 9 locked for N4
or 14(3) cage = {248}, locked for R5 => R5C456 = {579} => 17(3) cage at R4C1 (step 10e) = [458/476] => R4C4 = 4 => R2C4 = 6 (cannot be {49} because R4C4 “sees” both of R2C4 + R4C2), R2C3 = 7, R3C2 = 6, R6C2 = 9
-> 9 must be in 14(3) cage or R6C2, locked for N4, clean-up: no 4 in R3C2, no 9 in R2C3, no 4 in R2C4
17a. 9 in R4 only in R4C789, locked for 6

18. 9 in R2 only in R2C46, locked for N2
18a. 17(3) cage at R1C4 = {278/368/458/467}, no 1
18b. 9 in C5 only in R79C5, locked for N8

19. Consider combinations for 14(3) cage at R5C1 (step 13a) = {239/248}
14(3) cage = {239} => 4 in R5 must be in 10(3) cage at R5C7
or 14(3) cage = {248}, locked for N4 => R34C2 = [67], R67C2 = [95], R8C3 = 9, R8C7 = 6, R7C8 = 9, R6C8 = 4
-> 4 must be in 10(3) cage at R5C7 or R6C8, locked for N6

20. R1C2 + R2C1 = [16/25/34/52] (cannot be [43] which clashes with R2C37), no 4 in R1C2, no 3 in R2C1

21. Hidden killer pair 4,8 in R1C9 + R2C8 + R3C7 and R7C3 + R8C2 + R9C1 for D/, R1C9 + R2C8 + R3C7 cannot contain both of {48} (which would clash with 10(2) cage at R1C8), R7C3 + R8C2 + R9C1 cannot contain both of {48} (which would clash with R7C2 + 6(2) cage at R8C1, killer ALS block) -> R1C9 + R2C8 + R3C7 and R7C3 + R8C2 + R9C1 must each contain one of 4,8
21a. Killer pair 4,8 in 10(2) cage at R1C8 and R1C9 + R2C8 + R3C7, locked for N3
21b. Killer pair 4,8 in R7C3 + R8C2 + R9C1, R7C2 and 6(2) cage at R8C1, locked for N7
21c. Hidden killer pair 4,8 in R7C2 + 6(2) cage and R7C3 + R8C2 + R9C2 for N7 -> R7C2 + 6(2) cage must contain one of 4,8 = 5{24}/8{15}, 5 locked for N7
[Although I spotted this hidden killer pair, I missed that there is another hidden killer pair 3,7 on D/. 10(3) cage at R4C6 must contain one of 3,7 -> R7C3 + R8C2 + R9C1 must contain one of 3,7 -> R7C1 + R9C3 must contain one of 3,7.
I’d spotted 4(2+2) outies R1C7 + R3C9 + R7C1 + R9C3 = 15 but couldn’t see how to use this. Maybe the fact that R7C1 + R9C3 must contain one of 3,7, but 4(2+2) outies don’t contain 4,8 might make these outies useful, or it might require a bit more; Afmob also had 1 for N3 only in R1C7 + R3C9.]


22. 13(3) cage at R2C5 = {148/157/238/247/256/346}
22a. 45 rule on C5 3 innies R159C5 = 17 = {269/278/359/368/467} (cannot be {179} because 1,9 only in R9C5, cannot be {458} which clashes with 13(3) cage), no 1
22b. 5 of {359} must be in R5C5 -> no 5 in R19C5
22c. 13(3) cage = {148/157/238/247/346} (cannot be {256} which clashes with R159C5)

23. From analysis of the cages in N5, R46C5 = {16/38}/[54], no 5 in R6C5

24. 9 in C5 only in R159C5 (step 22a) = {269/359} or in 15(3) cage at R6C5 = {159/249} -> 15(3) cage = {159/168/249/258/267/348/357} (cannot be {456} which clashes with R159C5 = {159/249}, locking out cages)
24a. R46C5 (step 23) = {16/38}/[54]
Consider combinations for R46C5
R46C5 = {38} => 15(3) cage cannot be {348} which clashes with R46C5, CCC
or R46C5 = [54] => R6C8 = 7, R7C8 = 6, R8C7 = 9, R8C3 = 6, R8C4 = 8 => 15(3) cage cannot be {348}
-> 15(3) cage = {159/168/249/258/267/357} (cannot be {348})
24b. Consider combinations for R46C5
R46C5 = {38}, locked for N5 => R4C6 + R6C4 = {12} => R5C5 = 7 (cage total) => 17(3) cage at R4C4 (step 10e) = [476] => R4C2 = 7, R3C2 = 6, R6C2 = 9, R7C2 = 5, R8C3 = 9, R8C4 = 5 => 15(3) cage cannot be {258/357}
or R46C5 = [54] => 15(3) cage cannot be {258/357}
-> 15(3) cage = {159/168/249/267} (cannot be {258/357}, no 3, clean-up: no 8 in R4C5 (step 23)
24c. Consider combinations for R46C5
R46C5 = {16}, locked for N5 => R4C6 + R6C4 = {23} => R5C5 = 5 (cage sum) => 15(3) cage cannot be {159}
or R46C5 = [54] -> 15(3) cage cannot be {159}
-> 15(3) cage = {168/249/267} (cannot be {159}), no 5

25. 15(3) cage at R6C5 (step 24c) = {168/249/267}
25a. R159C5 (step 22a) = {359/368} (cannot be {269/278/467} which clash with 15(3) cage), no 2,4,7, 3 locked for C5, clean-up: no 8 in R6C5 (step 23)

26. R46C5 (step 23) = {16}/[54], R5C5 = {56}, killer pair 5,6 locked for C5 and N5

27. 3 in N5 only in 10(3) cage at R4C6, locked for D/

28. 15(3) cage at R6C5 (step 24c) = {249/267} (cannot be {168} which clashes with R46C5 = {16}, CCC), no 1,8, 2 locked for C5 and N8, clean-up: no 6 in R4C5 (step 26)
28a. R6C5 = {46} -> no 4 in R78C5

29. 14(2) cage at R8C3 + 13(2) cage at R8C6 = 27, R8C37 = {69} = 15 -> R8C46 = 12 = [57/84]
29a. 16(3) cage at R9C4 = {169/349/367} (cannot be {178} which clashes with R8C46, cannot be {358} which clashes with R8C4, cannot be {457} which clashes with R8C6), no 5,8

[And suddenly it crumbles …]
30. Killer pair 7,9 in R78C5 and 16(3) cage at R9C4, locked for N8 -> R8C6 = 4, R8C7 = 9, R7C8 = 6, R6C8 = 7, R3C8 = 3, R4C8 = 9, R2C7 = 7, R2C6 = 5, R2C3 = 4, R2C4 = 9, R3C2 = 9 (step 3), R4C2 = 4, R6C2 = 6, R7C2 = 8, R8C3 = 6, R8C4 = 8, R4C4 = 2, placed for D\, R5C4 = 7, R6C5 = 4, clean-up: no 2,3 in R1C2, no 2 in 6(2) cage at R8C1, no 2 in R8C9, no 1 in R9C8
30a. Naked pair {13} in R4C6 + R6C4, locked for N5 and D/ -> R5C5 = 6 (cage sum), placed for both diagonals, R4C5 = 5
30b. Naked pair {15} in 6(2) cage at R8C1, locked for N7

31. R9C1 = 4 (hidden single in N7), placed for D/

32. R1C8 = 4 (hidden single in N3), R2C9 = 6, R2C1 = 2, R1C2 = 5, R2C8 = 8, R2C5 = 1, R3C5 = 7 (cage sum), R2C2 = 3, placed for D\, R78C5 = [92], R9C5 = 3, R1C5 = 8, R9C2 = 1, R8C1 = 5, R8C8 = 1, placed for D\, R3C3 = 8, placed for D\, R6C6 = 9

and the rest is naked singles, without using the diagonals.

Rating Comment.
Afmob wrote:
Rating: 1.75. I used lots of chains and some Hidden Killer pairs.
That comment also applies to my solving path. I don't think my steps were any harder than Afmob's ones so I'll also rate my walkthrough at 1.75.


Last edited by Andrew on Mon Jun 04, 2012 10:47 pm, edited 3 times in total.

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