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PostPosted: Wed Jun 15, 2011 4:06 am 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Messy One #5 by Nasenbaer (August 2008) here
Puzzle Diagram:
Image
Images with "udosuk style Killer Cages" by Børge:
Image     Image
Code: Select, Copy & Paste into solver:
3x3::k:3328:3328:3074:2307:2307:6917:6917:6917:6917:3328:3074:3074:7180:7180:2318:3599:6917:6917:5394:5394:3604:3604:7180:2318:3599:3097:3097:3611:5394:3604:4382:7180:2848:2848:5154:3097:3611:2597:4382:4382:3368:3368:2848:5154:3097:6189:2597:3887:3376:3376:3368:4659:5154:7733:6189:2597:3887:3887:3887:4659:4659:7733:7733:6189:3136:3136:3136:7491:1860:1860:3398:7733:6189:6189:6189:7491:7491:7491:1860:3398:7733:
Solution:
+-------+-------+-------+
| 1 9 4 | 6 3 5 | 7 2 8 |
| 3 2 6 | 9 7 8 | 5 1 4 |
| 7 8 5 | 2 4 1 | 9 6 3 |
+-------+-------+-------+
| 5 6 7 | 4 8 2 | 3 9 1 |
| 9 4 8 | 5 1 3 | 6 7 2 |
| 2 1 3 | 7 6 9 | 8 4 5 |
+-------+-------+-------+
| 8 5 9 | 1 2 6 | 4 3 7 |
| 6 7 2 | 3 5 4 | 1 8 9 |
| 4 3 1 | 8 9 7 | 2 5 6 |
+-------+-------+-------+
Quote:
Nasenbaer: So, here's my donation for Messy One round 2. :cheesey: Actually it's Messy One #5v6 ;) . Tuning it for the right rating (and removing a uniqueness problem I overlooked :brickwall: ) took a lot of time. I think it's really messy, and the rating now is 1.02 although for me it feels more like a 0.75. There is also a nice shortcut (which isn't found by SSolver).
Have fun!

Afmob: Thanks for this fun Killer, Nasenbaer! I guess I didn't found the shortcut since SudokuSolver's path is not much different from mine though certainly longer. :cheesey:
Rating: 0.75 - (Hard) 0.75.

Jean-Christophe: I went the same way as Afmob. But after solving, I found this:
Hidden Text:
Innies @ r12 -> r2c4..7 = 29 = {5789} (NQ @ r2)

Nasenbaer: Actually I was thinking about this:
Hidden Text:
Outies of n7 = h(3+4) = 16 -> r5c2 r6c123 = {1234} and r7c45 r8c4 = {123}
Not an obvious move, but since I knew what to look for... :whistle:

Andrew: Thanks Nasenbaer for a fun puzzle. I think this was the easiest Messy One so far.
I was amazed when I went through Afmob's walkthrough to find that I hadn't used his first move. I'm not sure how I missed that one. Maybe it's because of the format I use on my Excel worksheet with coloured cages. However when I now look at my worksheet it's obvious. As a result my walkthrough is very different but probably not significantly slower or harder.
I also missed the shortcuts posted by J-C and Nasenbaer; I feel I ought to have seen J-C's one. Nasenbaer's is one that I think is much easier for the puzzle creator to see than for solvers to spot.
I'll rate my walkthrough at Hard 0.75 because a few of my steps are slightly harder than a normal 0.75.

azpaull: I think my breakthrough - and first placement - finally came from analyzing the
Hidden Text:
outies on Nonet 9, and that helped me work Column 7.
(Sorry, I'll have to work on my walk-thru skills - I have a tendency to do these puzzles in little bits and pieces in various places, instead of sitting at a computer or with a second sheet of paper.)

I'll give it a 1.0.

(P.S. I know I probably didn't need to use *hide", but I never have had the chance to use it, and I wanted the practice. :) )

Walkthrough by Afmob:
Thanks for this fun Killer, Nasenbaer! I guess I didn't found the shortcut since SudokuSolver's path is not much different from mine though certainly longer. :cheesey:

Messy One #5 Walkthrough:

1. C6789
a) Outies C89 = 12(2) <> 1,2,6
b) Outies N3 = 8(2+1) <> 7,8,9; R45C9 <> 5,6 because R1C6 >= 3
c) Killer pair (56) locked in 14(2) + 12(4) for N3
d) Outies C89 = 12(2): R1C7 <> 3,4
e) 7 locked in 27(6) @ N3 = 1257{39/48} -> 1,2 locked for N3
f) 12(4) = 12{36/45} -> R45C9 = {12} locked for C9+N6
g) Outies N3 = 8(3+1): R1C6 = 5 since R45C9 = {12}
h) Outies C89 = R1C7 = 7

2. C456
a) Hidden triple (123) in R157C5 for C5 -> R157C5 = {123}
b) 9(2) @ R1 = [63/81]
c) 28(4) = {4789} since {5689} blocked by R1C4 = (68)
d) Hidden Single: R6C5 = 6 @ C5 -> R6C4 = 7
e) 28(4) = {4789} -> 7 locked for C5+N2
f) 9(2) @ C6 = {18/36}
g) Naked quad (1368) locked in both 9(2) for N2
h) 28(4) = {4789} -> R4C5 = 8 and 4 locked for N2
i) 29(4) = {5789} -> R9C6 = 7, R9C4 = 8; {59} locked for C5+N8
j) R1C4 = 6 -> R1C5 = 3
k) 13(3) = {139} -> R5C5 = 1, {39} locked for C6+N5

3. N245
a) 17(3) = {458} because R45C4 = (245) -> R5C3 = 8; 4 locked for C4+N5
b) R2C4 = 9, R3C4 = 2
c) 14(3) = 2{39/57}
d) 14(2) = {59} locked for C1+N4
e) 21(3) = 8{49/67} since (59) only possible @ R3C2 -> 8 locked for R3+N1

4. R123
a) R3C6 = 1, R2C6 = 8
b) 14(2) = {59} -> R2C7 = 5, R3C7 = 9
c) 12(4) = {1236} -> R5C9 = 2, R4C9 = 1, {36} locked for R3+N3
d) 21(3) = {678} -> R4C2 = 6, {78} locked for R3+N1
e) R3C3 = 5 -> R4C3 = 7

5. N178
a) 10(3) = 5{14/23} because R5C2 = (34) -> R7C2 = 5; R6C2 <> 3,4
b) 24(6) = {123468} -> 6,8 locked for N7 and 8 also locked for C1
c) Hidden Single: R8C2 = 7 @ N7
d) 12(3) = 7[23/41]
e) Hidden Single: R7C6 = 6 @ N8
f) 18(3) = {468} -> 4,8 locked for C7
g) Hidden Single: R1C2 = 9 @ C2
h) 13(3) = {139} -> R1C1 = 1, R2C1 = 3

6. N9
a) 13(2) = [49/85/94]

7. Rest is singles.

Rating: 0.75 - (Hard) 0.75.
Walkthrough by Andrew:
Thanks Nasenbaer for a fun puzzle. I think this was the easiest Messy One so far.

I was amazed when I went through Afmob's walkthrough to find that I hadn't used his first move. I'm not sure how I missed that one. Maybe it's because of the format I use on my Excel worksheet with coloured cages. However when I now look at my worksheet it's obvious. As a result my walkthrough is very different but probably not significantly slower or harder.

I also missed the shortcuts posted by J-C and Nasenbaer; I feel I ought to have seen J-C's one. Nasenbaer's is one that I think is much easier for the puzzle creator to see than for solvers to spot.

I'll rate my walkthrough at Hard 0.75 because a few of my steps are slightly harder than a normal 0.75. I originally used combined cage R2367C7 to lock 8 for C7 but that didn't help much and would have pushed my rating up to at least Easy 1.0 so I removed it.

Here is my walkthrough, a short one for me.

Prelims

a) R1C56 = {18/27/36/45}, no 9
b) R23C6 = {18/27/36/45}, no 9
c) R23C7 = {59/68}
d) R45C1 = {59/68}
e) R6C45 = {49/58/67}, no 1,2,3
f) R89C8 = {49/58/67}, no 1,2,3
g) 21(3) cage at R3C1 = {489/579/678}, no 1,2,3
h) 11(3) cage at R4C6 = {128/137/146/236/245}, no 9
i) R456C8 = {389/479/569/578}, no 1,2
j) R567C2 = {127/136/145/235}, no 8,9
k) 7(3) cage at R8C6 = {124}, CPE no 1,2,4 in R8C89, clean-up: no 9 in R9C8
l) 28(4) cage at R2C4 = {4789/5689}, no 1,2,3, CPE no 8 in R1C5, clean-up: no 1 in R1C4
m) 12(4) cage at R3C8 = {1236/1245}, no 7,8,9, CPE no 1,2 in R12C9
n) 29(4) cage in N8 = {5789}, locked for N8

1. 45 rule on C6789 1 innie R9C6 = 1 outie R5C5 + 6 -> R5C5 = {123}, no 5 in R9C6

2. 45 rule on N1 1 outie R4C2 = 1 innie R3C3 + 1, no 1,2,9 in R3C3

3. 45 rule on C123 4 outies R3C4 + R7C45 + R8C4 = 1 innie R5C3
3a. Min R3C4 + R7C45 + R8C4 = 7 -> min R5C3 = 7
3b. Min R7C45 + R8C4 = 6 -> max R3C4 = 3
3c. Max R7C45 + R8C4 = 8 = {123/124/134}, no 6, 1 locked in R7C45 + R8C4, locked for N8
3d. R7C6 = 6 (hidden single in N8), clean-up: no 3 in R23C6
3e. R7C6 = 6 -> R67C7 = 12 = {39/48/57}, no 1,2
3f. 1 in 7(3) cage at R8C6 locked in R89C7, locked for C7 and N9
3g. Min R45C7 = 5 -> no 7,8 in R4C6

4. 45 rule on N9 3 remaining outies R6C79 + R8C6 = 17, max R8C6 = 4 -> min R6C79 = 13, no 1,2,3, clean-up: no 9 in R7C7 (step 3e)
4a. 1 in N6 locked in R45C9, locked for 12(4) cage at R3C8, no 1 in R3C89

5. 1 in N3 locked in R12C8, locked for 27(6) cage, no 1 in R1C6
5a. 45 rule on C8 4 innies R1237C8 = {1236/1245}, no 7,8,9

6. 45 rule on N3 3 outies R1C6 + R45C9 = 8
6a. Min R45C9 = 3 -> max R1C6 = 5
6b. Min R1C6 = 2 -> max R45C9 = 6, no 6

7. 45 rule on C789 3 remaining outies R148C6 = 11 = {245} (only remaining combination), locked for C6, clean-up: no 7 in R23C6
7a. Naked pair {18} in R23C6, locked for C6 and N2

8. 3 in C6 locked in R56C6 for N5
8a. 13(3) cage in N5 = {139} (only remaining combination) -> R5C5 = 1, R56C6 = {39}, locked for C6 and N5 -> R9C6 = 7, clean-up: no 4 in R6C45, no 6 in R8C8
8b. R4C9 = 1 (hidden single in C9)

9. R4C5 = 8 (hidden single in 28(4) cage at R2C4), clean-up: no 6 in R5C1, no 5 in R6C45
9a. R9C4 = 8 (hidden single in C4), clean-up: no 5 in R8C8
9b. Naked pair {59} in R89C5, locked for C5, clean-up: no 4 in R1C4
9c. R2C4 = 9 (hidden single in C4), clean-up: no 5 in R3C7
9d. 28(4) cage at R2C4 = {4789} (only remaining combination) -> R23C5 = {47}, locked for C5 and N2 -> R6C45 = [76], clean-up: no 2,5 in R1C4, no 2 in R1C5, no 5 in R7C7 (step 3e)
9e. R1C45 = [63], R3C4 = 2, R1C6 = 5, R7C5 = 2, R8C6 = 4, R4C6 = 2
9f. R5C9 = 2 (hidden single in 142(4) cage at R3C8), R3C89 = {36/45}

10. R3C4 = 2, R78C4 = {13} = 4, R7C5 = 2 -> R5C3 = 8 (step 3), clean-up: no 6 in R4C1
10a. Naked pair {59} in R45C1, locked in C1 and N4
10b. X-Wing on 5 in R45C14, 5 locked for R45

11. R3C4 = 2 -> R34C3 = 12 = [57], clean-up: no 4 in R3C89 (step 9f)
11a. Naked pair {36} in R3C89, locked for R3 and N3, clean-up: no 8 in R23C7
11b. R23C7 = [59], clean-up: no 3,7 in R7C7 (step 3e)
11c. Naked pair {48} in R67C7, locked for C7

12. R45C7 = {36} (hidden pair in C7), locked for N6
12a. R1C7 = 7 (hidden single in C7)
12b. Naked pair {48} in R12C9, locked for C9 and N3

13. R456C8 = {479} (only remaining combination, cannot be {578} because 5,8 only in R6C8) = R5C8 = 7, R46C8 = {49}, locked for C8 and N6 -> R67C7 = [84], R6C9 = 5, R7C8 = 3, R3C89 = [63], R89C8 = [85], R89C5 = [59], R9C9 = 6, R7C34 = [91], R78C9 = [79], R7C12 = [85], R8C4 = 3

14. Naked pair {47} in R3C15, locked for R3 -> R3C2 = 8, R23C6 = [81], R12C9 = [84], R23C5 = [74], R3C1 = 7, R4C2 = 6 (prelim g), R45C7 = [36]

15. R1C2 = 9 (hidden single in R1), R12C1 = 4 = [13]

16. 24(6) cage at R6C1 must contain 1 -> 1 locked in R9C23, locked for R9 and N7

and the rest is naked singles


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PostPosted: Wed Jun 15, 2011 4:21 am 
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Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
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 |
+--------------------------+--------------------------+--------------------------+
| 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 | |
+--------------------------+--------------------------+--------------------------+

Puzzle rating table, with links to archive entries; each of these has a link to the puzzle thread.
Human Solvable 2X and Human Solvable 2X Lite are in the same archive entry.
Assassin 119 V2 and Assassin 119 V3 are in the same archive entry.

Abbreviations used in Rating Table on this page:
Est = Estimated rating by puzzle maker
E = Easy
H = Hard
Az = azpaull
M = Mike (mhparker)
N = Nasenbaer
U = udosuk
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 |
+------------------------+-----------+-------+-------+-------+-----------------------+-------+
| 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 |
+------------------------+-----------+-------+-------+-------+-----------------------+-------+


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.


Last edited by Andrew on Thu Aug 04, 2011 1:18 am, edited 6 times in total.

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PostPosted: Thu Jun 16, 2011 10:31 pm 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Assassin 116 "Mars" by Afmob (August 2008) here
Puzzle Diagram:
Image
Note that R7C3 belongs to 40(8) @ R3C5
Images with "udosuk style Killer Cages" by Børge:
Image     Image
Code: Select, Copy & Paste into solver:
3x3::k:5632:5632:3586:3586:3586:2565:2565:2823:2823:5632:2826:2826:4108:4108:4108:5135:5135:2823:4370:2826:6676:3093:10262:10262:10262:5135:2842:4370:4370:6676:3093:3093:10262:10262:2594:2842:4370:6676:6676:3093:10262:6697:10262:2594:5676:2349:10798:10798:10798:6697:6697:6697:2594:5676:2349:10798:10262:10798:3386:3386:3386:4157:5676:3135:10798:10798:10798:3386:6980:4157:4157:2887:3135:3135:1866:1866:6980:6980:6980:2887:2887:
Solution:
+-------+-------+-------+
| 9 5 4 | 3 7 8 | 2 6 1 |
| 8 2 3 | 9 6 1 | 5 7 4 |
| 1 6 7 | 5 4 2 | 9 8 3 |
+-------+-------+-------+
| 5 7 9 | 4 2 6 | 1 3 8 |
| 4 8 2 | 1 3 9 | 7 5 6 |
| 3 1 6 | 7 8 5 | 4 2 9 |
+-------+-------+-------+
| 6 9 8 | 2 5 4 | 3 1 7 |
| 7 4 5 | 8 1 3 | 6 9 2 |
| 2 3 1 | 6 9 7 | 8 4 5 |
+-------+-------+-------+
Quote:
Afmob: This one is for the guys! :rambo:
It was really hard to create a Killer that had the mars symbol in it since a lot of the other attempts proved to be unsolvable. Maybe someone can make the female counterpart of this Assassin?
SS Score: 1.16. Estimated rating: (Hard) 1.0.

azpaull: Very creative designing, Afmob! Thanks, I'm looking forward to working on it!

udosuk: Not many tricky moves are required so I'll rate it a 0.75 (hard) or a 1.0 (easy). :ugeek: But the cage pattern is very nice, so congratulate Afmob for another thoughtful puzzle! :alien:

When Mike(mhparker) posted his walkthrough for A116 "Venus", he wrote: P.S. I suspect that the reason that no-one else has posted a WT for Afmob's impressive-looking "Mars" version is that (as with many Killers based on a very difficult cage pattern) it has a fairly narrow solving path that doesn't allow for much variation on udosuk's solving path. Maybe Andrew (or someone else) can nevertheless find some subtle variation that's worth posting. I hope so. In the meantime, many thanks to Afmob for the original puzzle and the creative spark. :-D

Andrew: I've now solved A116 Mars. Sorry Afmob that I'd implied (in my post about A116 "Venus")that it was a difficult puzzle. It wasn't.
This puzzle deserves a second walkthrough. My early steps aren't subtle (sorry Mike ;) ) but they do use different logic.
I'll rate A116 Mars as Hard 1.0 because ... is a bit more complicated than that used by udosuk.

Walkthrough by udusok:
Here is my walkthrough:

0. Prelims

40/8 @ r3c5={12346789} can't have 5
42/8 @ r6c2={12456789} can't have 3
11/3 @ r1c8 & r2c2 & r8c9 can't have 9
26/4 @ r3c3 & r5c6 can't have 1
13/4 @ r7c5 can't have {89}
27/4 @ r8c6 can't have {12}


1. c9,r12

Innies @ c9: r1289c9=12={1236|1245} ({12} @ c9 locked)
22/3 @ r5c9={589|679} must have 5|6
=> 11/2 @ r3c9 can't be {56}, must be {38|47}

Outies @ r1: r2c19=12=[75|84|93]
11/3 @ r1c8 with r2c9 from {345} can't be {128|335|344}
=> r1c89 can't have {38}


2. n3 (!)

Now 11/3 @ r1c8 can't be {128}, can't have both {12}
=> 11/3 @ r1c8={137|146|236|245} has exactly one of {12}
20/3 @ r2c7={389|479|569|578} can't have any of {12}
=> Innies @ n3: r13c7+r3c9=14 must have exactly one of {12}
But r3c9 from {3478}
=> r13c7 must sum to 11|10|7|6 with exactly one of {12}
=> r13c7 can't be {13|23|17|27}
=> r13c7 can't have {37}
=> 10/2 @ r1c6={19|28|46}


3. r12 (!)

22/3 @ r1c1={589|679} with r2c1 from {789}
=> r1c12 must have 5|6
=> 3 @ r1 locked @ 14/3 @ r1c3 can't be {356}
=> 14/3 @ r1c3={329|347} must have 2|4
=> 11/3 @ r1c8 can't be [{24}5]
=> r2c9 can't be 5
=> r2c19=12=[84|93]

Innies @ r1: r1c1289=21 from {12456789} can't be {3567}
=> r1c12 can't be {67}
=> 22/3 @ r1c1 can't be {679}, must be {589} (NT @ n1)
=> 5 @ r1,n1 locked @ r1c12


4. r23,n5

Outies @ r12: r3c28=14=[68]
HS @ r3: r3c4=5
12/4 @ r3c4: r4c45+r5c4=12-5=7={124} (NT @ n5)

5 @ r2,n3 locked @ r2c78
20/3 @ r2c7: r2c78=20-8=12={57} (NP @ r2,n3)
r23c9={34} (NP @ c9,n3)


5. c789,r123

Outies @ c9: r19c8=10=[64]
Outies @ c89: r28c7=11=[56]
=> r2c8=7

16/3 @ r7c8: r78c8=16-6=10 from {12359}={19} (NP @ c8,n9)
=> r89c9={25} (NP @ c9,n9)
=> 11/3 @ r1c8: r12c9=11-6=5=[14]
=> 11/2 @ r3c9=[38]
=> 10/2 @ r1c6=[82]
=> r1c12={59} (NP @ r1,n1)
=> r2c1=8, r7c9=7
=> r379c7=[938]

11/3 @ r2c2: r2c23=11-6=5 from {123}={23} (NP @ r2,n1)
=> r13c3={47} (NP @ c3,n1)
=> r3c1=1 (not elsewhere @ 17/4 @ r3c1)


6. r9,c4567,n4

r9c9 from {25}
=> 7/2 @ r9c3 can't be {25}, must be {16} (NP @ r9)

27/4 @ r8c6: r8c6+r9c56=27-8=19 from {34579}={379} (NT @ n8)
Innies @ n89: r789c4=16 from {12468}={268}
=> 7/2 @ r9c3=[16]
=> r78c4={28} (NP @ c4,n8,42/8 @ r6c2)
=> r45c4={14} (NP @ c4,n5)
=> r26c4=[97] (7 not elsewhere @ 42/8 @ r6c2)
=> r6c7=4
=> r45c7={17} (not elsewhere @ 40/8 @ r3c5)

26/4 @ r5c6: r5c6+r6c56=26-4=22 from {35689}={589}
=> r56c6={59} (NP @ c6,n5)
=> r89c6={37} (NP @ c6,n8)
=> r247c6=[164]

9/2 @ r6c1 from {23569}=[36]
17/4 @ r3c1: r4c12+r5c1=17-1=16 from {24579}={259|457}
=> 5 @ n4 locked @ r4c12+r5c1


All naked singles from here.

I might have missed some shortcuts here or there but I think the path is short enough. Not many tricky moves are required so I'll rate it a 0.75 (hard) or a 1.0 (easy). :ugeek: But the cage pattern is very nice, so congratulate Afmob for another thoughtful puzzle! :alien:
Walkthrough by Andrew:
I wrote:
Now to have another try at A116 Mars. I didn't get very far first time.
When I looked again I found that I'd done most of the hard work so was closer to solving it than I'd realised. What I hadn't done was stick to my methodical approach; I'd forgotten to do some clean-up which proved to be critical. :oops: After I added that clean-up I got two immediate placements and the rest was easy.

Sorry Afmob that I'd implied that it was a difficult puzzle. It wasn't.

Mike wrote:
P.S. I suspect that the reason that no-one else has posted a WT for Afmob's impressive-looking "Mars" version is that (as with many Killers based on a very difficult cage pattern) it has a fairly narrow solving path that doesn't allow for much variation on udosuk's solving path. Maybe Andrew (or someone else) can nevertheless find some subtle variation that's worth posting. I hope so.
This puzzle deserves a second walkthrough. My early steps aren't subtle (sorry Mike ;) ) but they do use different logic.

I'll rate A116 Mars as Hard 1.0 because my early combination analysis in steps 7, 8 and 9 is a bit more complicated than that used by udosuk.

Here is my walkthrough.

Prelims

a) R1C67 = {19/28/37/46}, no 5
b) R34C9 = {29/38/47/56}, no 1
c) R67C1 = {18/27/36/45}, no 9
d) R9C34 = {16/25/34}, no 7,8,9
e) 22(3) cage in N1 = {589/679}, 9 locked for N1
f) 11(3) cage in N3 = {128/137/146/236/245}, no 9
g) 20(3) cage in N3 = {389/479/569/578}, no 1,2
h) R456C8 = {127/136/145/235}, no 8,9
i) R567C9 = {589/679}, 9 locked for C9, clean-up: no 2 in R34C9
j) 11(3) cage in N9 = {128/137/146/236/245}, no 9
l) 26(4) cage at R3C3 = {2789/3689/4589/4679/5678}, no 1
m) 12(4) cage at R3C4 = {1236/1245}, no 7,8,9, CPE no 1,2 in R6C4
n) 26(4) cage at R5C6 = {2789/3689/4589/4679/5678}, no 1
o) 13(4) cage at R7C5 = {1237/1246/1345}, no 8,9, CPE no 1 in R7C4
p) 27(4) cage at R8C6 = {3789/4689/5679}, no 1,2
q) 40(8) cage at R3C5 = {12346789}, no 5
r) 42(8) cage at R6C2 = {12456789}, no 3

1. 45 rule on R1 2 outies R2C19 = 12 = [57/75/84/93]

2. 45 rule on C9 2 outies R19C8 = 10 = {28/37/46}, no 1,5

3. 45 rule on R12 2 outies R3C28 = 14 = [59/68/86]
3a. 11(3) cage in N1 = {128/146/236/245} (cannot be {137} because R3C2 only contains 5,6,8), no 7
3b. 5,6,8 must be in R3C2 -> no 5,6,8 in R2C23

4. 45 rule on C89 2 outies R28C7 = 11 = {38/47/56}/[92], no 1,9 in R8C7
4a. 11(3) cage in N3 = {137/146/236/245} (cannot be {128} because R2C9 only contains 3,4,5,7), no 8, clean-up: no 2 in R9C8 (step 2)
4b. 1 of {137} must be in R1C9 -> no 7 in R1C9
4c. 3 of {236} must be in R2C9 -> no 3 in R1C9

5. 45 rule on C9 4 innies R1289C9 = 12 = {1236/1245}, no 7,8, clean-up: no 5 in R2C1 (step 1)
5a. 3 of {1236} must be in R2C9 -> no 3 in R89C9
5b. Killer pair 5,6 in R1289C9 and R567C9, locked for C9
5c. 11(3) cage in N3 (step 4a) = {137/146/236/245}
5d. 3 of {137/236} must be in R2C9 -> no 3 in R1C8, clean-up: no 7 in R9C8 (step 2)

6. 45 rule on N1 3 innies R1C3 + R3C13 = 12 = {138/147/237/345} (cannot be {156} which clashes with 22(3) cage, cannot be {246} which clashes with 11(3) cage), no 6

7. 45 rule on R12 4 innies R2C2378 = 17 = {1259/1349/1457/2348/2357/2456} (cannot be {1268} because 20(3) cage in N3 cannot be {68}6, cannot be {1358/1367} because 11(3) cage cannot contain both of 1,3)
7a. 4 of {1349/1457/2348/2456} must be in R2C23 (1,3 of {1349} cannot be in R2C23 because 11(3) cage cannot contain both of 1,3, R2C78 cannot be {48} because 20(3) cage cannot be {48}8) -> no 4 in R2C78, clean-up: no 7 in R8C7 (step 4)

8. 45 rule on R2 6 innies R2C123789 (from steps 1 and 7) = {124589/134579/234578/234569}, 4,5 locked for R2
8a. Cannot be {124589} because 8 must be in R2C1 (R2C78 cannot be {58/89} because no 3,7 in R3C8) and R2C123 = 8{21} clashes with 11(3) cage
8b. R2C123789 = {134579/234578/234569}, 3 locked for R2
8c. 11(3) cage in N1 (step 3a) = {146/236/245} (cannot be {128} which clashes with R2C123789), no 8, clean-up: no 6 in R3C8 (step 3)
8d. Killer pair 5,6 in 22(3) cage and R3C2, locked for N1

9. 45 rule on R1 4 innies R1C1289 = 21 = {1569/1578/2469/2568} (cannot be {1479} because no 6 in R2C1, cannot be {2478} which clashes with 22(3) cage in N1)
9a. 7 of {1578} must be in R1C8 -> no 7 in R1C12
9b. 1 of {1569/1578} must be in R1C9, 5 of {2568} must be in R1C12 (R1C12 cannot be {68} which clashes with 22(3) cage) -> no 5 in R1C9

10. R1C345 = {149/158/239/248/347} (cannot be {167/257/356} which clash with R1C1289), no 6

11. 45 rule on N3 3 innies R1C7 + R3C79 = 14 = {149/167/239/248} (cannot be {347} which clashes with 11(3) cage)
11a. 3,7 of {167/239} must be in R3C9 -> no 3,7 in R13C7, clean-up: no 3,7 in R1C6

12. 3 in R1 locked in R1C345 (step 10) = {239/347}, no 1,5,8
12a. R1C1289 (step 9) = {1569/1578/2568} (cannot be {2469} which clashes with R1C345), no 4, clean-up: no 6 in R9C8 (step 2)

13. 11(3) cage in N3 (step 4a) = {137/146/236} (cannot be {245} because 4,5 only in R2C9), no 5, clean-up: no 7 in R2C1 (step 1), clean-up: no 6 in R1C12 (prelim e)
13a. Naked triple {589} in 22(3) cage, locked for N1 -> R3C2 = 6, R3C8 = 8 (step 3), clean-up: no 2 in R1C6, no 2 in R1C8 (step 2), no 3 in R4C9
13b. 5 in R2 locked in R2C78 -> R2C78 = 12 = {57}, locked for R2 and N3 -> R1C8 = 6, R9C8 = 4 (step 2), clean-up: no 4 in R1C67, no 4 in R4C9, no 3 in R9C34

14. R1C345 = {347} (hidden triple in R1)
14a. 2 in R1 locked in R1C79, locked for N3
14b. 9 in N3 locked in R13C7, locked for C7
14c. 9 in N6 locked in R56C9, locked for C9
14d. Naked pair {34} in R23C9, locked for N3

15. R456C8 = {127/235}, 2 locked for C8
15a. Killer pair 5,7 in R2C8 and R456C8, locked for C8

16. 9 in N9 locked in 16(3) cage = {169} (only remaining combination, cannot be {259} because 2,5 only in R8C7) -> R8C7 = 6, R78C8 = {19}, locked for C8 and N9, clean-up: no 7 in R456C8 (step 15)
16a. Naked triple {235} in R456C8, locked for C8 and N6 -> R2C78 = [57]
16b. Naked pair {25} in R89C9, locked for C9 and N9 -> R1C9 = 1, R13C7 = [29], R1C6 = 8, R2C9 = 4 (step 13), R2C1 = 8 (step 1), R3C9 = 3, R4C9 = 8, R7C9 = 7, R79C7 = [38], clean-up: no 1 in R2C23 (step 7), no 1,2,6 in R6C1, no 1 in R7C1, no 6 in R7C56 (prelim o)
16c. Naked pair {23} in R2C23, locked for R2 and N1
16d. Naked pair {47} in R13C3, locked for C3 and N1 -> R3C1 = 1

17. R3C4 = 5 (hidden single in R3), clean-up: no 3,6 in 12(4) cage at R3C4 (prelim m), no 2 in R9C3
17a. Naked triple {124} in R4C45 + R5C4, locked for N5

18. Naked quad {1247} in R3C56 + R45C7, locked for 40(8) cage at R3C5
18a. 3 in 40(8) cage at R3C5 locked in R4C6 + R5C5, locked for N5

19. 5 in N5 locked in R5C6 + R6C56 -> 26(4) cage at R5C6 = {4589/5678} -> R6C5 = 8
19a. Naked pair {36} in R4C6 + R5C5, locked for N5 and 40(8) cage at R3C5 -> R7C3 = 8
19b. 26(4) cage at R5C6 (step 19) = {4589} (only remaining combination) -> R6C7 = 4, R56C6 = {59}, locked for C6 and N5, R6C4 = 7, clean-up: no 2,5 in R7C1
19c. R8C4 = 8 (hidden single in C4)

20. Naked pair {17} in R45C7, locked for 40(8) cage at R3C5
20a. Naked pair {24} in R3C56, locked for R3 and N2 -> R2C3 = 7, R1C345 = [437]

21. 13(4) cage at R7C5 = {1345} (last remaining combination), 1,4,5 locked in R7C56 + R8C5 for N8, clean-up: no 6 in R9C3

22. 27(4) cage at R8C6 = {3789} (only remaining combination) -> R9C5 = 9, R89C6 = {37}, locked for C6 -> R4C6 = 6, R5C5 = 3, R2C456 = [961], R7C6 = 4, R3C56 = [42], R7C1 = 6, R6C1 = 3, R79C4 = [26], R9C3 = 1

23. Naked triple {459} in R7C2 + R8C23, locked for N7 and 42(8) cage at R6C2 -> R6C23 = [16]
23a. Naked pair {27} in R89C1, locked for C1 and N7

and the rest is naked singles and a cage sum

I enjoyed the cage patterns for both Mars and Venus, particularly in the later stages where the large cages and their interactions, possibly more so in Venus, were very helpful in making eliminations.


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PostPosted: Thu Jun 16, 2011 11:07 pm 
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Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Assassin 116 "Venus" by Ed (August 2008) here
Puzzle Diagram:
Image
NOTE: 4 cages run along the diagonals in n1379 respectively. Hard to get a pic clear enough to show these.
Images with "udosuk style Killer Cages" by Børge:
Image     Image
Code: Select, Copy & Paste into solver:
3x3:d:k:4865:3586:3586:3331:2564:2053:3078:3078:4871:3080:4865:3586:3331:2564:2053:3078:4871:3593:3080:3080:4865:10250:10250:10250:4871:3593:3593:2059:4620:4877:10250:10766:10250:2831:3344:5393:2059:4620:4877:10250:10250:10250:2831:3344:5393:2059:4620:4877:3858:10766:3091:2831:3344:5393:5396:5396:3858:3858:10766:3091:3091:2325:2325:5396:1558:3351:10766:10766:10766:6424:2841:2325:1558:3351:3351:3351:10766:6424:6424:6424:2841:
Solution:
+-------+-------+-------+
| 6 9 1 | 7 8 5 | 4 3 2 |
| 7 8 4 | 6 2 3 | 5 9 1 |
| 2 3 5 | 9 1 4 | 8 7 6 |
+-------+-------+-------+
| 1 5 8 | 2 9 7 | 3 6 4 |
| 4 7 2 | 8 3 6 | 1 5 9 |
| 3 6 9 | 4 5 1 | 7 2 8 |
+-------+-------+-------+
| 8 4 6 | 5 7 2 | 9 1 3 |
| 9 1 7 | 3 6 8 | 2 4 5 |
| 5 2 3 | 1 4 9 | 6 8 7 |
+-------+-------+-------+
Quote:
Afmob wrote:
Maybe someone can make the female counterpart of this Assassin?
Ed: Yep - here is Venus. She didn't want to give an SSscore of around 1.4-1.5 but instead of dumping it, Afmob has solved it for me with an est. rating of 1.50. Thanks Afmob! Now I can relax with her for the next week.
OT question for Afmob: Why Mars & Venus symbols? Olympics?
SS(v3.2.1)Score: 1.88. Estimated rating: 1.5.

Afmob: Thanks Ed for giving us the female variant!
With V1 I wanted to create a Killer that had a symbol in it and my first idea was the male symbol (Mars). After I created A116 Mars I thought it would only be fair to create a second Killer with the Venus symbol as V2. But I encountered too many uniqueness problems and that's why I couldn't find one until Friday.
So the symbols have got nothing to do with the Olympics, they were just my initial idea (probably because that way I could use a remote cage).
I hope to see some more wts for Mars and Venus!
Rating: 1.5 - (Hard) 1.5.

Afmob wrote:
Thanks Ed for giving us the female variant!
Mike(mhparker): Indeed, there are some puzzles that just seem to work out well, this high-quality puzzle being one of them. Interestingly, I was also working on a potential "Venus" version, and had even got to the stage where I was looking up the websites of companies like Chanel, Helena Rubenstein and Estée Lauder, in order to find some good-looking lipstick colors I could use for highlighting the cages! Fortunately, Ed beat me to it. Thanks, Ed! :-D
I only used three moderately difficult moves to crack it, all of which I would individually place in the 1.25 rating category. Therefore, I'll also rate the whole puzzle at 1.25.

Andrew: Thanks Ed for a challenging puzzle.
There were some fun steps on the diagonals which I seem to have used more than either Afmob or Mike. I enjoyed going through both of their walkthroughs. Afmob's step 1d was neat, particularly for so early in a solution. I was also impressed that Mike solved it without using any chains.
I'll rate A116 Venus at 1.5 the way I solved it. However Mike has shown that it's at most a Hard 1.25.

Walkthrough by Afmob:
Thanks Ed for giving us the female variant!

With V1 I wanted to create a Killer that had a symbol in it and my first idea was the male symbol (Mars). After I created A116 Mars I thought it would only be fair to create a second Killer with the Venus symbol as V2. But I encountered too many uniqueness problems and that's why I couldn't find one until Friday.
So the symbols have got nothing to do with the Olympics, they were just my initial idea (probably because that way I could use a remote cage).

I hope to see some more wts for Mars and Venus!

A116 Venus Walkthrough:

1. C123 !
a) 8(3) = 1{25/34} -> 1 locked for C1+N4
b) 6(2): R8C2 <> 5
c) Outies N7 = 10(3) <> 8,9
d) ! Killer quint (12345) locked in 12(3) + R4569C1 for C1 since 12(3)
must have at least two of (12345)
e) 12(3) can only have one of (12345) @ C1 -> R3C2 <> 6,7,8,9 and 12(3) <> {345}
f) Innies+Outies N7: -5 = R9C4 - R7C3 -> R9C4 <> 5,6,7 and R7C3 = (6789)
g) 3 locked in 13(4) @ N7 = 13{27/45}; R9C4 <> 3
h) 21(3) = 8{49/67} because {579} blocked by Killer pair (57) of 13(4)
-> 8 locked for N7
i) Innies+Outies C1: 2 = R378C2 - R1C1 -> R7C2 <> 9

2. C123 !
a) Hidden Killer pair (69) in R7C3 for N7 since 21(3) must have exactly one of (69) -> R7C3 <> 7
b) 15(3) = {159/267/456} <> 3 because R7C3 = (69) and Outies N7 cannot have 2 and 4; R67C4 <> 6
c) Outies N7 = 10(3) = 1{27/45} -> 1 locked for C4
d) Innies+Outies N7: -5 = R9C4 - R7C3 -> R9C4 <> 2
e) 13(4): R89C3+R9C2 <> 4 because {345}1 blocked by Killer pair (45) of 6(2)
f) ! 6(2) <> [24] since it's a Killer pair of 13(4)
g) 8(3) = {134} locked for C1+N4 because R9C1 = (25) blocks {125}
h) 18(3) = 7{29/56} -> 7 locked for C2+N4
i) 19(3) @ N4 = 8{29/56} -> 8 locked for C3
j) Killer pair (69) locked in 19(3) @ N4 + R7C3 for C3
k) 4 locked in R78C2 @ N7 for C2

3. C123
a) Hidden Killer pair (25) in 12(3) for C1 -> 12(3) = {129/156/237} <> 8
and R3C2 <> 2,5
b) Innies+Outies C1: 2 = R378C2 - R1C1 -> R7C2 <> 8 because R38C2 <> 2
c) 21(3) = 8{49/67} -> 8 locked for C1; R78C1 <> 6 because R7C2 = (46)
d) 6 locked in R123C1 @ C1 for N1
e) 6 locked in R7C23 @ N7 for R7
f) 19(3) @ N1: R2C2 <> 2,5 because 8 only possible there
g) 14(3) <> {257} since (25) is a Killer pair of 12(3)
h) 14(3): R1C2 <> 1,2,5 because R12C3 <> 8,9
i) Hidden Killer pair (25) in R9C2 for C2 since 18(3) must have exactly one of (25)
-> R9C2 = (25)
j) Naked pair (25) locked in R9C12 for R9+N7
k) 13(4) = 13{27/45} -> 3 locked for C3

4. N89
a) 2 locked in R8C789 @ R8 for N9
b) 9(3): R8C9 <> 4,6 because R7C89 <> 2
c) 9(3) = 3{15/24} -> 3 locked for N9
d) 11(2) <> 8; R8C8 <> 6,9
e) Innies+Outies N9: R9C6 = R7C7 <> 3,5,6
f) 8 locked in Innies N9 = 25(4) = 8{179/269/467} <> 5

5. C456
a) 5 locked in 42(7) @ C5 -> R8C46 <> 5
b) R3C46 <> 1,2 because they see all 1,2 of C5
c) 3 locked in Innies C1234 = 22(4) = 39{28/46} since {3478} blocked by
Killer pair (47) of Outies N7 -> 9 locked for C4
d) 13(2) <> 4
e) Innies N2 = 14(3) <> 6 because (167) blocked by Killer triple (567)
of 13(2) + 8(2)
f) 40(8) must have 6 -> 6 locked for N5

6. C456
a) Innies C6789 = 25(4) = 8{179/269/467} <> 3 because {3679} blocked
by Killer triple (367) of 8(2) -> 8 locked for C6
b) Innies+Outies N9: R9C6 = R7C7 <> 8
c) 8 locked in 42(7) @ N8 -> R46C5 <> 8
d) 8 locked in 40(8) @ N5 -> R3C456 <> 8

7. N3 + D/
a) 8 locked in R3C789 @ R3 for N3
b) 19(3) <> {469} because R7C3 = (69)
c) 19(3): R3C7 <> 2,4,5,6 because 8 only possible there

8. D/ !
a) Innies D/ = 20(4) = {1379/1568/2369/2468/3467} because R7C3 = (69)
and because of Killer pairs (12,14,25) of 6(2)
b) Innies D/ = 20(4): R4C6+R5C5 <> 6 because 9 in R7C3 forces R6C4 = (15)
c) ! Innies D/ = 20(4): R5C5 <> 7 because 3 only possible there

9. C456
a) 40(8) must have 7 -> CPE: R12C6 <> 7
b) 8(2) <> 1
c) Killer pair (56) locked in 8(2) + 13(2) for N2
d) 10(2) <> 4
e) 4 locked in Innies N2 = 4{19/37} for R3+40(8)
f) 1 locked in R123C5 @ N2 for C5

10. D\ + C456 !
a) ! 1 locked in 12(3) @ D\ = 1{29/47}; R7C6 <> 1
b) 3 locked in 8(2) @ C6 = {35} locked for N2
c) 13(2) = {67} locked for C4+N2
d) Innies N2 = 14(3) = {149} -> R3C5 = 1; 9 locked for R3+N2+40(8)
e) R3C2 = 3 -> R23C1 = 9(2) = {27} locked for C1+N1
f) R3C3 = 5 -> R2C2 = 8 -> R1C1 = 6
g) R1C2 = 9, R9C1 = 5
h) 40(8) must have 6,7,8 -> R5C6 = 6, R4C6 = 7, R5C4 = 8

11. C789 + D\
a) 19(3) = {289} -> R3C7 = 8, R1C9 = 2, R2C8 = 9
b) 9(3) = {135} locked for N9
c) Innies+Outies N9: R9C6 = R7C7 = (49)
d) 7 locked in 11(2) @ D\ = {47} locked for N9+D\
e) R7C7 = 9, R9C7 = 6, R8C7 = 2
f) 11(3) = {137} locked for C7+N6
g) 14(3) = {167} because R3C89 = (67) -> R2C9 = 1; 7 locked for R3+N3

12. Rest is singles.

Rating: 1.5 - (Hard) 1.5. I used Hidden Killer pairs, Killer triples, one Killer quint and a small chain (step 8b).
Walkthrough by Mike:
Afmob wrote:
Thanks Ed for giving us the female variant!

Indeed, there are some puzzles that just seem to work out well, this high-quality puzzle being one of them. Interestingly, I was also working on a potential "Venus" version, and had even got to the stage where I was looking up the websites of companies like Chanel, Helena Rubenstein and Estée Lauder, in order to find some good-looking lipstick colors I could use for highlighting the cages! Fortunately, Ed beat me to it. Thanks, Ed! :-D

Afmob wrote:
I hope to see some more wts for Mars and Venus!

Here's my WT for Ed's Venus. I only used three moderately difficult moves (steps 7, 8 and 21) to crack it, all of which I would individually place in the 1.25 rating category. Therefore, I'll also rate the whole puzzle at 1.25.

Note: Of course, having to spot three moves in this category (or equivalent replacements) may make this puzzle subjectively harder than a 1.25-rated puzzle where only a single move on the solving path belongs to this category. However, following the strict approach that the hardest technique determines the rating, both such puzzles would rate identically.

Edit1: Typo corrected in step 21. Thanks, Afmob!
Edit2: Typo corrected in step 29. Thanks, Andrew!

Assassin 116 Venus Walkthrough (31 steps)

Prelims

a) 19(3) at R1C1, R1C9 and R4C3 = {289/379/469/478/568} (no 1)
b) 13(2) at R1C4 = {49/58/67} (no 1..3)
c) 10(2) at R1C5 = {19/28/37/46} (no 5)
d) 8(2) at R1C6 = {17/26/35} (no 4,8,9)
e) 40(8) at R3C4 = {12346789} (no 5)
f) 8(3) at R4C1 = {125/134} (no 6..9)
g) 42(7) at R4C5 = {3456789} (no 1,2)
h) 11(3) at {128/137/146/236/245} (no 9)
i) 21(3) at R4C9 and R7C1 = {489/579/678} (no 1..3)
j) 9(3) at R7C8 = {126/135/234} (no 7..9)
k) 6(2) at R8C2 = {15/24} (no 3,6..9)
l) 13(4) at R8C3 = {1237/1246/1345} (no 8,9)
m) 11(2) at R8C8 = {29/38/47/56} (no 1)

1. 1 of 8(3) at R4C1 (prelim f) locked in R456C1 for C1 and N4
1a. cleanup: no 5 in R8C2

2. Innie/Outie difference (IOD), N7: R7C3 = R9C4 + 5
2a. -> no 1..5 in R7C3, no 5..7 in R9C4

3. 3 in N7 locked in 13(4) at R8C3 (prelim l) = {1237/1345} (no 6)
3a. no 3 in R9C4 (same cage)
3b. 2 of {1237} cannot go in R9C4 (blocked by hidden IOD cage at R7C3+R9C4 (step 2))
3c. -> no 2 in R9C4
3d. cleanup: no 7,8 in R7C3 (step 2)

4. 8 in N7 locked in 21(3) at R7C1 (prelim i) = {489/678} (no 5)

5. Outies N7: R679C4 = 10(3) = {127/145} (no 3,6,8,9)
(Note: {235} blocked by R9C4, {136} blocked because R67C4 cannot contain both of {36} due to 15(3) cage sum)
5a. 1 locked for C4

6. 5 in C5 locked in 42(7) at R4C5
6a. -> no 5 in R8C46 (same cage)

7. 5 in C4 locked in combined 23(5) cage at R12679C4 (prelim b, step 5) = ({58}+{127})/({67}+{145})
7a. -> 13(2) at R1C4 = {58/67} (no 4,9)
7b. 7 locked in R1267C4 for C4

8. 40(8) at R3C4 (prelim e) and 42(7) at R4C5 (prelim g) form grouped X-Wing on 7 within C56
8a. -> no 7 elsewhere in C56
8b. cleanup: no 3 in R12C5; no 1 in R12C6

9. IOD, N9: R7C7 = R9C6
9a. -> no 7 in R7C7

10. 1 in N2 locked in R123C5+R3C6
10a. -> no 1 in R5C5 (CPE)

11. 1 in D\ locked in R6C6+R7C7
11a. -> (from step 9) 1 locked in R69C6 for C6
11b. no 1 in R6C7 (CPE)

12. Hidden single (HS) in 40(8) at R3C5 = 1
12a. cleanup: no 9 in R12C5

13. 9 in N2 locked in N2 innies at R3C46 = 13(2) = {49} (no 2,3,6,7,8), locked for R3, N2 and 40(8)
13a. cleanup: no 6 in R12C5

14. Naked pair (NP) at R12C5 = {28}, locked for C5 and N2
14a. cleanup: no 5 in R12C4, no 6 in R12C6

15. NP at R12C4 = {67}, locked for C4

16. R679C4 (step 5) = {145} (no 2), locked for C4

17. R3C46 = [94]
17a. no 4 in R7C7 (step 9)

18. NP at R12C6 = {35}, locked for C6
18a. no 3,5 in R7C7 (step 9)

19. From step 11, 1 in D\ locked in 12(3) at R6C6 = {129} (no 6,8) (last combo)
19a. no 6,8 in R9C6 (step 9)

20. Naked triple (NT) at R679C6 = {129}, locked for C6

21. 19(3) at R1C1 (prelim a) and 11(2) at R8C8 form hidden killer pair on {45} within D\
21a. -> 11(2) at R8C8 (prelim m) = = {(4/5)..} = {47/56} (no 2,3,8,9) and...
21b. ...19(3) at R1C1 = {(4/5)..} = {478/568} (no 2,3,9)
(Note: {469} blocked by 11(2) at R8C8 (step 21a))
21c. -> 8 locked in R1C1+R2C2+R3C3 for N1 and D\

22. 1 in N1 locked in 14(3) at R1C2 = {149} (no 2,3,5..7) (last combo), locked for N1
(Note: {167} blocked by 19(3) at R1C1 (step 21b))

23. 19(3) at R1C1 (step 21b) = {568} (no 7) (last combo), locked for N1 and D\

24. NP at R8C8+R9C9 = {47}, locked for N9 and D\

25. Naked single (NS) at R5C5 = 3
25a. -> R45C4 = [28]
25b. -> R8C4 = 3
25c. cleanup: no 2 in R9C6 (step 9)

26. 9 in C1 locked in 21(3) at R7C1 (step 4) = {489} (no 6,7), locked for N7
26a. cleanup: no 2 in R8C2+R9C1

27. 6(2) at R8C2 = [15]
27a. -> R6C4+R7C3 = [46]
27b. -> R7C4 = 5 (cage sum), R45C6 = [76], R9C4 = 1
27c. -> R89C6 = [89]
27d. -> 12(3) at R6C6 = [129]

28. NP at R7C89 = {13}, locked for N9
28a. -> R8C9 = 5 (cage sum)

29. NT at R389C7 = {268}, locked for C7
29a. -> 11(3) at R4C7 = {137} (no 4,5), locked for C7 and N6
29b. -> 21(3) at R4C9 = {489} (no 6), locked for C9 and N6

30. 8(3) at R4C1 (prelim f) = {134} (no 2), locked for C1 and N4

31. NP at R12C7 = {45}, locked for N3
31a. -> R1C8 = 3 (cage sum)

Rest is all naked singles now.

P.S. I suspect that the reason that no-one else has posted a WT for Afmob's impressive-looking "Mars" version is that (as with many Killers based on a very difficult cage pattern) it has a fairly narrow solving path that doesn't allow for much variation on udosuk's solving path. Maybe Andrew (or someone else) can nevertheless find some subtle variation that's worth posting. I hope so. In the meantime, many thanks to Afmob for the original puzzle and the creative spark. :-D
Walkthrough by Andrew:
Thanks Ed for a challenging puzzle. There were some fun steps on the diagonals which I seem to have used more than either Afmob or Mike.

I enjoyed going through both of their walkthroughs. Afmob's step 1d was neat, particularly for so early in a solution. I was also impressed that Mike solved it without using any chains.

I used three chains in my solution although I now know that the last two weren't necessary, as shown by Afmob's step 2f and Mike's step 11; I don't know why I didn't spot that one. :oops:

Because of the chains I'll rate A116 Venus at 1.5 the way I solved it. However Mike has shown that it's at most a Hard 1.25.

Here is my walkthrough. I've given the eliminations on the diagonals because it's easy for those of use who do manual eliminations to overlook them.

Prelims

a) R12C4 = {49/58/67}, no 1,2,3
b) R12C5 = {19/28/37/46}, no 5
c) R12C6 = {17/26/35}, no 4,8,9
d) 6(2) diagonal cage at R8C2 = {15/24}
e) 11(2) diagonal cage at R8C8 = {29/38/47/56}, no 1
f) 19(3) diagonal cage at R1C1 = {289/379/469/478/568}, no 1
g) 19(3) diagonal cage at R1C9 = {289/379/469/478/568}, no 1
h) R456C1 = {125/134}, 1 locked for C1 and N4, clean-up: no 5 in R8C2
i) R456C7 = {128/137/146/236/245}, no 9
j) R456C9 = {489/579/678}, no 1,2,3
k) 21(3) cage in N7 = {489/579/678}, no 1,2,3
l) 9(3) cage in N9 = {126/135/234}, no 7,8,9
m) 13(4) cage at R8C3 = {1237/1246/1345}, no 8,9
n) 40(8) cage at R3C4 = {12346789}, no 5
o) 42(7) separated cage at R4C5 = {3456789}, no 1,2

1. 45 rule on N7 1 innie R7C3 = 1 outie R9C4 + 5, R7C3 = {6789}, R9C4 = {1234}

2. 3 in N7 locked in R8C3 + R9C23, locked for 13(4) cage, no 3 in R9C4, clean-up: no 8 in R7C3 (step 1)
2a. 13(4) cage at R8C3 = {1237/1345}, no 6
2b. 45 rule on N7 4 innies R78C3 + R9C23 = 18 = {1359/2367} (cannot be {2349} because 13(4) cage at R8C3 would be {234}4, cannot be {3456} which clashes with 6(2) diagonal cage), no 4
2c. 6 of {2367} must be in R7C3 -> no 7 in R7C3, clean-up: no 2 in R9C4 (step 1)
2d. 8 in N7 locked in 21(3) cage = {489/678}, no 5

3. 15(3) cage at R6C4 = {159/168/267/456} (cannot be {249} because R679C4 would be {24}4, cannot be {258/348/357} because R7C3 only contains 6,9), no 3
3a. R7C3 = {69} -> no 6,9 in R67C4

4. 45 rule on N7 3 outies R679C4 = 10 = {127/145}, no 8, 1 locked for C4

5. 3 in C4 locked in R3458C4
5a. 45 rule on C1234 4 innies R3458C4 = 22 = {2389/3469/3568} (cannot be {3478} which clashes with R12C4), no 7

6. R456C1 = {125/134}, R9C1 = {245} -> 4 locked in R456C1 and R9C1 for C1
6a. 21(3) cage in N7 (step 2c) = {489/678}
6b. 4 of {489} must be in R7C2 -> no 9 in R7C2

7. 12(3) cage in N1 = {129/138/156/237/246} (cannot be {147} because 1,4 only in R3C2, cannot be {345} because R23C1 = {35} clashes with R456C1)
7a. 1,4 of {129/138/156/246} must be in R3C2
7b. 7 of {237} must be in R23C1 (R23C1 cannot be {23} which clashes with R456C1)
7c. -> R3C2 = {1234}

8. 45 rule on N2 3 innies R3C456 = 14 = {149/167/239/248/347}
8a. 6 of {167} must be in R3C4 -> no 6 in R3C56

9. Hidden killer pair 2,9 in 19(3) diagonal cage at R1C1, 11(2) diagonal cage at R8C8 and R4C4 + R5C5 + R6C6 + R7C7, 2 can only be in 19(3) diagonal cage at R1C1 or 11(2) diagonal cage at R8C8 if 9 is in the same cage -> R4C4 + R5C5 + R6C6 + R7C7 can only contain 2 if it also contains 9
9a. 1 on D\ locked in R5C5 + R6C6 + R7C7
9b. 45 rule on D\ 4 innies R4C4 + R5C5 + R6C6 + R7C7 = 15 = {1239/1347/1356} (cannot be {1248/1257} which contain 2 but not 9), no 8, 3 locked for D\, clean-up: no 8 in 11(2) diagonal cage at R8C8
9c. 8 in D\ locked in 19(3) diagonal cage at R1C1, locked for N1
9d. 19(3) diagonal cage at R1C1 = {289/478/568}
9e. 12(3) cage in N1 (step 7) = {129/156/237} (cannot be {246} which clashes with 19(3) diagonal cage at R1C1), no 4

10. 45 rule on D/ 4 innies R4C6 + R5C5 + R6C4 + R7C3 = 20 = {1379/1568/2369/2468/3467} (cannot be {1289/1469/1478/2459/2567} which clash with 6(2) diagonal cage at R8C2, cannot be {2378/3458} because R7C3 only contains 6,9)
10a. R6C4 + R7C3 cannot be [59] -> no 1 in R7C4 (step 3)

11. 1 on D/ cannot be in R4C6 or R5C5
1 in R4C6 or R5C5 => no 1 in R6C4 + R8C2 => 1 in N7 can only be in R8C3 + R9C23 => no 1 in R9C4 -> cannot place 1 in C4
11a. 1 in C5 locked in R123C5, locked for N2, clean-up: no 7 in R12C6

12. R7C3 = R9C4 + 5 (step 1), 1 in C4 locked in R69C4 -> R6C4 + R7C3 must be either [19] or {2457}6
12a. R4C6 + R5C5 + R6C4 + R7C3 (step 10) = {1379/2369/2468/3467} (cannot be {1568} because of step 12), no 5
12b. 2 of {2369} must be in R6C4, 8 of {2468} must be in R4C6 -> no 2 in R4C6
12c. 6 of {2369/2468/3467} must be in R7C3 (for {2369} this is because of step 12) -> no 6 in R4C6 + R5C5

13. 15(3) cage at R6C4 (step 3) = {159/267/456}
13a. 5 of {456} must be in R7C4 -> no 4 in R7C4

14. 5 in N2 locked in combined cage R12C46 = 21 = {2568/3459/3567}
14a. R12C5 = {19/28/37} (cannot be {46} which clashes with R12C46)

15. 8 in N9 locked in 25(4) cage at R8C7, no 8 in R9C6

16. 1 on D\ locked in R6C6 + R7C7, locked for 12(3) cage at R6C6, no 1 in R7C6
16a. 12(3) cage at R6C6 = {129/138/147/156}
16b. 8 of {138} must be in R7C6 -> no 3 in R7C6

17. 1 in N8 locked in R9C46, locked for R9
17a. 1 in N7 locked in R8C23, locked for R8
17b. 13(4) cage at R8C3 = {1237/1345}
17c. 1 of {1345} must be in R8C3 -> no 5 in R8C3
17d. 5 in N7 locked in R9C123, locked for R9, clean-up: no 6 in R8C8

18. 45 rule on N9 1 outie R9C6 = 1 innie R7C7, no 5 in R7C7

19. R5C6 cannot be 1
R5C6 = 1 => R7C7 = 1 (hidden single on D\) => R9C6 = 1 (step 18) clashes with R5C6
19a. R3C5 = 1 (hidden single in 40(8) cage at R3C4, clean-up: no 9 in R12C5
19b. R3C5 = 1 -> R3C456 (step 8) = {149/167}, no 2,3,8
19c. 1 in N5 locked in R6C46, locked for R6

20. 12(3) cage in N1 = {237} (only remaining combination), locked for N1, 7 locked in R23C1 for C1, clean-up: no 4,9 in 19(3) diagonal cage at R1C1 (step 9d)
20a. Naked triple {568} in 19(3) diagonal cage at R1C1, locked for D\ and N1, clean-up: no 6 in R9C6 (step 18)
20b. Naked triple {689} in R78C1 + R7C3, locked for N7
20c. 8 in N7 locked in R78C1, locked for C1
20d. 12(3) cage at R6C6 (step 16a) = {129/138/147} (cannot be {156} because 5,6 only in R7C6), no 5,6

21. 4 cannot be in R9C1
R9C1 = 4 => R7C2 = 7, R9C4 = 1 => R8C3 + R9C23 = {237} (step 17b) clashes with R7C2
-> no 4 in R9C1, clean-up: no 2 in R8C2

22. 4 in C1 locked in R456C1 = {134} (prelim h), locked for C1 and N4
22a. Naked pair {27} in R23C1, locked for C1 and N1 -> R3C2 = 3, R9C1 = 5, R8C2 = 1, both locked for D/, R1C1 = 6, clean-up: no 7 in R2C4, no 2 in R2C6
22b. Naked pair {89} in R78C1, locked for N7 -> R7C3 = 6, locked for D/, R9C4 = 1 (step 1), R7C2 = 4 (step 2c), R1C2 = 9, clean-up: no 4 in R2C4, no 1 in R7C7, no 4 in R9C6 (both step 18)

23. R6C6 = 1 (hidden single in C6)
23a. R6C6 = 1 -> R7C67 = 11 = [29/83/92], no 7, clean-up: no 7 in R9C6 (step 18)
23b. Killer pair 8,9 in R7C1 and R7C67, locked for R7
23c. 7 in R7 locked in R7C45, locked for N8

24. 1 in N9 locked in 9(3) cage = {126/135}, no 4

25. 2,3,8 in 40(8) cage at R3C4 locked in R4C46 + R5C456, locked for N5
25a. R679C4 (step 4) = {127/145}
25b. 2 of {127} must be in R7C4 -> no 7 in R7C4
25c. R7C5 = 7 (hidden single in R7), clean-up: no 3 in R12C5
25d. Naked pair {28} in R12C5, locked for C5 and N2, clean-up: no 5 in R12C4, no 6 in R2C6

26. 8 in 42(8) cage at R4C5 locked in R8C46, locked for R8 and N8 -> R78C1 = [89], clean-up: no 3 in R7C7 (step 20d), no 3 in R9C6 (step 18), no 2 in R9C9
26a. Naked pair {29} in R7C67, locked for R7 -> R7C4 = 5, R6C4 = 4 (step 13), locked for D/, R1C4 = 7, R2C4 = 6, R3C4 = 9, R3C6 = 4, R5C5 = 3, locked for D/, R4C4 = 2, locked for D\, R7C7 = 9, R79C6 = [29], R58C4 = [83], R4C6 = 7, locked for D/, R5C6 = 6, R8C6 = 8

27. 19(3) diagonal cage at R1C9 = {289} -> R2C8 = 9, R1C9 + R3C7 = {28}, locked for N3

28. Naked pair {13} in R7C89, locked for N9, R8C9 = 5 (step 24)

29. 9 in C9 locked in R456C9 = {489} (only remaining combination), locked for C9 and N6 -> R1C9 = 2, R3C7 = 8, R12C5 = [82], R23C1 = [72], R3C3 = 5, R2C2 = 8, R9C9 = 7, R8C8 = 4, R3C89 = [76], R2C9 = 1 (cage sum), R12C3 = [14], R9C23 = [23], R8C3 = 7, R89C5 = [64], R8C7 = 2, R9C78 = [68], R7C89 = [13], R6C1 = 3

30. R456C7 = {137} (only remaining combination) = [317]

and the rest is naked singles

Now to have another try at A116 Mars. I didn't get very far first time.


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PostPosted: Thu Jun 16, 2011 11:40 pm 
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Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Assassin 117 "Hammer Throw" by Ed (August 2008) here
Puzzle Diagram:
Image
Images with "udosuk style Killer Cages" by Børge:
Image     Image
Code: Select, Copy & Paste into solver:
3x3::k:3841:7170:5635:5635:5635:4612:2821:3334:3334:3841:3841:7170:3079:3079:4612:2821:3334:6152:1801:2570:2571:7170:3079:4612:2821:6152:4620:1801:2570:2571:2573:7170:4612:6152:4366:4620:3599:1808:1808:4881:2573:6152:4366:4366:4620:3599:1808:4881:5650:5907:2573:3604:3093:2326:3599:4881:2839:5650:4376:5907:3604:3093:2326:4881:6169:2839:5650:4376:4376:5907:2330:2330:6169:6169:2839:5650:2331:2331:2331:5907:2330:
Solution:
+-------+-------+-------+
| 4 5 6 | 9 7 2 | 1 8 3 |
| 8 3 9 | 5 4 1 | 6 2 7 |
| 2 1 7 | 6 3 8 | 4 9 5 |
+-------+-------+-------+
| 5 9 3 | 1 8 7 | 2 6 4 |
| 7 4 1 | 2 5 6 | 8 3 9 |
| 6 2 8 | 3 9 4 | 5 7 1 |
+-------+-------+-------+
| 1 6 4 | 7 2 3 | 9 5 8 |
| 3 8 5 | 4 6 9 | 7 1 2 |
| 9 7 2 | 8 1 5 | 3 4 6 |
+-------+-------+-------+
Quote:
Ed: Don't know how I managed to find time to make this killer. Can't get enough of the O's.
Solving is quite fun with one reverse spin move :D .
I'm not planning a V2 for A117, but the cage pattern deserves one. I hope that Mike will give us Venus2 after A118 is taken. Though, still have to finish Venus. (Archive note: Nobody posted a V2)
SS(v3.2.1)score = 1.31. Estimated Rating: Easy 1.25.

Joe Casey: Thank you Ed.
Apart from the fault-finding, which is my day-job of course (see A115), I also do the puzzles.
This one was cute, cos it looked impossible, these long spiral cages making innies and outies rather futile. then I found:

Afmob: Thanks Ed for this interesting Assassin! Beautiful cage pattern!
After going through the solving paths of JSudoku and SudokuSolver it seems that the solving path is quite narrow ...
Rating: 1.25.

Andrew: Thanks Ed for a challenging puzzle with an interesting cage pattern!
It took me quite a long time before I spotted the key step which turned out to be fortunate because at that stage ...
I'll rate A117 as a solid 1.25.

udosuk: Afmob's critical move is the most brilliant one, but I think he missed some cleanup moves which could have made the solving path considerably shorter.

Outline by Joe Casey:
Thank you Ed.
Apart from the fault-finding, which is my day-job of course (see A115), I also do the puzzles.
This one was cute, cos it looked impossible, these long spiral cages making innies and outies rather futile.
then I found: .. that in N4 the two 7-cages and the 14-cage allowed very few combinations, and it soon tumbled out from there. So from seeming to be way over 1.25 and needing some of these clever technical tricks I don't understand, instead it gave way to my dumb-ass serendipity 'methods' after all.
Walkthrough by Afmob:
Thanks Ed for this interesting Assassin! Beautiful cage pattern!

After going through the solving paths of JSudoku and SudokuSolver it seems that the solving path is quite narrow and the breakthrough area is the same though I still found different reasons for eliminating candidates. I also got to use some large Outies though it would have been probably easier to regard Innies of R1234 = 13(4) instead of Outies of N12 = 32(5).

A117 Walkthrough:

1. C123
a) 24(3) = {789} locked for N7
b) 7(3) = {124} locked for N4
c) Both 10(2): R3C23 <> 6,8,9
d) 7(2): R3C1 <> 3,5,6
e) 14(3) <> {149/248/356} because R56C1 <> 1,2,4 and R4C1 = (356) blocks {356}
f) 14(3) must have one of (124) -> R7C1 = (124)
g) Hidden Killer triple (789) in 15(3) @ C1 since 14(3) can only have one of (789)
-> R2C2 <> 7,8,9 and 15(3) <> {456}

2. N1236
a) Innies N3 = 21(3) <> 1,2,3
b) Outies N12 = 32(5) = 89{267/357/456} <> 1; 8,9 locked for R4
c) Outies N2 = 35(3+2): R1C23+R2C3 <= 23 because 15(3) @ N1 must have one of (789)
-> R5C56 >= 12 -> R4C6 <> 2
d) Outies N12 = 32(5) = 589{37/46} -> 5 locked for R4

3. C123 !
a) Innies+Outies C123: -18 = R5C4 - (R1C23+R2C3) -> R5C4 <> 6,7,8,9
since R1C23+R2C3 cannot be {789} (step 2c)
b) 19(4) must have one of (789) -> R6C3 = (789)
c) 14(3) must have exactly one of (356), so R4C123 must have two of (356) @ N4
d) ! Outies N12 = 32(5): R4C123 must have two of (356) but they cannot have
3 and 6 -> R4C123 must have 5 -> R4C1 = 5
e) Cage sum: R3C1 = 2
f) 14(3) = 7{16/34} -> 7 locked for C1+N4
g) 24(3) = {789} -> 7 locked for C2
h) 10(2) @ C2 <> 3,8
i) 10(2) @ C3 = [19/46/73]

4. C123
a) Hidden Single: R6C3 = 8 @ N4
b) 9 locked in R4C23 @ N4 for R4
c) Naked triple (124) locked in R356C2 for C2
d) 15(3) can only have one of (356) and R2C2 = (356) -> R12C1 <> 3,6
e) Hidden Single: R2C2 = 3 @ N1 -> R12C1 = 12(2) = {48} locked for C1+N1
f) R3C2 = 1 -> R4C2 = 9, R3C3 = 7, R4C3 = 3
g) Innies N7 = 10(3) = {136} -> R7C1 = 1, R7C2 = 6, R8C1 = 3
h) Cage sum: R5C4 = 2
i) R1C2 = 5

5. R123
a) 22(3) = {679} locked for R1, 7 also locked for N2
b) Outies N2 = 30(2+2): R4C56 = 15(2) = {78} locked for R4+N5 because R12C3 = {69} = 15(2)
c) 28(4) = {5689} -> R4C5 = 8
d) R4C6 = 7
e) Naked triple (679) locked in R1C45+R3C4 for N2
f) 12(3) = 3{18/45} -> R3C5 = 3; R2C4 <> 1

6. R456
a) R5C2 = 4, R5C3 = 1
b) 10(3) = 1{36/45} -> 1 locked for N5
c) 10(3): R4C4+R6C6 <> 5,6 because R5C5 = (56)
d) 2,6 locked in R4C789 @ R4 for N6
e) 14(2) = {59} locked for C7
f) Outies N89 = 159{37/46} because R6C1 = (67) blocks {34567}
-> R6C9 = 1; R6C8 <> 3 because 7 only possible there
g) Cage sum: R7C9 = 8
h) 18(3): R3C9 <> 4,6 because R4C9 = (246)
i) Hidden Single: R4C4 = 1 @ N5

7. N23
a) Innies N3 = 21(3) = 9{48/57} because R3C9 = (59) -> 9 locked for N3
b) Innies N3 = 21(3): R2C9 <> 5,9 because 7 only possible there
c) 9 locked in R3C89 @ N3 for R3
d) R3C4 = 6

8. N689
a) 22(4) = {3478} locked for C4; 7,8 also locked for N8
b) 17(3) = {269} locked for N8, 6 also locked for R8
c) 9(3) must have 3 xor 6 -> R9C9 = (36)
d) 18(3) <> 3 because {369} blocked by R9C9 = (36)
e) 3 locked in 17(3) @ N6 = {368} because R4C8 = (246)
-> R4C8 = 6, {38} locked for R5
f) 24(4): R2C9+R3C8 <> 4 because R4C7 = (24)
g) R2C9 = 7
h) Hidden Single: R6C8 = 7 @ N6 -> R7C8 = 5

9. Rest is singles.

Rating: 1.25. I used some Killer triples.
Walkthrough by Andrew:
Thanks Ed for a challenging puzzle with an interesting cage pattern!

It took me quite a long time before I spotted the key step which turned out to be fortunate because at that stage there was only one remaining combination.

I'll rate A117 as a solid 1.25 even though I found the key step hard to spot but it isn't a difficult move.

Here is my walkthrough. It's a bit different from my normal style because I've made more use of maximum and minimum values for hidden cages.

Prelims

a) R34C1 = {16/25/34}, no 7,8,9
b) R34C2 = {19/28/37/46}, no 5
c) R34C3 = {19/28/37/46}, no 5
d) R67C7 = {59/68}
e) R67C8 = {39/48/57}, no 1,2,6
f) R67C9 = {18/27/36/45}, no 9
g) R1C345 = {589/679}, 9 locked for R1
h) R123C7 = {128/137/146/236/245}, no 9
i) 7(3) cage in N4 = {124}, locked for N4, clean-up: no 3,5,6 in R3C1, no 6,8,9 in R3C23
j) 10(3) diagonal cage in N5 = {127/136/145/235}, no 8,9
k) 24(3) cage in N7 = {789}, locked for N7
l) 9(3) cage in N9 = {126/135/234}, no 7,8,9
m) R9C567 = {126/135/234}, no 7,8,9
n) 28(4) diagonal cage at R1C2 = {4789/5689}, no 1,2,3, CPE no 9 in R2C5

1. 45 rule on N3 3 innies R2C9 + R3C89 = 21 = {489/579/678}, no 1,2,3

2. 45 rule on C1 2 innies R89C1 = 1 outie R2C2 + 9, max R89C1 = 15 -> max R2C2 = 6

3. 45 rule on N47 4(3+1) outies R3C123 + R5C4 = 12, min R3C123 = 6 -> max R5C4 = 6
3a. 19(4) diagonal cage at R5C4 = {1369/1459/1468/1567/2359/2368/2458/2467/3457} (cannot be {1279/1378} because 7,8,9 only in R6C3)
3b. 7,8,9 can only be in R6C3 -> R6C3 = {789}
3c. 5 in N4 locked in R456C1, locked for C1

4. 45 rule on N36 4(3+1) outies R5C6 + R7C789 = 28, max R7C789 = 24 -> min R5C6 = 4
4a. Max R5C6 = 9 -> min R7C789 = 19, no 1, clean-up: no 8 in R6C9

5. R789C3 = {146/236/245}
5a. 45 rule on C3 4 innies R1256C3 = 24 = {1689/2589/4578} (cannot be {2679/4569} which clash with R789C3), 8 locked for C3, clean-up: no 2 in R3C3
5b. 4 of {4578} must be in R5C3 -> no 4 in R2C3
5c. Hidden killer pair 7,9 in R1256C3 and R34C3 for C3 -> R34C3 must contain one of 7,9 = {19/37}, no 4,6

6. Hidden killer triple 7,8 9 in R12C1, R567C1 and R9C1 for C1, R12C1 and R567C1 cannot have more than one of 7,8,9 -> R12C1 and R567C1 must each have one of 7,8,9
6a. R567C1 = {158/167/239/257/347} (cannot be {149/248} because 1,2,4 only in R7C1, cannot be {356} which doesn’t contain 7,8 or 9)
6b. 1,2,4 can only be in R7C1 -> R7C1 = {124}
6c. 2 locked in R7C1 + R789C3, locked for N7

7. 45 rule on N2 5 outies R1C23 + R2C3 + R4C56 = 35
7a. R12C1 must contain one of 7,8,9 (step 6) -> max R1C23 + R2C3 = 23 (because R12C1 must contain one of 7,8,9) -> min R4C56 = 12, no 1,2 in R4C6
7b. Max R1C23 + R2C3 + 15(3) cage = 38 -> min R3C123 = 7 -> max R5C4 = 5 (step 3)

8. 45 rule on N7 3 innies R7C12 + R8C1 = 10 = {136/145/235}
8a. 1 of {136} must be in R7C1, 5 of {145} must be in R7C2 -> no 1,4 in R7C2
8b. R7C2 + R8C1 = [36/51/53/54/63]

9. 19(4) diagonal cage at R5C4 (step 3a) = {1369/1459/2359/2368/2458/3457} (cannot be {1468/1567/2467} which clash with R7C2 + R8C1
9a. 5 of {1369/1459/2359/2458/3457} must be in R7C2 (5 in R5C4 doesn’t give valid permutations for R7C2 + R8C1) -> no 5 in R5C4

10. R567C1 = {158/167/257/347} (cannot be {239} which clashes with R7C12 + R8C1), no 9

11. 45 rule on R1234 4 outies R5C6789 = 1 innie R4C4 + 25
11a. Min R5C6789 = 26, no 1
11b. Max R5C6789 = 30 -> max R4C4 = 5

12. Max R5C4 = 4 -> min R3C123 = 8 (step 3) -> max R4C123 = 19 (R34C123 = 27)
12a. 45 rule on N12 5 outies R4C12356 = 32 = {35789} (cannot be {45689} because max R4C123 = 19, no 4 in R4C123 and no 5,6,8 in R4C3), locked for R4, clean-up: no 1 in R3C1, no 4 in R3C2
12b. 6 in N4 locked in R56C1, locked for C1
12c. 6 in R4 locked in R4C789, locked for N6, clean-up: no 8 in R7C7, no 3 in R7C9

13. R567C1(step 10) = {167} (only remaining combination) -> R7C1 = 1, R56C1 = {67}, locked for C1 and N4, clean-up: no 3 in R3C23
13a. 2 in N7 locked in R789C3, locked for C3
13b. 2 in N4 locked in R56C2, locked for C2, clean-up: no 8 in R4C2

14. R34C1 = [25] (cannot be [43] which clashes with R8C1)
14a. Naked pair {39} in R4C23, locked for R4 and N4 -> R6C3 = 8, clean-up: no 6 in R7C7, no 4 in R8C7
14b. Naked pair {17} in R3C23, locked for R3 and N1
14c. R3C123 = 2{17} = 10 -> R5C4 = 2 (step 3)
14d. Naked pair {14} in R5C23, locked for R5 and N4 -> R6C2 = 2, clean-up: no 7 in R7C9
14e. Naked pair {78} in R4C56, locked for N5
14f. Naked pair {59} in R67C7, locked for C7

15. 10(3) diagonal cage in N5 = {136/145}, 1 locked for N5
15a. 5 of {145} must be in R5C5 -> no 5 in R6C6

16. R12C1 must have one of 8,9 (step 6) -> 15(3) cage in N1 = {348} (only remaining combination), locked for N1, 8 locked for C1 -> R9C1 = 9
16a. Naked pair {78} in R89C2, locked for C2 -> R3C23 = [17], R5C23 = [41], R2C2 = 3, R4C23 = [93], clean-up: no 6 in R789C3 (step 5)
16b. Naked triple {245} in R789C3, locked for C3 and N7 -> R7C2 = 6, R8C1 = 3, R1C2 = 5, clean-up: no 8 in R1C45 (prelim g), no 3 in R6C9
16c. Naked triple {679} in R1C345, locked for R1, 7 locked in R1C45 for N2

17. 28(4) diagonal cage at R1C2 = {5689} (only remaining combination) -> R4C5 = 8, R4C6 = 7
17a. Naked triple {679} in R1C45 + R3C4, locked for N2

18. 12(3) cage in N2 = {138/345} -> R3C5 = 3, R2C45 = [45/54/81]
18a. Killer pair 4,8 in R2C1 and R2C45, locked for R2
18b. 2 in N2 locked in R12C6, locked for C6

19. 13(3) cage in N3 = {139/148/238/346} (cannot be {157/256} because 5,6,7 only in R2C8, cannot be {247} which clashes with R2C9 + R3C89), no 5,7
19a. 2 of {238} must be in R2C8 -> no 2 in R1C89
19b. 5 in N3 locked in R2C9 + R3C89 (step 1) = {579} (only remaining combination) -> R2C9 = 7, R3C89 = {59}, locked for R3 and N3 -> R3C4 = 6, R2C3 = 9, R1C3 = 6, clean-up: no 2 in R7C9

20. R123C7 = {128/146} (cannot be {236} because R3C7 only contains 4,8), no 3, 1 locked for C7 and N3
20a. Naked triple {348} in R1C189, locked for R1

21. 24(4) diagonal cage at R2C9 = {2679} (only remaining combination) -> R3C8 = 9, R4C7 = 2, R5C6 = 6, R3C9 = 5, R5C5 = 5, R56C1 = [76], R12C7 = [16], R3C7 = 4 (step 20), R13C6 = [28], R2C6 = 1 (cage sum), R2C45 = [54], R12C1 = [48], R2C8 = 2, R6C5 = 9, R1C45 = [97], R7C5 = 2, clean-up: no 3 in R6C6 (step 15), no 3 in R67C8, no 4 in R67C9

and the rest is naked singles and a cage sum.
Walkthrough by udosuk using Afmob's brilliant critical move:
Afmob's critical move is the most brilliant one, but I think he missed some cleanup moves which could have made the solving path considerably shorter.

Here is a walkthrough based on Afmob's brilliant critical move but using shorter cleanup moves.

Walkthrough for A117 "Hammer Throw"

1. 24/3 @ r8c2={789} (NT @ n7)
7/3 @ r5c2={124} (NT @ n4)
=> 7/2 @ r3c1=[16|25|43]
=> 10/2 @ r3c2=[19|28|37|46|73]
=> 10/2 @ r3c3=[19|28|37|46|73]

2. Killer Hidden Triple @ c1:
Each of 15/3 @ r1c1, 14/3 @ r5c1 & r9c1
can have at most one from {789}
=> Each of r12c1, r56c1 & r9c1
must have exactly one from {789} @ c1

3. Outies @ n2: r1c23+r2c3+r4c56=35
But from (2) r12c1 must have one from {789}
=> Max r1c23+r2c3=6+8+9=23
=> Min r4c56=35-23=12
=> r4c56 must be from {3456789}

4. Outies @ n12: r4c12356 from {3456789}=32
=> r4c12356={(37|46)589} can't have both of {36}

5. Outies @ n47: r3c123+r5c4=12
Min r3c123=1+2+3=6
=> Max r5c4=12-6=6
=> r5c4 must be from {123456}

6. 19/4 @ r5c4 must have at least one from {789}
(max total from {123456}=3+4+5+6=18)
Now r5c4+r7c2+r8c1 all from {123456}
=> r6c3 must be from {789}

7. Killer Hidden Triple @ n4:
From (1,2,6) each of r4c23, r56c1 & r6c3
must have exactly one from {789} @ n4
=> r4c123 must have exactly two from {356}

8. But from (4) r4c123 can't have both of {36}
=> r4c123 must have 5
=> r4c1=5 (only possible 5 @ r4c123)
=> 7/2 @ r3c1=[25]
=> 10/2 @ r3c2=[19|37|46|73]
=> 10/2 @ r3c3=[19|37|46|73]

9. 14/3 @ r5c1 can't be {158|248|239} since r34c1=[25]
It also can't be {149} since r56c1 has none of {14}
=> 14/3 @ r5c1 can't have {89}
=> 14/3 @ r5c1 from {13467}={(16|34)7}
=> 7 @ c1,n4 locked @ r56c1
=> 7 @ c2,n7 locked @ r89c2

10. HS @ n4: r6c3=8
=> 9 @ r4,n4 locked @ r4c23
=> One of the 10/2 @ r34c23 must be [19]
=> 1 @ r3,n1 locked @ r3c23

11. 15/3 @ r1c1 from {345689}={(38|56}4} (4 @ n1 locked)
=> 10/2 @ r3c2 from {1369}=[19]
=> 10/2 @ r3c3 from {367}=[73]
=> From (4): r4c56=32-5-9-3=15={78} (NP @ r4,n5)
=> From (5): r5c4=12-2-1-7=2
=> r5c23+r6c2=[412]

12. Outies @ n89: r6c45789=25
=> Innies @ r6: r6c16=10=[64|73]
=> 10/3 @ r4c4 from {134569}={1(36|45)}
=> r4c4=1, r5c5+r6c6=[54|63]

13. Outies @ r6789: r4c4+r5c12345=20
=> r5c15=20-1-4-1-2=12 from {567}=[75]
=> From (12): r6c16=[64]
=> r6c45={39} (NP @ r6,n5)
=> r5c6=6

14. 14/2 @ r6c7=[59]
=> 12/2 @ r6c8=[75]
=> 9/2 @ r6c9=[18]

15. r5c78 from {389} can't sum to 13|15
=> 17/3 @ r4c8: r4c8 can't be 4|2, must be 6
=> 17/3 @ r4c8: r5c78=17-6=11={38} (NP @ r5)
=> r5c9=9
=> 18/3 @ r3c9: r34c9=18-9=9=[54]
=> r5c7=2
=> 24/4 @ r2c9: r2c9+r3c8=24-2-6=16=[79]

16. 11/3 @ r1c7 from {13468}={146} (NT @ c7,n3)
=> 9/3 @ r9c5: r9c7 can't have 7
=> r89c7=[73]
=> 23/4 @ r6c5: r6c5+r7c6+r9c8=23-7=16 from {12349}=[934]
=> 9/3 @ r9c5: r9c56=9-3=6=[15]
=> r78c2=[68]
=> r78c5 from {2467} can't sum to 15
=> 17/3 @ r7c5: r8c6 can't be 2, must be 9
=> 17/3 @ r7c5: r78c5=17-9=8=[26]

All naked singles from here.


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PostPosted: Fri Jun 17, 2011 12:41 am 
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Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Assassin 118 by Jean-Christophe (August 2008) here
Puzzle Diagram:
Image
Images with "udosuk style Killer Cages" by Børge:
Image     Image
Code: Select, Copy & Paste into solver:
3x3::k:2049:2049:3074:3074:6403:6403:3588:3588:5381:4614:2055:2055:6403:6403:5640:5381:5381:5381:4614:4614:2313:2313:6403:5640:2570:2827:5381:5132:5132:9229:2313:5640:5640:2570:2827:2827:5132:5132:9229:9229:9229:9229:9229:6414:6414:3855:3855:3088:4369:4369:3346:9229:6414:6414:5395:3855:3088:4369:7956:3346:3346:4629:4629:5395:5395:5395:4369:7956:7956:2838:2838:4629:5395:3095:3095:7956:7956:2072:2072:2073:2073:
Solution:
+-------+-------+-------+
| 7 1 8 | 4 2 6 | 5 9 3 |
| 5 6 2 | 3 9 8 | 4 7 1 |
| 4 9 3 | 1 5 7 | 2 8 6 |
+-------+-------+-------+
| 6 7 9 | 5 3 4 | 8 1 2 |
| 3 4 1 | 7 8 2 | 6 5 9 |
| 8 2 5 | 6 1 9 | 3 4 7 |
+-------+-------+-------+
| 9 5 7 | 2 4 3 | 1 6 8 |
| 1 3 6 | 8 7 5 | 9 2 4 |
| 2 8 4 | 9 6 1 | 7 3 5 |
+-------+-------+-------+
Quote:
Jean-Christophe: SSolver 3.2.1 Rating: 1.29.

Afmob: Thanks JC for this fun Killer! You really had to look for ..
Rating: 1.25.

Jean-Christophe: My idea for this cage template [Hint]

Andrew: I'll rate my solution as 1.25. It's probably a bit more difficult than Afmob's but not sufficiently so to rate it as Hard 1.25.
(and on Jean-Christophe's cage template) That's a very interesting concept although I wouldn't have called it a Hint. I went through my walkthrough again and Afmob's one after reading the concept and I can't see how it could help to reach the breakthrough any quicker. However that doesn't detract from it being an interesting cage pattern concept.

azpaull: I just finished 118 - it seemed like it took me hours before I finally found the key. Thanks for the fun puzzle, J-C! (At first, it looked like it should be easy, but, wow!) As I felt I should have found it sooner, I'll rate it a hard 1.0.

Walkthrough by Afmob:
Thanks JC for this fun Killer! You really had to look for Hidden Cages to solve this one and spotting and using some Killer subsets helped too.

A118 Walkthrough:

1. R1234
a) Innies = 22(3) = 9{58/67} -> 9 locked for R4+N4
b) Innies N1 = 11(2) = [56/74/83/92]
c) 12(2): R1C4 <> 8,9
d) Innies N3 = 10(2) <> 5; R3C7 <> 1
e) Outies N3 = 11(3)

2. R6789
a) 12(2) @ R6C3: R7C3 <> 3
b) Innies N7 = 12(2): R7C3 <> 1,2,6,9
c) Innies N9 = 8(2) <> 4,8,9
d) Outies N7 = 15(3)
e) Innies R6789 = 14(3)

3. R456
a) Using Outies N3 and Innies R6789: Innies N6 = 20(3) <> 1,2
b) Using Outies N7 and Innies R1234: Innies N4 = 8(3) = 1{25/34}
-> 1 locked for R5+N4
c) Innies N47 = 10(2) <> 5
d) Innies N36 = 9(2) <> 9; R6C7 <> 7,8

4. R123 !
a) ! 12(2) <> {57} because 8(2) @ R1 and 14(2) must have two of (567)
b) Innies N1 = 11(2): R3C3 <> 4,6
c) 4 locked in 18(3) @ N1 = 4{59/68}
d) Outies N1 = 10(3): R34C4 <> 3,4 because R1C4 = (34)
e) 9(3) = 1{26/35} -> 1 locked for C4
f) 9(3): R34C4 <> 2 because R3C3 = (23)

5. N47
a) Innies N47 = 10(2) <> {28} since it's a Killer pair of Innies N1
b) 12(2) @ N4 <> {39} because it's a Killer pair of Innies N1
c) Innies N7 = 12(2) <> 3
d) OUties N7 = 15(3) <> 5{37/46} because those combos blocked by Killer pairs (35,45) of Innies N4
e) 15(3) <> 5{37/46} because R6C3 = R7C2 (Innies+Outies N7)

6. C123+R9 !
a) 12(2) @ R9 <> {57} since two of (567) already at both 8(2) @ R9
b) Outies C12 = 12(3) <> 7 because {147} blocked by Killer pair (47) of 12(2) @ N4
and {237} blocked by R3C3 = (23)
c) 8(2) @ R2C2: R2C2 <> 1
d) Outies C12 = 12(3) = {129/138/246/345} because R9C3 <> 1,5,6
e) ! Killer pair (23) locked in Outies C12 + R3C3 for C3
f) Innies N47 = 10(2) <> 7
g) 7 locked in 12(2) @ R6C3 @ C3 -> 12(2) = {57} locked for C3
h) 8(2) @ R2C2 <> 3
i) Innies N7 = 12(2) = {57} locked for R7+N7
j) 15(3) = 2{58/67} because R7C2 = (57) -> 2 locked for R6+N6; R6C12 <> 5,7

7. R456
a) Innies N4 = 8(3) = {134} locked for R4
b) 2 locked in 36(7) @ R5 for N5 -> 36(7) = 279{1368/1458/3456}
-> 7 locked for R5
c) Innies N36 = 9(2) = [54/63/81]
d) Innies N6 = 20(3) = {569} locked for R5+N6
e) Hidden Single: R4C3 = 9 @ 36(7)
f) Innie N47 = R5C3 = 1
g) R1C3 = 8 -> R1C4 = 4

8. R123
a) Innie N1 = R3C3 = 3
b) R9C3 = 4 -> R9C2 = 8
c) 14(2) = {59} locked for R1+N3
d) Innies N3 = 10(2) = {28/46}

9. C789
a) 10(2) = {28} locked for C7 since (46) is a Killer pair of Innies N36
b) Innies N9 = 8(2) = {17} because (35) is a Killer pair of Innies N36
-> R7C7 = 1, R9C7 = 7
c) Innies R6789 = 14(3) = {347} locked for R6+N6
d) 13(3) = 1{39/48} -> R67C6 = [84/93]
e) Innies N3 = 10(2) = {28} locked for R3+N3

10. N25
a) Hidden pair (34) in R4C56 for N5 -> R4C56 = {34} locked for 22(4)
b) 22(4) = 34{69/78}; R2C6 <> 7
c) Outies N12 = 12(3) = {345} -> R4C4 = 5
d) Cage sum: R3C4 = 1
e) Hidden Single: R6C5 = 1 @ N5, R6C4 = 6 @ N5, R6C6 = 9 @ N5
f) Cage sum: R7C6 = 3
g) 17(4) = {1268} -> 2,8 locked for C4+N8

11. N9
a) 11(2) = [38/92] because (56) is a Killer pair of 8(2) @ R9C8
b) 4 locked in 18(3) = 4{59/68}

12. Rest is singles.

Rating: 1.25. I used Killer triples.
Jean-Christophe's Idea for the Cage Template:
My idea for this cage template

[Hint] Almost Law of Leftovers on r5 -> r5c1289 = r4c3+r6c7+9
r4c3,r6c7 is a subset of r5c1289
IOW: whichever digit goes in r4c3 is locked in r5c89 for r5, n6; in r6c456 for n5, r6
Similarly for r6c7
Whichever digit cannot go in r5c1289, cannot go in r4c3,r6c7 either

Note: the v0.9 can be unlocked by some kakuro-like moves in crossing hidden cages:
r5c789=12, r56c7=7 -> r5c89 <> 5 (12-7)
5 @ c3 locked @ r456c3 for n4
Almost LoL @ r5 -> r4c3,r6c7 <> 5
Walkthrough by Andrew:
I finished A118 yesterday evening but I only went through Afmob's walkthrough today.

Afmob wrote:
You really had to look for Hidden Cages to solve this one and spotting and using some Killer subsets helped too.
There are plenty of Hidden Cages in this cage pattern, many of which were very helpful for solving A118.

I'll rate my solution as 1.25. It's probably a bit more difficult than Afmob's but not sufficiently so to rate it as Hard 1.25.

Here is my walkthrough. Thanks Afmob for pointing out that I should have given "no 5" in step 20a; it has therefore been deleted from step 25b.

Prelims

a) R1C12 = {17/26/35}, no 4,8,9
b) R1C34 = {39/48/57}, no 1,2,6
c) R1C78 = {59/68}
d) R2C23 = {17/26/35}, no 4,8,9
e) R34C7 = {19/28/37/46}, no 5
f) R67C3 = {39/48/57}, no 1,2,6
g) R8C78 = {29/38/47/56}, no 1
h) R9C23 = {39/48/57}, no 1,2,6
i) R9C67 = {17/26/35}, no 4,8,9
j) R9C89 = {17/26/35}, no 4,8,9
k) 9(3) cage at R3C3 = {126/135/234}, no 7,8,9
l) 11(3) cage at R3C8 = {128/137/146/236/245}, no 9
m) 36(7) cage at R4C3 must contain 9
n) 31(5) cage in N8 must contain 9, locked for N8

1. 45 rule on R1 3 innies R1C569 = 11 = {128/137/146/236/245}, no 9

2. 9 in R1 locked in R1C3478
2a. Combined cage R1C3478 = 26 = {3689/4589} (cannot be {4679} which clashes with R1C78}), no 7, 8 locked for R1, clean-up: no 5 in R1C34
2b. R1C569 (step 1) = {137/146/236/245}
2c. Killer pair 3,4 in R1C34 and R1C569, locked for R1, clean-up: no 5 in R1C12

3. 45 rule on N1 2 innies R13C3 = 11 = [83/92], clean-up: no 8,9 in R1C4

4. 45 rule on N1 3 outies R134C4 = 10 = {136/145} (cannot be {235} because 9(3) cage at R3C3 cannot be {225}), no 2, 1 locked for C4
4a. R1C4 = {34} -> no 3,4 in R34C4
[If preferred, step 4 can be done in two separate steps using R134C4 = {136/145/235} and then 9(3) cage at R3C3 to eliminate 2 from R34C4.]

5. 4 in N1 locked in 18(3) cage = {459/468}, no 1,2,3,7

6. 45 rule on R1234 3 innies R4C123 = 22 = {589/679}, 9 locked for R4 and N4, clean-up: no 1 in R3C7, no 3 in R7C3

7. 45 rule on N12 3 outies R4C456 = 12 = {138/147/246/345} (cannot be {156} which clashes with R4C123, cannot be {237} because R4C4 only contains 1,5,6)
7a. R4C4 = {156} -> no 1,5,6 in R4C56

8. 45 rule on N47 2 innies R45C3 = 10 = [64/73/82/91], no 5, no 6,7,8 in R5C3

9. 45 rule on N36 2 innies R56C7 = 9 = {18/27/36/45}, no 9

10. 45 rule on N3 2 innies R3C78 = 10 = {28/37/46}/[91], no 5 in R3C8

11. 45 rule on N7 2 innies R7C23 = 12 = [39]/{48/57}, no 1,2,6,9 in R7C2

12. 45 rule on N9 2 innies R79C7 = 8 = {17/26/35}, no 4,8,9 in R7C7

13. 45 rule on N12 2 innies R23C6 = 1 outie R4C4 + 10 -> min R23C6 = 11, no 1

14. 45 rule on N7 3 outies R6C123 = 15, R4C123 (step 7) = 22 -> R5C123 = 8 = {125/134}, 1 locked for R5 and N4, clean-up: no 8 in R6C7 (step 9)

15. 45 rule on N3 3 outies R4C789 = 11
15a. 45 rule on R6789 3 innies R6C789 = 14 -> R5C789 = 20 = {389/479/569/578}, no 2, clean-up: no 7 in R6C7 (step 9)

16. R6C123 = 15 (step 14) = {258/267/348} (cannot be {357/456} which clash with R4C123)
16a. 7 of {267} must be in R6C3 -> no 7 in R6C12

17. 20(4) cage at R5C1 = {1379/1469/2567/3458/3467} (cannot be {1289} because no 5 in R45C3, cannot be {1478/1568} which clash with R4C123, cannot be {2369/2378/2459/2468} which clash with R5C123)
17a. R4C12 cannot be {59} -> no 8 in R4C3 (step 6), clean-up: no 2 in R5C3 (step 8)

18. 45 rule on C12 3 outies R289C3 = 12 = {129/138/156/246/345} (cannot be {147} which clashes with R45C3, cannot be {237} which clashes with R3C3), no 7, clean-up: no 1 in R2C2, no 5 in R9C2
18a. 9 of {129} must be in R9C3 -> no 9 in R8C3

19. 45 rule on C89 2 innies R18C8 = 1 outie R2C7 + 7, IOU no 7 in R8C8, clean-up: no 4 in R8C7
[The same result is achieved with 45 rule on C89 2 outies R28C7 = 1 innie R1C8 + 4, IOU no 4 in R8C7, clean-up: no 7 in R8C8]

20. 45 rule on N89 3 outies R6C456 = 16, R4C456 = 12 (step 7) -> R5C456 = 17
[Alternatively R45C3 = 10 (step 8), R56C7 = 9 (step 9) -> R5C456 = 17]
20a. R5C456 = {269/278/368/467} (cannot be {359/458} which clash with R5C123), no 5
20b. 36(7) cage at R4C3 = {1236789/1245789/1345689/2345679} with 9 in R4C3 or R5C456 -> R45C3 = [73/91] (cannot be [64] which clashes with R5C456 = {269}), no 6 in R4C3, no 4 in R5C3
20c. R5C456 (step 20a) = {269/278/368} (cannot be {467} because R45C3 cannot be [93]), no 4
20d. R5C789 (step 15a) = {479/569/578} (cannot be {389} which clashes with R5C456), no 3, clean-up: no 6 in R6C7 (step 9)

21. Killer triple 7,8,9 in R1C3, R4C3 and R67C3, locked for C3, clean-up: no 3,4 in R9C2

22. R4C456 (step 7) = {138/147/345} (cannot be {246} which clashes with R5C456}, no 2,6

23. 2 in R4 locked in R4C789, locked for N6, clean-up: no 7 in R5C7 (step 9)
23a. R4C789 = 11 (step 15) = {128/236/245}, no 7, clean-up: no 3 in R3C7, no 7 in R3C8 (step 10)

24. 45 rule on R9 3 innies R9C145 = 17 = {179/269/359/458} (cannot be {278/368/467} which are blocked by the two 8(2) cages)
24a. Hidden killer pair 8,9 in R9C145 and R9C2 -> R9C2 must have one of 8,9 -> R9C23 = [84/93], no 5,7

25. 6 in C3 locked in R28C3
25a. R289C3 (step 18) = {246} (only remaining combination, cannot be {156} because R9C3 only contains 3,4) -> R9C3 = 4, R9C2 = 8, R28C3 = {26}, locked for C3 -> R3C3 = 3, R5C3 = 1, R1C3 = 8 (step 3), R1C4 = 4, R4C3 = 9 (step 8), clean-up: no 6 in R1C78, no 6 in 18(3) cage in N1 (step 5), no 5,7 in R2C2, no 6 in R3C4 (step 4), no 7 in R3C7 (step 10), no 5 in R4C1 (step 6), no 3 in R4C7, no 8 in R5C7 (step 9), no 3 in R7C2 (step 11)
25b. R5C456 (step 20c) = {278/368}, 8 locked for R5 and N5
25c. 9 in R5 locked in R5C89, locked for N6

26. Naked pair {26} in R2C23, locked for R2 and N1
26a. Naked pair {17} in R1C12 , locked for R1
26b. Naked pair {59} in R1C78, locked for R1 and N3, clean-up: no 1 in R3C8 (step 10), no 1 in R4C7
26c. Naked pair {15} in R34C4, locked for C4

27. R4C456 (step 22) = {147/345}, 4 locked for R4 and N5, clean-up: no 6 in R3C7, no 4 in R3C8 (step 10), no 5 in R4C89 (step 23a)

28. R6C123 (step 16) = {258/267} (cannot be {348} because R6C3 only contains 5,7}, no 3,4, 2 locked for R6 and N4, clean-up: no 5 in R5C12 (step 14)
28a. 5 of {258} must be in R6C3 -> no 5 in R6C12

29. Naked pair {34} in R5C12, locked for R5, clean-up: no 6 in R5C456 (step 25b), no 7 in R5C89 (step 15a), no 5 in R6C7 (step 9)
29a. Naked triple {278} in R5C456, locked for N5, clean-up: no 1 in R4C4 (step 27)
29b. R34C4 = [15], clean-up: no 8 in R4C1 (step 6)

30. Naked pair {67} in R4C12, locked for R4 and N4 -> R6C123 = [825], R7C23 = [57], R2C23 = [62], R8C3 = 6, R5C12 = [67], R1C12 = [71], clean-up: no 4 in R3C7, no 6 in R3C8 (step 10), no 5 in R8C78, no 1,3 in R9C7 (step 12), no 5,7 in R9C6

31. Naked pair {34} in R4C56, locked for R4, N5 and 22(4) cage at R2C6
31a. Naked triple {169} in R6C456, locked for R6

32. Naked pair {28} in R3C78, locked for R3 and N3
32a. Naked pair {28} in R34C7, locked for C7, clean-up: no 6 in R79C7 (step 12) , no 3,9 in R8C8, no 2,6 in R9C6
32b. 6 in N3 locked in R13C9, locked for C9, clean-up: no 2 in R9C8

33. R5C7 = 6 (hidden single in C7), R6C7 = 3 (step 9), R7C7 = 1, R9C7 = 7 (step 12), R9C6 = 1, R2C7 = 4, R8C7 = 9, R8C8 = 2, R1C78 = [59], R3C78 = [28], R4C7 = 8, R4C89 = [12], R5C89 = [59], R8C12 = [13], R5C12 = [34], R3C2 = 9, R23C1 = [54], clean-up: no 6 in R9C8, no 3 in R9C9
33a. R9C89 = [35], R2C8 = 7, R123C9 = [316], R6C89 = [47], R7C8 = 6

34. 45 rule on N2 2 remaining innies R23C6 = 15 = [87], R3C5 = 5, R5C6 = 2, R1C56 = [26], R6C6 = 9, R6C45 = [61], R7C6 = 3 (cage sum), R4C56 = [34], R2C45 = [39], R8C6 = 5, R9C5 = 6

35. 45 rule on N8 2 remaining innies R78C4 = 10 = [28]

and the rest is naked singles

Jean-Christophe wrote:
My idea for this cage template
[Hint]Almost Law of Leftovers on r5 -> r5c1289 = r4c3+r6c7+9
r4c3,r6c7 is a subset of r5c1289
IOW: whichever digit goes in r4c3 is locked in r5c89 for r5, n6; in r6c456 for n5, r6
Similarly for r6c7
Whichever digit cannot go in r5c1289, cannot go in r4c3,r6c7 either
That's a very interesting concept although I wouldn't have called it a Hint. I went through my walkthrough again and Afmob's one after reading the concept and I can't see how it could help to reach the breakthrough any quicker. However that doesn't detract from it being an interesting cage pattern concept.


Last edited by Andrew on Fri Jun 17, 2011 8:59 pm, edited 1 time in total.

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PostPosted: Fri Jun 17, 2011 2:43 am 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Assassin 118 V0.9 by Jean-Christophe (August 2008) here
Puzzle Diagram:
Image
Images with "udosuk style Killer Cages" by Børge:
Image     Image
Code: Select, Copy & Paste into solver:
3x3::k:2305:2305:2818:2818:5635:5635:3844:3844:5381:4102:3847:3847:5635:5635:4616:5381:5381:5381:4102:4102:3081:3081:5635:4616:2570:3851:5381:5388:5388:8973:3081:4616:4616:2570:3851:3851:5388:5388:8973:8973:8973:8973:8973:5646:5646:4623:4623:2320:4369:4369:4370:8973:5646:5646:5651:4623:2320:4369:6420:4370:4370:4373:4373:5651:5651:5651:4369:6420:6420:2326:2326:4373:5651:3351:3351:6420:6420:1304:1304:2841:2841:
Solution:
+-------+-------+-------+
| 5 4 3 | 8 7 1 | 9 6 2 |
| 1 8 7 | 2 9 6 | 5 4 3 |
| 6 9 2 | 4 3 5 | 8 1 7 |
+-------+-------+-------+
| 8 7 1 | 6 4 3 | 2 9 5 |
| 4 2 6 | 7 5 9 | 3 8 1 |
| 9 3 5 | 1 2 8 | 4 7 6 |
+-------+-------+-------+
| 3 6 4 | 9 1 2 | 7 5 8 |
| 2 1 9 | 5 8 7 | 6 3 4 |
| 7 5 8 | 3 6 4 | 1 2 9 |
+-------+-------+-------+
Quote:
Jean-Christophe: An easier version 0.9
SSolver 3.2.1 Rating: 0.92.

udosuk: For a while I thought v0.9 was almost as hard as v1, if not harder. :rambo:
But then I worked out this 10-short-step walkthrough, with some very tidy analysis. :dude:
I'll give it a rating of 1.0 (easy). :ugeek:

Jean-Christophe: My idea for this cage template [Hint]

Andrew: Thanks J-C for another fun puzzle.
udosuk wrote:
For a while I thought v0.9 was almost as hard as v1, if not harder.
I thought the same at first.
I'll rate my solution as Hard 1.0; that may even be a bit too low.

udosuk: Using JC's cage template tips, here is another walkthrough for v0.9 which is one step shorter. The trickiest moves are similar in terms of difficulty though so same rating.

Walkthrough by udosuk:
For a while I thought v0.9 was almost as hard as v1, if not harder. :rambo:

But then I worked out this 10-short-step walkthrough, with some very tidy analysis. :dude:

My complete walkthrough for A118 v0.9.

1. Innies @ n1: r13c3=5={14|23} has 3|4
Innies @ n47: r45c3=7={16|25} (can't be {34} for r13c3)
Outies @ c12: r289c3=24={789} (NT @ c3)
=> 9/2 @ r6c3={36|45}
Innies @ n7: r7c23=10=[46|64|73]
=> 9/2 @ r6c3=[36|54|63]
=> 5 @ c3,n4 locked @ r456c3

2. Outies @ n7: r6c123=17
r6c123 can't be {179|278} with r6c3 from {356}
r6c123 can't be {269} since r45c3={16|25} has 2|6
=> r6c12 can't have {12}
18/3 @ r6c1 from {346789} can't be {477}
=> r6c12 can't have 7
Now r6c123=17 from {345689}={359|368|458}

3. Innies @ n36: r56c7=7={16|25|34}
35/7 @ r4c3: r5c456=35-7-7=21={489|579|678}
Now r45c3,r5c456,r56c7 each must have one of {456}
=> {456} locked @ 35/7 @ r4c3
=> 4 locked @ r5c456+r56c7
=> r5c89 can't have 4

4. Outies @ n3: r4c789=16
Innies @ r6789: r6c789=17
=> Innies @ n6: r5c789=12
r6c789 can't be {359} since r6c123=17 has 3|5
r6c789 can't be {368} since r6c123=17 has 3|8
=> r6c789 can't have 3
=> r56c7=7: r5c7 can't be 4
=> r5c789=12 without 4 can't be {345}, must have 1|2

5. Innies @ r1234: r4c123=16
Innies @ n4: r5c123=12
r5c123 can't be {129} since r5c789=12 has 1|2
r5c123 can't be {138} since r6c123=17 has 3|8
r5c123 can't be {147} since r5c456=21 has 4|7
r5c123 can't be {156} since r6c123=17 has 5|6
=> r5c123 can't have 1

6. Now 1 @ r4,n4 locked @ r4c123=16={169|178}
=> r45c3=7=[16] (no elsewhere @ 35/7)
=> r5c12=12-6=6 from {234789}={24} (NP @ r5,n4)
=> r5c456=21 from {5789}={579} (NT @ r5,n5)
=> r56c7=7=[34]
=> r5c89={18} (NP @ r5,n6)

7. 9/2 @ r6c3 from {345}=[54]
=> r6c12=17-5=12 from {389}={39} (NP @ r6,n4)
=> r7c2=10-4=6
=> 13/2 @ r9c2 from {1235789}=[58]
=> 15/2 @ r2c2 from {1234789}=[87]

8. 5/2 @ r9c6=[32|41]
Innies @ n9: r79c7=8 from {125789}=[71]
=> 5/2 @ r9c6: r9c6=5-1=4
=> 10/2 @ r3c7 from {25689}=[82]
Innies @ n3: r3c8=1
=> r5c89=[81]

9. 15/2 @ r1c7 from {2345679}={69} (NP @ r1,n3)
=> r2c7=5, 9/2 @ r1c1 from {12345}=[54], 11/2 @ r1c3=[38]
=> r38c3=[29], 9/2 @ r8c7=[63]
=> r3c12=[69], r9c89={29} (NP @ r9,n9)
=> r7c89=[58]

10. Innies @ n8: r7c46+r8c4=16 from {123579}={259}
=> r7c46={29} (NP @ r7,n8)
=> r8c4=5
17/4 @ r6c4: r6c45+r7c4=17-5=12 from {12689}={129}
=> r6c45={12} (NP @ r6,17/4)
=> r57c4=[79]
12/2 @ r3c3: r34c4=12-2=10 from {346}=[46]

All naked singles from here.

I'll give it a rating of 1.0 (easy), with the trickiest moves (pointing cells, cage blocking) in steps 3-5. :ugeek:
Jean-Christophe's Idea for the Cage Template:
My idea for this cage template

[Hint] Almost Law of Leftovers on r5 -> r5c1289 = r4c3+r6c7+9
r4c3,r6c7 is a subset of r5c1289
IOW: whichever digit goes in r4c3 is locked in r5c89 for r5, n6; in r6c456 for n5, r6
Similarly for r6c7
Whichever digit cannot go in r5c1289, cannot go in r4c3,r6c7 either

Note: the v0.9 can be unlocked by some kakuro-like moves in crossing hidden cages:
r5c789=12, r56c7=7 -> r5c89 <> 5 (12-7)
5 @ c3 locked @ r456c3 for n4
Almost LoL @ r5 -> r4c3,r6c7 <> 5
Walkthrough by Andrew:
Thanks J-C for another fun puzzle.

udosuk wrote:
For a while I thought v0.9 was almost as hard as v1, if not harder.
I thought the same at first.

udosuk wrote:
But then I worked out this 10-short-step walkthrough, with some very tidy analysis.
This made better use of the interactions between the hidden cages than in my solution.

I had to work a bit harder so I'll rate my solution as Hard 1.0; that may even be a bit too low.

Here is my walkthrough for V0.9.

Prelims

a) R1C12 = {18/27/36/45}, no 9
b) R1C34 = {29/38/47/56}, no 1
c) R1C78 = {69/78}
d) R2C23 = {69/78}
e) R34C7 = {19/28/37/46}, no 5
f) R67C3 = {18/27/36/45}, no 9
g) R8C78 = {18/27/36/45}, no 9
h) R9C23 = {49/58/67}, no 1,2,3
i) R9C67 = {14/23}
j) R9C89 = {29/38/47/56}, no 1
k) 35(7) cage at R4C3 must contain 5

1. 45 rule on R1 3 innies R1C569 = 10 = {127/136/145/235}, no 8,9

2. 45 rule on N1 2 innies R13C3 = 5 = [23/32/41], clean-up: R1C4 = {789}

3. 45 rule on N9 2 innies R79C7 = 8 = [53/62/71], clean-up: no 1 in R9C6

4. 45 rule on N3 2 innies R3C78 = 9 = {18/27/36}/[45], no 9, no 4 in R3C8, clean-up: no 1 in R4C7

5. 45 rule on N7 2 innies R7C23 = 10 = {28/37/46}/[91], no 5, no 1 in R7C2, clean-up: no 4 in R6C6

6. 45 rule on N47 2 innies R45C3 = 7 = {16/25} (cannot be {34} which clashes with R13C3)
6a. Killer pair 1,2 in R13C3 and R45C3, locked for C3, clean-up: no 7,8 in R67C3, no 2,3,8,9 in R7C2 (step 5)
6b. Killer pair 5,6 in R45C3 and R67C3, locked for C3, clean-up: no 9 in R2C2, no 7,8 in R9C2

7. 45 rule on N36 2 innies R56C7 = 7 = {16/25/34}
7a. R45C3 = 7, R56C7 = 7 -> R5C456 = 21 = {489/579/678}, no 1,2,3
7b. 4,5,6 locked in 35(7) cage at R4C3 = {1245689/1345679/2345678}
[Here I missed CPE no 4 in R5C89.]

8. 45 rule on N89 3 outies R6C456 = 11 = {128/137/146/236/245}, no 9

9. Hidden triple {789} in R289C3, clean-up: no 9 in R9C2
[And here I missed 5 in C3 locked in R456C3, locked for N4 which would have simplified analysis of R6C123 and 18(3) cage at R6C1.]

10. 45 rule on C89 3 outies R128C7 = 20 = {389/479/569/578}, no 1,2, clean-up: no 7,8 in R8C8

11. 1,2 in N7 locked in 22(5) cage = {12379/12469/12568} (cannot be {12478} which clashes with R7C23)
11a. R9C23 = [49/58] (cannot be [67] which clashes with 22(5) cage), no 6,7

[At this stage I spotted that because there are two 12(3) hidden cages in R5 (see steps 14 and 15) this might limit how they can be paired. Initially I incorrectly thought that there were only two such pairs but on checking I found that there are three pairs so at least one pair has to be eliminated.]

12. 45 rule on N7 3 outies R6C123 = 17 = {359/368/458} (cannot be {179/278} because R6C3 only contains 3,5,6, cannot be {269} which clashes with R45C3, cannot be {467} because 18(3) cage at R6C1 would be {47}7), no 1,2,7
12a. Killer pair 5,6 in R45C3 and R6C123, locked for N4

13. 7 in N4 locked in 21(4) cage = {1479/2379/2478}

14. 45 rule on R1234 3 innies R4C123 = 16, R6C123 (step 12) = 17 -> R5C123 = 12
14a. R5C123 = {129/246} (cannot be {138} because 21(4) cage doesn’t contain both of 3,8, cannot be {147} which clashes with R5C456, cannot be {156} because 5,6 only in R5C3, cannot be {237} because no 3 in R5C3 leading to clash with 21(4) cage, cannot be {345} because 21(4) cage doesn’t contain both of 3,4), no 3,5,7,8, 2 locked for R5 and N4, clean-up: no 5 in R6C7 (step 7)

15. 45 rule on N3 3 outies R4C789 = 16, 45 rule on R6789 3 innies R6C789 = 17 -> R5C789 = 12
15a. 3 in R5 locked in R5C789, locked for N6, clean-up: no 7 in R3C7, no 2 in R3C8 (step 4), no 4 in R5C7 (step 7)
15b. R5C789 = {138/345}, no 6,7,9, clean-up: no 1 in R6C7 (step 7)

16. 7 in R5 locked in R5C456 for N5
16a. R5C456 (step 7a) = {579/678}, no 4
16b. 35(7) cage at R4C3 (step 7b) = {1345679/2345678} -> R56C7 = [34] (hidden pair in cage), clean-up: no 6 in R3C7, no 3,5,6 in R3C8 (step 4), no 6,7 in R4C7, no 5 in R5C89 (step 15b), no 5 in R7C7 (step 3), no 5,6 in R8C8, no 2 in R9C6

17. Naked pair {18} in R5C89, locked for R5 and N6, clean-up: no 2 in R3C7, no 7 in R3C8 (step 4), no 6 in R4C3 (step 6), no 9 in R5C12 (step 14a), no 6 in R5C456 (step 16a)

18. Naked pair {24} in R5C12, locked for N4 -> R5C3 = 6, R4C3 = 1 (step 6), clean-up: no 4 in R1C3 (step 2), no 7 in R1C4, no 3,9 in R4C12 (step 13), no 3 in R67C3, no 4,7 in R7C2 (step 5)
18a. R67C3 = [54], R7C2 = 6, R9C2 = 5, R9C3 = 8, R7C7 = 7, R9C7 = 1 (step 3), R9C6 = 4, R3C7 = 8, R3C8 = 1, R4C7 = 2, R5C89 = [81], clean-up: no 3,4 in R1C1, no 7 in R1C8, no 7 in R2C2, no 9 in R2C3, no 2 in R8C8, no 3,6 in R9C89
18b. R2C23 = [87], R4C12 = [87], R8C3 = 9, clean-up: no 1,2 in R1C12

19. 9 in C7 locked in R12C7, locked for N3 -> R1C8 = 6, R12C7 = [95], R8C7 = 6, R8C8 = 3, R1C1 = 5, R1C2 = 4, R1C4 = 8, R1C3 = 3, R3C3 = 2, R3C12 = [69], R2C1 = 1, R5C12 = [42], R6C12 = [93], R6C89 = [76], R8C2 = 1

20. Naked pair {29} in R9C89, locked for R9 and N9 -> R7C89 = [58], R8C9 = 4, R4C89 = [95], R9C89 = [29], R2C8 = 4

21. R3C3 = 2 -> R34C4 = 10 = [46/73]
21a. R4C5 = 4 (hidden single in R4), R3C4 = 4 (hidden single in R3), R4C4 = 6, R4C6 = 3, R9C5 = 6 (hidden single in R9), R2C6 = 6 (hidden single in R2), R3C6 = 5 (cage sum)

22. 45 rule on N8 3 remaining innies R7C46 + R9C4 = 16 = {259} (only remaining combination) -> R8C4 = 5, R7C46 = {29}, locked for R7 and N8 -> R789C1 = [327], R7C5 = 1, R9C4 = 3
22a. R5C5 = 5 (hidden single in R5)

23. R8C4 = 5 -> R6C45 + R7C4 = 12 = {129} (only remaining combination), no 8

and the rest is naked singles
Second Walkthrough by udosuk, using Jean-Christophe's Template Tips:
Using JC's cage template tips, here is another walkthrough for v0.9 which is one step shorter. The trickiest moves are similar in terms of difficulty though so same rating.

My 2nd walkthrough for v0.9.

1. Innies @ n1: r13c3=5={14|23} has 3|4
Innies @ n47: r45c3=7={16|25} (can't be {34} for r13c3)
Outies @ c12: r289c3=24={789} (NT @ c3)
=> 9/2 @ r6c3 from {123456}={36|45}
Innies @ n7: r7c23=10=[46|64|73]
=> 9/2 @ r6c3=[36|54|63]
=> 5 @ c3,n4 locked @ r456c3

2. Outies @ n7: r6c123=17
r6c123 can't be {179|278} with r6c3 from {356}
r6c123 can't be {269} since r45c3={16|25} has 2|6
=> r6c12 can't have {12}
18/3 @ r6c1 from {346789} can't be {477}
=> r6c12 can't have 7
Now r6c123=17 from {345689}={359|368|458}
=> r45c3 and r6c123 form killer NP {56} @ n4

3. Innies @ r1234: r4c123=16
=> Innies @ n4: r5c123=12
But r5c123 can't be [345|435] since r6c123 has 3|4
=> r5c3 can't be 5

4. Outies @ n3: r4c789=16
Innies @ r6789: r6c789=17
=> Innies @ n6: r5c789=12
Innies @ n36: r56c7=7={16|25|34}
=> r5c89-r6c7=12-7=5
=> r5c89=r6c7+5 can't have 5
=> 5 @ r5,35/7 @ r4c3 locked @ r5c4567

5. Now r45c3=7 from {126}={16} (NP @ c3,n4,35/7 @ r4c3)
=> 9/2 @ r6c3 from {345}=[54]
=> r7c2=10-4=6
=> 13/2 @ r9c2 from {1235789}=[58]
=> 15/2 @ r2c2 from {1234789}=[87]
=> r13c3={23} (NP @ n1)
=> 9/2 @ r1c1 from {14569}=[54]

6. r6c2 from {39}
=> r6c12=17-5=12={39} (NP @ r6,n4)
=> r45c2={27} (NP @ c2,n4)
=> r5c123=12 can't be {138} with r5c2 from {27}
=> r5c123 can't have 8
=> r45c1=[84]

7. Innies @ r5: r5c456=21 from {235789}={579} (NT @ r5,n5)
=> r5c123=12=[426], r56c7=7 from {234}=[34]
=> 5/2 @ r9c6=[32|41]
Innies @ n9: r79c7=8 from {125789}=[71]
=> 5/2 @ r9c6: r9c6=5-1=4
=> 10/2 @ r3c7 from {25689}=[82]
Innies @ n3: r3c8=1
=> r5c89=[81]

8. 15/2 @ r1c7 from {2345679}={69} (NP @ r1,n3)
=> r2c7=5, 11/2 @ r1c3 from {12378}=[38]
=> r38c3=[29], 9/2 @ r8c7=[63]
=> r3c12=[69], r9c89={29} (NP @ r9,n9)
=> r7c89=[58]

9. Innies @ n8: r7c46+r8c4=16 from {123579}={259}
=> r7c46={29} (NP @ r7,n8)
=> r8c4=5
17/4 @ r6c4: r6c45+r7c4=17-5=12 from {12689}={129}
=> r6c45={12} (NP @ r6,17/4)
=> r57c4=[79]
12/2 @ r3c3: r34c4=12-2=10 from {346}=[46]

All naked singles from here.

(Edited: typo fixed thanks to Andrew)


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PostPosted: Fri Jun 17, 2011 5:05 am 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Human Solvable 2X by HATMAN (September 2008) here
Puzzle Diagram:
Image
Images with "udosuk style Killer Cages" by Børge:
Image     Image
Code: Select, Copy & Paste into solver (doesn't include the blue pair in the diagrams):
3x3:d:k:3073:15:3333:3333:2317:3849:3849:16:3336:17:3073:18:19:2317:20:21:3336:22:3332:23:24:25:26:27:28:29:3596:3332:30:31:32:33:34:35:36:3596:1550:1550:37:38:39:40:41:42:43:3595:44:45:46:47:48:49:50:3334:3595:51:52:53:54:55:56:57:3334:58:3331:59:60:61:62:63:2306:64:3331:65:3850:3850:66:3335:3335:67:2306:
Solution:
+-------+-------+-------+
| 3 2 8 | 5 1 6 | 9 4 7 |
| 7 9 5 | 2 8 4 | 3 6 1 |
| 4 1 6 | 3 9 7 | 2 5 8 |
+-------+-------+-------+
| 9 7 4 | 1 2 3 | 5 8 6 |
| 1 5 2 | 6 4 8 | 7 9 3 |
| 8 6 3 | 9 7 5 | 1 2 4 |
+-------+-------+-------+
| 6 4 1 | 7 5 2 | 8 3 9 |
| 2 8 9 | 4 3 1 | 6 7 5 |
| 5 3 7 | 8 6 9 | 4 1 2 |
+-------+-------+-------+
Quote:
HATMAN: It has taken me a while, but here is the second one, not as hard as the prevous one. JSudoku does it in more than ten fishes.
I'm away from base in Nigeria so have not been able to check the difficulty on SudokuSolver.
The blue pair is a 12/2 with that my solution is OK; without it my solutionfeels like heavyT&E.

udosuk(after Afmob had posted HS 2X Lite and his walkthrough for it): Even the heaviest version (without the 12/2 @ r5c8) isn't that hard. :ugeek:
If rated by the trickiest move (my step 5) then 1.25 (hard), if by sheer length then 1.0 (easy).

Andrew (in 2012): After finishing Human Solvable 1, I decided to have another look at Human Solvable 2 starting with the "Lite" version. Then I had a go at both versions of HS2, first with and then without the blue 12(2) cage.
Because my breakthrough steps apply to all three versions, my solving paths were very similar.
I found Afmob's and udosuk's walkthroughs interesting …
Rating: Easy 1.5.

HATMAN: Andrew
I would not expect an HS to go above 1.5 - that would defeat the objective to me. Basically because I can solve a 1.5 with a good wind behind me, on a sunny day, and I count myself as human. But I'm not sure about the rest of the forum given your solving skills. Of course your occasional mistakes help me believe that you are.
My friend udosuk I'm not so sure about - but his terrible humour was convincingly human - miss him.
Cheers, Maurice

Walkthrough by udosuk:
Even the heaviest version (without the 12/2 @ r5c8) isn't that hard. :ugeek:

My walkthrough.

1.
15/2 @ r1c6={69|78} has 6|7
=> 13/2 @ r1c3 can't be {67}, must be {49|58}
15/2 @ r9c3={69|78} has 6|7
=> 13/2 @ r9c6 can't be {67}, must be {49|58}
14/2 @ r3c9={59|68} has 5|8
=> 13/2 @ r6c9 can't be {58}, must be {49|67}
14/2 @ r6c1={59|68} has 5|8
=> 13/2 @ r3c1 can't be {58}, must be {49|67}

2.
r1c3467=13+15=28={(47|56)89} ({89} @ r1 locked)
r9c3467=15+13=28={(47|56)89} ({89} @ r9 locked)
r3467c1=13+14=27={(48|57)69} ({69} @ c1 locked)
r3467c9=14+13=27={(48|57)69} ({69} @ c9 locked)

(Cleanup)
12/2 @ r1c1=[39|48|{57}]
13/2 @ r1c9=[49|58|76]
13/2 @ r8c2=[67|85|94]

3.
Now r1c3467 has 4|5 & 5|7
=> r1c19 can't be [54|57]
Hence r1c1 can't be 5
=> 12/2 @ r1c1=[39|48|75]

4. (!)
Now r19c1+r28c2 can't be [3499]
=> r19c1 can't be [34]
Also r3467c1 has 4|7
=> r19c1 can't be [74]
Hence r9c1 can't be 4
=> 13/2 @ r8c2=[67|85]
Now r9c1 from {57}
=> r3467c1 can't be {5769}, must be {4869} (NQ @ c1)
=> 12/2 @ r1c1=[39|75], 13/2 @ r3c1={49}, 14/2 @ r6c1={68}

5. (!!)
6/2 @ r5c1={15|24} must have 4|5
=> r1349c1+r2c2 can't be [79455]
=> r3c1 can't be 9
=> 13/2 @ r3c1=[49]

6. (!)
Now 14/2 @ r3c9=[68|86|95]
13/2 @ r6c9={49|67} must have 4|6
=> r134c9+r2c8 can't be [4{68}9]
=> r1c9+r2c8 can't be [49]
=> 13/2 @ r1c9=[58|76]

7. (Mop up)
Now r1c9+r9c1={57} (NP @ d/, PP @ r1c1+r9c9)
=> 12/2 @ r1c1=[39]
=> 13/2 @ r1c3={58} (NP @ r1)
=> 13/2 @ r1c9=[76]
=> 15/2 @ r1c6=[69], 13/2 @ r8c2=[85]
=> 14/2 @ r3c9=[86], 14/2 @ r6c1=[86], 13/2 @ r9c6=[94]
=> 13/2 @ r6c9=[49], 9/2 @ r8c8=[72], 15/2 @ r9c3=[78]
=> 13/2 @ r1c3=[85]

HS @ c1: r2c1=7
=> 9/2 @ r1c5=[18]
=> r5c5=4
=> 6/2 @ r5c1=[15]

All naked singles (on X) from here.

If rated by the trickiest move (my step 5) then 1.25 (hard), if by sheer length then 1.0 (easy).
Walkthrough by Andrew (in 2012):
After finishing Human Solvable 1, I decided to have another look at Human Solvable 2 starting with the "Lite" version. Then I had a go at both versions of HS2, first with and then without the blue 12(2) cage.
Because my breakthrough steps apply to all three versions, my solving paths were very similar.
I found Afmob's and udosuk's walkthroughs interesting. Afmob made good use of large innies and then used two Finned Jellyfish steps. After looking at those steps I think I now understand what a Finned Jellyfish is, and might even spot one. :) udosuk's use of two-dimensional permutation analysis gave a very short solving path.

Prelims

a) 12(2) cage at R1C1 = {39/48/57}, no 1,2,6
b) R1C34 = {49/58/67}
c) R12C5 = {18/27/36/45}, no 9
d) R1C67 = {69/78}
e) 13(2) cage at R1C9 = {49/58/67}, no 1,2,3
f) R34C1 = {49/58/67}
g) R34C9 = {59/68}
h) R5C12 = {15/24}
i) R5C89 = {39/48/57}, no 1,2,6
j) R67C1 = {59/68}
k) R67C9 = {49/58/67}
l) 13(2) cage at R8C2 = {49/58/67}
m) R89C5 = {18/27/36/45}, no 9
n) 9(2) cage at R8C8 = {18/27/36/45}, no 9
o) R9C34 = {69/78}
p) R9C67 = {49/58/67}

Steps resulting from Prelims
1. R1C34 = {49/58} (cannot be {67} which clashes with R1C67)
1a. R34C1 = {49/67} (cannot be {58} which clashes with R67C1)
1b. R67C9 = {49/67} (cannot be {58} which clashes with R34C9)
1c. R9C67 = {49/58} (cannot be {67} which clashes with R9C34)
1d. Killer pair 8,9 in R1C34 and R1C67, locked for R1, clean-up: no 3,4 in R2C2, no 1 in R2C5, no 4,5 in R2C8
1e. Killer pair 6,9 in R34C1 and R67C1, locked for C1, clean-up: no 4,7 in R8C2
1f. Killer pair 6,9 in R34C9 and R67C9, locked for C9, clean-up: no 7 in R2C8, no 3 in R5C8, no 3 in R8C8
1g. Killer pair 8,9 in R9C34 and R9C67, locked for R9, clean-up: no 5 in R8C2, no 1 in R8C5, no 1 in R8C8

2. 45 rule on R1 2 outies R2C28 = 3 innies R1C258 + 8
2a. Max R2C28 = 17 -> max R1C258 = 9, no 7, clean-up: no 2 in R2C5

3. 45 rule on C1 2 outies R28C2 = 3 innies R258C1 + 7
3a. Max R28C2 = 17 -> max R258C1 = 10, no 8
3b. 8 in C1 only in R67C1 = {68}, locked for C1, clean-up: no 7 in R34C1
3c. Naked pair {49} in R34C1, locked for C1, clean-up: no 8 in R2C2, no 2 in R5C2, no 9 in R8C2
3d. Naked pair {68} in R7C1 and R8C2, locked for N7, clean-up: no 7,9 in R9C4

4. 45 rule on C9 3 outies R258C8 = 2 innies R28C9 + 16
4a. Max R258C8 = 24 -> max R28C9 = 8, no 8

5. 45 rule on R9 3 outies R8C258 = 2 innies R9C28 + 14
5a. Max R8C258 = 21 -> max R9C28 = 7, no 7

6. Combined cage R1C3467 = 28 = {4789/5689}
6a. Killer single 5 in R1C3467 and R1C9, locked for R1, clean-up: no 7 in R2C2, no 4 in R2C5

7. Combined cage R3467C9 = 27 = {4689/5679}
7a. Killer single 4 in R1C9 and R3467C9, locked for C9, clean-up: no 8 in R5C8, no 5 in R8C8

8. Combined cage R9C3467 = 28 = {4789/5689}
8a. Killer pair 5,7 in R9C1 and R9C3467, locked for R9, clean-up: no 2,4 in R8C5, no 2,4 in R8C8
8b. 7 in R9 only in R9C13, locked for N7

9. R2C28 = R1C258 + 8 (step 2)
9a. Min R1C258 = 6 -> min R2C28 = 14 -> R2C28 = [59/96/98], 9 locked for R2, CPE no 9 in R5C5

10. R19C1 = [35/37/75] -> R28C2 = [58/96/98]
10a. R28C2 = [96] => R2C8 = 8 using D/
10b. Combining steps 10 and 10a, 8 must be in R2C8 + R8C2, locked for D/, CPE no 8 in R8C2, clean-up: no 1 in R9C9
10c. 8 on D/ only in R2C8 + R8C2 -> 5 must be in R1C9 + R9C1 (locking 13(2) cages), locked for D/
10d. Killer pair 3,7 in R1C1 and 9(2) cage at R8C8, locked for D\

11. 1 in R9 only in R9C258
11a. 45 rule on R9 2 outies R8C28 = 3 innies R9C258 + 5
11b. R8C28 = {67/68/78} = 13,14,15 -> R9C258 = 8,9,10 = {134/126/136}
11c. When R8C28 = {68} = [86] = 14 => R9C258 = 9 = {126} => 6 of {126} must be in R9C5 -> no 2 in R9C5, clean-up: no 7 in R8C5

12. 1 in C9 only in R28C9
12a. R258C8 = R28C9 + 16 (step 4)
12b. Max R258C8 = 24 = [897] -> R8C29 = 8 can only be [71] -> no 7 in R8C9

13. Consider permutations for R5C12 = [15/24/51]
R5C12 = [15] => R2C2 = 9 => R3C1 = 4
or R5C12 = [24] => R4C1 = 9 => R3C1 = 4
or R5C12 = [51] => R9C1 = 7 => R1C1 = 3 => R2C2 = 9 => R3C1 = 4
-> R3C1 = 4, R4C1 = 9, clean-up: no 9 in R1C4, no 5 in R3C9
[Alternatively this result can be obtained by analysing permutations for R1349C1 + R2C2, and eliminating any which clash with R5C12, as in udosuk’s walkthrough for Human Solvable 2.]

14. R13467C9 = 5[68]{49}/7{86}{49} (cannot be 4[95]{67}/5[86]{49} which clash with R1C9 + R2C8) -> R1C9 = {57}, R34C9 = {68}, locked for C9, R67C9 = {49}, clean-up: no 9 in R2C8, no 4 in R5C8

15. R2C2 = 9 (hidden single in R2), R1C1 = 3, both placed for D\, R9C9 = 2, placed for D\, R8C8 = 7, clean-up: no 4 in R1C4, no 6 in R2C5, no 5 in R5C9

16. Naked pair {58} in R1C34, locked for R1 -> R1C9 = 7, R2C8 = 6, both placed for D/, R1C67 = [69], R34C9 = [86], R8C2 = 8, R9C1 = 5, R67C1 = [86], R5C9 = 3, R5C8 = 9, R67C9 = [49], clean-up: no 3 in R2C5, no 1 in R5C2, no 1 in R9C5, no 8 in R9C67

17. R9C67 = [94], R9C3 = 7, R9C4 = 8, R1C34 = [85], clean-up: no 4 in R1C5, no 5 in R8C5

18. R9C5 = 6 (hidden single in R9), R8C5 = 3

19. Naked pair {14} in R4C4 + R5C5, locked for N5 and D\ -> R6C6 = 5, placed for D\, R3C3 = 6, R7C7 = 8

20. R2C1 = 7 (hidden single in C1), R2C5 = 8, R1C5 = 1, R5C5 = 4, placed for D/, R5C2 = 5, R5C1 = 1, R56C3 = [23], R4C23 = [74], R4C5 = 2, R4C6 = 3, placed for D/

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

Rating Comment. I'll rate my walkthroughs for all three versions of Human Solvable 2 at Easy 1.5 because I used a short forcing chain and the two-dimensional permutation analysis feels like it should have a similar rating. I used the same breakthrough steps for all three versions.
Walkthrough (without the blue 12(2) cage) by Andrew (in 2012):
Prelims

a) 12(2) cage at R1C1 = {39/48/57}, no 1,2,6
b) R1C34 = {49/58/67}
c) R12C5 = {18/27/36/45}, no 9
d) R1C67 = {69/78}
e) 13(2) cage at R1C9 = {49/58/67}, no 1,2,3
f) R34C1 = {49/58/67}
g) R34C9 = {59/68}
h) R5C12 = {15/24}
i) R67C1 = {59/68}
j) R67C9 = {49/58/67}
k) 13(2) cage at R8C2 = {49/58/67}
l) 9(2) cage at R8C8 = {18/27/36/45}, no 9
m) R9C34 = {69/78}
n) R9C67 = {49/58/67}

Steps resulting from Prelims
1. R1C34 = {49/58} (cannot be {67} which clashes with R1C67)
1a. R34C1 = {49/67} (cannot be {58} which clashes with R67C1)
1b. R67C9 = {49/67} (cannot be {58} which clashes with R34C9)
1c. R9C67 = {49/58} (cannot be {67} which clashes with R9C34)
1d. Killer pair 8,9 in R1C34 and R1C67, locked for R1, clean-up: no 3,4 in R2C2, no 1 in R2C5, no 4,5 in R2C8
1e. Killer pair 6,9 in R34C1 and R67C1, locked for C1, clean-up: no 4,7 in R8C2
1f. Killer pair 6,9 in R34C9 and R67C9, locked for C9, clean-up: no 7 in R2C8, no 3 in R8C8
1g. Killer pair 8,9 in R9C34 and R9C67, locked for R9, clean-up: no 5 in R8C2, no 1 in R8C8

2. 45 rule on R1 2 outies R2C28 = 3 innies R1C258 + 8
2a. Max R2C28 = 17 -> max R1C258 = 9, no 7, clean-up: no 2 in R2C5

3. 45 rule on C1 2 outies R28C2 = 3 innies R258C1 + 7
3a. Max R28C2 = 17 -> max R258C1 = 10, no 8
3b. 8 in C1 only in R67C1 = {68}, locked for C1, clean-up: no 7 in R34C1
3c. Naked pair {49} in R34C1, locked for C1, clean-up: no 8 in R2C2, no 2 in R5C2, no 9 in R8C2
3d. Naked pair {68} in R7C1 and R8C2, locked for N7, clean-up: no 7,9 in R9C4

4. Combined cage R1C3467 = 28 = {4789/5689}
4a. Killer single 5 in R1C3467 and R1C9, locked for R1, clean-up: no 7 in R2C2, no 4 in R2C5

5. Combined cage R3467C9 = 27 = {4689/5679}
5a. Killer single 4 in R1C9 and R3467C9, locked for C9, clean-up: no 5 in R8C8

6. Combined cage R9C3467 = 28 = {4789/5689}
6a. Killer pair 5,7 in R9C1 and R9C3467, locked for R9, clean-up: no 2,4 in R8C8
6b. 7 in R9 only in R9C13, locked for N7

7. R2C28 = R1C258 + 8 (step 2)
7a. Min R1C258 = 6 -> min R2C28 = 14 -> R2C28 = [59/96/98], 9 locked for R2, CPE no 9 in R5C5

8. R19C1 = [35/37/75] -> R28C2 = [58/96/98]
8a. R28C2 = [96] => R2C8 = 8 using D/
8b. Combining steps 8 and 8a, 8 must be in R2C8 + R8C2, locked for D/, CPE no 8 in R8C2, clean-up: no 1 in R9C9
8c. 8 on D/ only in R2C8 + R8C2 -> 5 must be in R1C9 + R9C1 (locking 13(2) cages), locked for D/
8d. Killer pair 3,7 in R1C1 and 9(2) cage at R8C8, locked for D\

9. 1 in R9 only in R9C258
9a. 45 rule on R9 2 outies R8C28 = 3 innies R9C258 + 5
9b. R8C28 = {67/68/78} = 13,14,15 -> R9C258 = 8,9,10 = {134/126/136}
9c. When R8C28 = {68} = [86] = 14 => R9C258 = 9 = {126} => 6 of {126} must be in R9C5 -> no 2 in R9C5

10. Consider permutations for R5C12 = [15/24/51]
R5C12 = [15] => R2C2 = 9 => R3C1 = 4
or R5C12 = [24] => R4C1 = 9 => R3C1 = 4
or R5C12 = [51] => R9C1 = 7 => R1C1 = 3 => R2C2 = 9 => R3C1 = 4
-> R3C1 = 4, R4C1 = 9, clean-up: no 9 in R1C4, no 5 in R3C9
[Alternatively this result can be obtained by analysing permutations for R1349C1 + R2C2, and eliminating any which clash with R5C12, as in udosuk’s walkthrough.]

11. R13467C9 = 5[68]{49}/7{86}{49} (cannot be 4[95]{67}/5[86]{49} which clash with R1C9 + R2C8) -> R1C9 = {57}, R34C9 = {68}, locked for C9, R67C9 = {49}, clean-up: no 9 in R2C8

12. R2C2 = 9 (hidden single in R2), R1C1 = 3, both placed for D\, R9C9 = 2, placed for D\, R8C8 = 7, clean-up: no 4 in R1C4, no 6 in R2C5

13. Naked pair {58} in R1C34, locked for R1 -> R1C9 = 7, R2C8 = 6, both placed for D/, R1C67 = [69], R34C9 = [86], R8C2 = 8, R9C1 = 5, R67C1 = [86], clean-up: no 3 in R2C5, no 1 in R5C2, no 8 in R9C67

14. R9C67 = [94], R67C9 = [49], R9C3 = 7, R9C4 = 8, R1C34 = [85], clean-up: no 4 in R1C5

15. R9C5 = 6 (hidden single in R9)

16. Naked pair {14} in R4C4 + R5C5, locked for N5 and D\ -> R6C6 = 5, placed for D\, R3C3 = 6, R7C7 = 8

17. R2C1 = 7 (hidden single in C1), R2C5 = 8, R1C5 = 1, R5C5 = 4, placed for D/, R5C2 = 5, R5C1 = 1, R5C9 = 3, R56C3 = [23], R4C23 = [74], R13C2 = [21], R2C3 = 5, R2C9 = 1, R8C9 = 5, R8C1 = 2, R8C5 = 3, R4C5 = 2, R4C6 = 3, placed for D/
[Removing the 9(2) cage at R8C5 made very little difference to my solving path. I just added a few more naked singles in step 17. Then removing the 12(2) cage at R5C8 was similar; I removed a couple of steps for C9 and a few clean-ups.]

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

Rating Comment. I'll rate my walkthroughs for all three versions of Human Solvable 2 at Easy 1.5 because I used a short forcing chain and the two-dimensional permutation analysis feels like it should have a similar rating. I used the same breakthrough steps for all three versions.



Human Solvable 2X Lite by Afmob (September 2008) here
Puzzle Diagram:
Image
Images with "udosuk style Killer Cages" by Børge:
Image     Image
Code: Select, Copy & Paste into solver:
3x3:d:k:3072:1:3330:3330:2308:3845:3845:7:3336:9:3072:11:12:2308:14:15:3336:17:3346:19:20:21:22:23:24:25:3610:3346:28:29:30:31:32:33:34:3610:1572:1572:38:39:40:41:42:3115:3115:3629:46:47:48:49:50:51:52:3381:3629:55:56:57:58:59:60:61:3381:63:3392:65:66:2371:68:69:2374:71:3392:73:3914:3914:2371:3405:3405:79:2374:
Solution:
+-------+-------+-------+
| 3 2 8 | 5 1 6 | 9 4 7 |
| 7 9 5 | 2 8 4 | 3 6 1 |
| 4 1 6 | 3 9 7 | 2 5 8 |
+-------+-------+-------+
| 9 7 4 | 1 2 3 | 5 8 6 |
| 1 5 2 | 6 4 8 | 7 9 3 |
| 8 6 3 | 9 7 5 | 1 2 4 |
+-------+-------+-------+
| 6 4 1 | 7 5 2 | 8 3 9 |
| 2 8 9 | 4 3 1 | 6 7 5 |
| 5 3 7 | 8 6 9 | 4 1 2 |
+-------+-------+-------+
Quote:
Afmob: I wanted to tackle H2 X but the PS code didn't work for SumoCue so I had to recreate HATMAN's killer using SumoCue but I magically inserted a cage that wasn't there (9(2) @ R8C5) but I don't know why I did it. Maybe because of the symmetry? Well I solved the "new" Killer thinking it was HS2 X and I just wanted to post my walkthrough and I noticed that I solved the wrong version.
:bigoops:
Well, guess I was lucky to have found the right cage sum. :cheesey: The beginning of the solving path is identical to HS2 X but the breakthrough move (steps 7a, 7b) cannot be applied because you somehow have to remove 9 from R8C5.
SS Score: 1.37. But it uses T&E! Estimated rating: At least hard 1.25 (depends on how you rate steps 7a, 7b).

HATMAN: Afmob. This was my original post, which I replaced very quickly because I thought it was too easy - so maybe I underestimated it.

Andrew (in 2012): After finishing Human Solvable 1, I decided to have another look at Human Solvable 2 starting with the "Lite" version. I found that I'd almost finished it, only missing the second breakthrough step because of careless eliminations from my Excel worksheet. When I came back to this puzzle I re-worked my first breakthrough step; the note outlines how I did it originally.
Rating: Easy 1.5

Walkthrough by Afmob:
HS2 X Lite Walkthrough:

1. R19 + C19
a) Killer pair (67) in both 15(2) @ R19 blocks {67} of both 13(2) (not 13(2) @ D/)
b) Killer pair (89) locked in 13(2) + 15(2) for R19
c) Killer pair (58) of both 14(2) @ C19 blocks {58} of both 13(2) (not 13(2) @ D/)
d) Killer pair (69) locked in 13(2) + 14(2) for R19
e) Both 13(2) @ D/: R2C8 + R8C2 <> 4,5,7
f) 12(2) @ R1: R2C2 <> 3,4
g) Both 9(2) @ C5: R28C5 <> 1
h) 12(2) @ R5: R5C8 <> 3
i) 9(2) @ C9: R8C8 <> 1,3

2. R1
a) Innies+Outies R1: 17 = R2C258 - R1C28
-> R1C28 <= 7 <> 7 and R2C258 >= 20 <> 2
b) 1,2 locked in R1C258
c) Innies R1 = 17(5) = 123{47/56}: R1C258 <> 5 because 6 only possible there
and R1C258 must have 1 and 2
d) 9(2): R1C5 <> 7 and R2C5 <> 4
e) Innies R1 = 17(5): R1C1 <> 5 because R1C9 <> 3,6
f) 12(2): R2C2 <> 7

3. C1 !
a) 1,2 locked in R258C1
b) Innies C1 = 18(5) = 123{48/57}: R258C1 <> 4 because 8 only possible there
and R1C258 must have 1 and 2
c) 6(2): R5C2 <> 2
d) Innies C1 = 18(5): R1C1 <> 4 because R9C1 <> 3,8
e) 12(2) <> 8
f) ! Innies+Outies C1: 7 = R28C2 - R258C1: R8C2 <> 9 because R258C1 <> 4
g) 13(2) @ R8C2 <> 4
h) 4 locked in 13(2) @ R3C1 @ C1 = {49} locked for C1
i) 14(2) = {68} locked for C1

4. R789
a) Innies R9 = 17(3) = 123{47/56}: R9C2589 <> 5,7 because R9C1 = (57)
b) Both 9(2): R8C58 <> 2,4
c) Naked pair (68) locked in R7C1+R8C2 for N7
d) 15(2): R9C4 <> 7,9
e) 7 locked in R9C13 @ R9 for N7

5. C9
a) Innies C9 = 18(5) = 123{48/57}: R2589C9 <> 4 because R1C9 <> 1,2,3,8
b) 12(2): R5C8 <> 8
c) 9(2) <> 5

6. R1
a) Innies+Outies R1: 8 = R2C28 - R1C258: R1C258 = 12{3/4/6} (step 2b)
-> R2C28 = 14/15/17(2) = [59/96/98] -> 9 locked for R2; CPE: R5C5 <> 9

7. R1589 ! + D\
a) ! Finned Jellyfish (9) in R1589 for C3467 with fin being R5C8
-> So either Jellyfish in R1589 for C3467 or R5C8 = 9
-> CPE: R46C7 <> 9
b) ! More Finned Jellyfish (9): If R5C8 = 9 then R2C2 = 9 (HS @ R2)
-> so either Finned Jellyfish from step 7a or R2C2 = 9
-> CPE: R3C3+R4C4+R6C6+R7C7 <> 9
c) Hidden Single: R2C2 = 9 @ D\ -> R1C1 = 3
d) R3C1 = 4, R4C1 = 9
e) 13(2) @ R1C3 = {58} locked for R1
f) 13(2) @ R1C9 = {67} -> R1C9 = 7, R2C8 = 6
g) R8C2 = 8, R9C1 = 5, R8C8 = 7 -> R9C9 = 2
h) R1C7 = 9, R1C6 = 6

8. R9
a) 13(2) = {49} -> R9C7 = 4, R9C6 = 9
b) R9C3 = 7 -> R9C4 = 8
c) 9(2) = {36} locked for C5+N8

9. C9 + D/
a) 13(2) = {49} -> R7C9 = 9, R6C9 = 4
b) 12(2) = {39} -> R5C8 = 9, R5C9 = 3
c) 14(2) = {68} -> R3C9 = 8, R4C9 = 6
d) Hidden Single: R6C4 = 9 @ D/
e) R1C4 = 5, R7C1 = 6, R6C1 = 8

10. D\
a) Naked pair (14) locked in R4C4+R5C5 for D\ + N5
b) Hidden Single: R4C6 = 3 @ N5
c) R6C6 = 5

11. R8
a) Naked triple (124) locked in R8C146 for R8
b) R8C9 = 5, R2C9 = 1, R3C7 = 2

12. Rest is singles without considering the diagonals.
Walkthrough by Andrew (in 2012):
Prelims

a) 12(2) cage at R1C1 = {39/48/57}, no 1,2,6
b) R1C34 = {49/58/67}
c) R12C5 = {18/27/36/45}, no 9
d) R1C67 = {69/78}
e) 13(2) cage at R1C9 = {49/58/67}, no 1,2,3
f) R34C1 = {49/58/67}
g) R34C9 = {59/68}
h) R5C12 = {15/24}
i) R5C89 = {39/48/57}, no 1,2,6
j) R67C1 = {59/68}
k) R67C9 = {49/58/67}
l) 13(2) cage at R8C2 = {49/58/67}
m) R89C5 = {18/27/36/45}, no 9
n) 9(2) cage at R8C8 = {18/27/36/45}, no 9
o) R9C34 = {69/78}
p) R9C67 = {49/58/67}

Steps resulting from Prelims
1. R1C34 = {49/58} (cannot be {67} which clashes with R1C67)
1a. R34C1 = {49/67} (cannot be {58} which clashes with R67C1)
1b. R67C9 = {49/67} (cannot be {58} which clashes with R34C9)
1c. R9C67 = {49/58} (cannot be {67} which clashes with R9C34)
1d. Killer pair 8,9 in R1C34 and R1C67, locked for R1, clean-up: no 3,4 in R2C2, no 1 in R2C5, no 4,5 in R2C8
1e. Killer pair 6,9 in R34C1 and R67C1, locked for C1, clean-up: no 4,7 in R8C2
1f. Killer pair 6,9 in R34C9 and R67C9, locked for C9, clean-up: no 7 in R2C8, no 3 in R5C8, no 3 in R8C8
1g. Killer pair 8,9 in R9C34 and R9C67, locked for R9, clean-up: no 5 in R8C2, no 1 in R8C5, no 1 in R8C8

2. 45 rule on R1 2 outies R2C28 = 3 innies R1C258 + 8
2a. Max R2C28 = 17 -> max R1C258 = 9, no 7, clean-up: no 2 in R2C5

3. 45 rule on C1 2 outies R28C2 = 3 innies R258C1 + 7
3a. Max R28C2 = 17 -> max R258C1 = 10, no 8
3b. 8 in C1 only in R67C1 = {68}, locked for C1, clean-up: no 7 in R34C1
3c. Naked pair {49} in R34C1, locked for C1, clean-up: no 8 in R2C2, no 2 in R5C2, no 9 in R8C2
3d. Naked pair {68} in R7C1 and R8C2, locked for N7, clean-up: no 7,9 in R9C4

4. 45 rule on C9 3 outies R258C8 = 2 innies R28C9 + 16
4a. Max R258C8 = 24 -> max R28C9 = 8, no 8

5. 45 rule on R9 3 outies R8C258 = 2 innies R9C28 + 14
5a. Max R8C258 = 21 -> max R9C28 = 7, no 7

6. Combined cage R1C3467 = 28 = {4789/5689}
6a. Killer single 5 in R1C3467 and R1C9, locked for R1, clean-up: no 7 in R2C2, no 4 in R2C5

7. Combined cage R3467C9 = 27 = {4689/5679}
7a. Killer single 4 in R1C9 and R3467C9, locked for C9, clean-up: no 8 in R5C8, no 5 in R8C8

8. Combined cage R9C3467 = 28 = {4789/5689}
8a. Killer pair 5,7 in R9C1 and R9C3467, locked for R9, clean-up: no 2,4 in R8C5, no 2,4 in R8C8
8b. 7 in R9 only in R9C13, locked for N7

9. R2C28 = R1C258 + 8 (step 2)
9a. Min R1C258 = 6 -> min R2C28 = 14 -> R2C28 = [59/96/98], 9 locked for R2, CPE no 9 in R5C5

10. R19C1 = [35/37/75] -> R28C2 = [58/96/98]
10a. R28C2 = [96] => R2C8 = 8 using D/
10b. Combining steps 10 and 10a, 8 must be in R2C8 + R8C2, locked for D/, CPE no 8 in R8C2, clean-up: no 1 in R9C9
10c. 8 on D/ only in R2C8 + R8C2 -> 5 must be in R1C9 + R9C1 (locking 13(2) cages), locked for D/
10d. Killer pair 3,7 in R1C1 and 9(2) cage at R8C8, locked for D\

11. 1 in R9 only in R9C258
11a. 45 rule on R9 2 outies R8C28 = 3 innies R9C258 + 5
11b. R8C28 = {67/68/78} = 13,14,15 -> R9C258 = 8,9,10 = {134/126/136}
11c. When R8C28 = {68} = [86] = 14 => R9C258 = 9 = {126} => 6 of {126} must be in R9C5 -> no 2 in R9C5, clean-up: no 7 in R8C5

12. 1 in C9 only in R28C9
12a. R258C8 = R28C9 + 16 (step 4)
12b. Max R258C8 = 24 = [897] -> R8C29 = 8 can only be [71] -> no 7 in R8C9

13. Consider permutations for R5C12 = [15/24/51]
R5C12 = [15] => R2C2 = 9 => R3C1 = 4
or R5C12 = [24] => R4C1 = 9 => R3C1 = 4
or R5C12 = [51] => R9C1 = 7 => R1C1 = 3 => R2C2 = 9 => R3C1 = 4
-> R3C1 = 4, R4C1 = 9, clean-up: no 9 in R1C4, no 5 in R3C9
[Alternatively this result can be obtained by analysing permutations for R1349C1 + R2C2, and eliminating any which clash with R5C12, as in udosuk’s walkthrough for Human Solvable 2.]

14. R13467C9 = 5[68]{49}/7{86}{49} (cannot be 4[95]{67}/5[86]{49} which clash with R1C9 + R2C8) -> R1C9 = {57}, R34C9 = {68}, locked for C9, R67C9 = {49}, clean-up: no 9 in R2C8, no 4 in R5C8

15. R2C2 = 9 (hidden single in R2), R1C1 = 3, both placed for D\, R9C9 = 2, placed for D\, R8C8 = 7, clean-up: no 4 in R1C4, no 6 in R2C5, no 5 in R5C9

16. Naked pair {58} in R1C34, locked for R1 -> R1C9 = 7, R2C8 = 6, both placed for D/, R1C67 = [69], R34C9 = [86], R8C2 = 8, R9C1 = 5, R67C1 = [86], R5C9 = 3, R5C8 = 9, R67C9 = [49], clean-up: no 3 in R2C5, no 1 in R5C2, no 1 in R9C5, no 8 in R9C67

17. R9C67 = [94], R9C3 = 7, R9C4 = 8, R1C34 = [85], clean-up: no 4 in R1C5, no 5 in R8C5

18. R9C5 = 6 (hidden single in R9), R8C5 = 3

19. Naked pair {14} in R4C4 + R5C5, locked for N5 and D\ -> R6C6 = 5, placed for D\, R3C3 = 6, R7C7 = 8

20. R2C1 = 7 (hidden single in C1), R2C5 = 8, R1C5 = 1, R5C5 = 4, placed for D/, R5C2 = 5, R5C1 = 1, R56C3 = [23], R4C23 = [74], R4C5 = 2, R4C6 = 3, placed for D/

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

Rating Comment. I'll rate my walkthroughs for all three versions of Human Solvable 2 at Easy 1.5 because I used a short forcing chain and the two-dimensional permutation analysis feels like it should have a similar rating. I used the same breakthrough steps for all three versions.


Last edited by Andrew on Mon Jun 04, 2012 11:10 pm, edited 1 time in total.

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PostPosted: Fri Jun 17, 2011 9:26 pm 
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Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Assassin 119 by Afmob (September 2008) here
Puzzle Diagram:
Image
Images with "udosuk style Killer Cages" by Børge:
Image     Image
Code: Select, Copy & Paste into solver:
3x3::k:3584:3584:5378:5378:7684:3077:3077:5895:5895:3584:4362:5378:7684:1549:7684:3077:2576:5895:3584:4362:7684:1549:1549:2839:7684:2576:5895:4123:4362:4362:2590:2590:2839:3361:3361:3107:4123:3365:3365:3365:3624:3624:3114:3114:3107:4123:5166:5166:3888:4145:1330:2099:2099:3107:6710:5166:6968:3888:4145:1330:6968:3389:4414:6710:5166:2369:6968:4145:6968:3909:3389:4414:6710:6710:2369:2369:6968:3909:3909:4414:4414:
Solution:
+-------+-------+-------+
| 1 2 9 | 4 8 5 | 3 6 7 |
| 5 3 8 | 7 1 6 | 4 2 9 |
| 6 7 4 | 2 3 9 | 5 8 1 |
+-------+-------+-------+
| 9 1 6 | 3 7 2 | 8 5 4 |
| 4 5 7 | 1 6 8 | 9 3 2 |
| 3 8 2 | 9 5 4 | 1 7 6 |
+-------+-------+-------+
| 8 4 5 | 6 2 1 | 7 9 3 |
| 7 6 1 | 8 9 3 | 2 4 5 |
| 2 9 3 | 5 4 7 | 6 1 8 |
+-------+-------+-------+
Quote:
Afmob: This didn't came out as symmetrical as I wanted it to be though it's way too symmetrical to be messy. :cheesey:
SS Score: 0.92. Estimated rating: 1.0.

azpaull: Looks like it is going to be a fun one! Thanks, Afmob!

Andrew: Yes this one does look fun! Many thanks!
Afmob wrote:
This didn't came out as symmetrical as I wanted it to be though it's way too symmetrical to be messy. :cheesey:
It's got the right rating for a Messy One but if you'd posted it as that, then you'd have had to create another puzzle for A119. ;)

udosuk: Rating: 1.0 (easy) by trickiest move ..., 0.75 by length.
Look forward to v2. :ugeek:

Andrew: My early breakthrough used different logic than in udosuk's walkthrough to achieve the same result.
I'll rate A119 as 1.0 the way that I solved it.

azpaull: Phew! Twice, I had to start over (on the original version) because of silly mistakes. Maybe I should start making walkthrus so I can walk-back when I get sloppy. But, thanks again for the fun puzzle, Afmob!

Walkthrough by udosuk:
My walkthrough.

1. Innies @ r5: r5c19=6={15|24}
Innies @ r1234: r4c19=13={49|58|67}
Innies @ r6789: r6c19=9={18|27|36|45}
Innies @ c89: r456c8=15
Outies @ c89: r456c7=18

2. 14/2 @ r5c5={59|68} has 5|8, r5c19={15|24} has 4|5
=> r5c1569 has 4|8
=> 12/2 @ r5c7 can't be {48}, must be {39|57} has 5|9
=> 14/2 @ r5c5 can't be {59}, must be {68} (NP @ r5,n5)

3. 12/2 @ r5c7={39|57} has 3|5
=> 8/2 @ r6c7 can't be {35}, must be {17|26} has 6|7
=> 13/2 @ r4c7 can't be {67}, must be {49|58}
=> 13/2 @ r4c7 & 12/2 @ r5c7 form KNP {59} @ n6
=> r4c19=13=[58|{67}|94], r5c19=6=[{24}|51]

4. Now r45c1 from {245679}
16/3 @ r4c1 can't be {466}
=> r6c1 can't be 6
=> r6c19=9 can't be [63]

5. 3 @ n6 locked @ 12/2 @ r5c7={39} (NP @ r5,n6)
=> r5c7 from {39}, r6c7 from {1267}
=> r56c7 can't sum to 13
=> r4c7=18-r56c7 can't sum to 5
=> 13/2 @ r4c7 from {458}=[85]

6. r56c7=18-8=10=[37|91]
=> 8/2 @ r6c7={17} (NP @ r6,n6)
=> 15/2 @ r6c4=[96]
=> 10/2 @ r4c4 from {12347}={37} (NP @ r4,n5)

7. r4c19=13 from {469}=[94]
=> r5c19=6=[42], r6c19=9=[36]
=> 11/2 @ r3c6=[92]
=> 5/2 @ r6c6=[41]
=> r6c5=5

8. Now r4c23={16}, r6c23={28}
=> 17/4 @ r2c2: r23c2=17-1-6=10 can't be {19|28|46}
=> r23c2={37} (NP @ c2,n1)
=> 13/3 @ r5c2=[571]

9. 14/4 @ r1c1 can't have 9
Outies @ c1: r19c2=11 from {124689}=[29]
=> 18/4 @ r6c2=[8246]
=> 13/2 @ r7c8 from {1234789}=[94]
=> r56c8=15-5=10=[37]
=> r56c7=[91], 10/2 @ r2c8 from {1268}={28} (NP @ c8,n3)
Innies @ n3: r123c7=12 from {34567}={345} (NT @ c7,n3)

10. HS @ n8: r8c5=9
=> 16/3 @ r6c5=[529]
=> 9/3 @ r8c3 from {134578}={135}
6/3 @ r2c5={123}
=> r23c5={13} (NP @ c5,n2)
14/4 @ r1c1: r123c1=14-2=12 from {1568}={156} (NT @ c1,n1)

All naked singles from here.

Rating: 1.0 (easy) by trickiest move (KNP), 0.75 by length.

Look forward to v2. :ugeek:

(Edited: typo fixed thanks to Andrew)[/quote]
Walkthrough by Andrew:
My early breakthrough used different logic than in udosuk's walkthrough to achieve the same result.

I'll rate A119 as 1.0 the way that I solved it.

Here is my walkthrough. Several of my steps proved not to be part of the solution path but I've left them in because they were interesting.

Prelims

a) R23C8 = {19/28/37/46}, no 5
b) R34C6 = {29/38/47/56}, no 1
c) R4C45 = {19/28/37/46}, no 5
d) R4C78 = {49/58/67}, no 1,2,3
e) R5C56 = {59/68}
f) R5C78 = {39/48/57}, no 1,2,6
g) R67C4 = {69/78}
h) R67C6 = {14/23}
i) R6C78 = {17/26/35}, no 4,8,9
j) R78C8 = {49/58/67}, no 1,2,3
k) 21(3) cage at R1C3 = {489/579/678}, no 1,2,3
l) 6(3) cage in N2 = {123}, locked for N2, clean-up: no 8,9 in R4C6
m) 9(3) cage at R8C3 = {126/135/234}, no 7,8,9
n) 14(4) cage in N1 = {1238/1247/1256/1346/2345}, no 9
o) 26(4) cage in N7 = {2789/3689/4589/4679/5678}, no 1

1. 45 rule on R123 3 outies R4C236 = 9 = {126/135/234}, no 7,8,9, clean-up: no 4 in R3C6

2. 45 rule on R1234 2 innies R4C19 = 13 = {49/58/67}, no 1,2,3

3. 45 rule on R5 2 innies R5C19 = 6 = {15/24}

4. 45 rule on R6789 2 innies R6C19 = 9 = {18/27/36/45}, no 9

5. 45 rule on C1 2 outies R19C2 = 11 = [29]/{38/47/56}, no 1, no 2 in R9C2

6. 45 rule on C9 2 outies R19C8 = 7 = {16/25/34}, no 7,8,9

7. 45 rule on N3 1 outie R1C6 = 1 innie R3C7, no 1,2,3 in R3C7

8. Hidden killer triple 7,8,9 in R5C234, R5C56 and R5C78 for R5 -> R5C234 must contain one of 7,8,9 -> no 6 in R5C234

9. 6 in R5 locked in R5C56 = {68}, locked for R5, clean-up: no 5 in R3C6, no 2,4 in R4C45, no 4 in R5C78, no 7,9 in R7C4
9a. R6C78 = {17/26} (cannot be {35} which clashes with R5C78), no 3,5
9b. R4C78 = {49/58} (cannot be{67} which clashes with R6C78), no 6,7
[I then missed killer pair 5,9 in R4C78 and R5C78, locked for N6, which would have simplified step 12.]

10. R4C236 (step 1) = {126/234} (cannot be {135} which clashes with R4C45), no 5, clean-up: no 6 in R3C6

11. 30(5) diagonal cage at R1C5 = {25689/34689/35679/45678} (cannot be {15789/24789} which clash with R3C6 because all cells of the 30(5) cage “see” R3C6), no 1
11a. Min R1C5 + R2C46 + R3C7 = 22 -> max R3C3 = 8

12. R456C9 = {138/147/246} (cannot be {129} which clashes with R6C78, cannot be {156/237} which clash with R6C78, cannot be {345} which clashes with R5C78), no 5,9, clean-up: no 4,8 in R4C1 (step 2), no 1 in R5C1 (step 3), no 4 in R6C1 (step 4)
12a. 3 in {138} must be in R6C9 -> no 8 in R6C9, clean-up: no 1 in R6C1 (step 4)
12b. 1 in C1 locked in R123C1, locked for N1

13. R456C1 = {259/268/349/457} (cannot be {358} because 3,8 only in R6C1, cannot be {367} because R5C1 only contains 2,4,5)
13a. 6 of {268} must be in R4C1 -> no 6 in R6C1, clean-up: no 3 in R6C9 (step 4)

14. R456C9 (step 12) = {147/246}, no 8, clean-up: no 5 in R4C1 (step 2)
14a. Naked quint {12467} in R456C9 + R6C78, locked for N5, also 4 locked in R456C9 for C9, clean-up: no 9 in R4C78, no 5 in R5C78
14b. Naked pair {39} in R5C78, locked in R5

15. R456C1 (step 13) = {259/268/349/457}
15a. 7 of {457} must be in R4C1 -> no 7 in R6C1, clean-up: no 2 in R6C9 (step 4)

16. 45 rule on C89 3 outies R456C7 = 18 = {189/378} (cannot be {279/567} because 2,6,7 only in R6C7, cannot be {369} because 3,9 only in R5C7) -> R4C7 = 8, R4C8 = 5, R56C7 = [37/91], clean-up: no 8 in R1C6 (step 7), no 2 in R19C8 (step 6), no 2,6 in R6C8, no 8 in R78C8
16a. Naked pair {17} in R6C78, locked for R6 and N6 -> R6C4 = 9, R7C4 = 6, clean-up: no 6 in R4C1 (step 2), no 1 in R4C45, no 5 in R5C1 (step 3), no 2,8 in R6C1 (step 4), no 4 in R7C6, no 7 in R8C8
16b. Naked pair {37} in R4C45, locked for R4 and N5 -> R4C1 = 9, R4C9 = 4 (step 2), R5C19 = [42], R6C9 = 6, R6C1 = 3 (step 4), R4C6 = 2, R3C6 = 9, R6C6 = 4, R7C6 = 1, R6C5 = 5, R5C4 = 1, clean-up: no 1 in R2C8, no 4 in R3C7 (step 7)

17. Naked pair {16} in R4C23, locked for 17(4) cage at R2C2
17a. R4C23 = {16} = 7 -> R23C2 = 10 = {37} (cannot be {28} which clashes with R6C2), locked for C2 and N1 -> R5C23 = [57], clean-up: no 4,6,8 in R19C2 (step 5)
17b. R19C2 = [29], R6C23 = [82], R7C2 = 4, R8C2 = 6 (cage sum), R4C23 = [16], clean-up: no 7 in R7C8, no 9 in R8C8
17c. R78C8 = [94], clean-up: no 3 in R19C8 (step 6)

18. R23C8 = {28} (hidden pair in C8), locked for N3
18a. R19C8 = {16}, locked for C8 -> R6C78 = [17], R5C7 = 9 (step 16), R5C8 = 3

19. 12(3) cage at R1C6 = {345} (only remaining combination) -> R1C6 = 5, R3C7 = 5 (step 7), R12C7 = {34}, locked for C7 and N3

20. Naked pair {27} in R78C7, locked for N9 -> R9C7 = 6, R19C8 = [61]

21. 15(3) cage at R8C7 = {267} (only remaining combination) -> R8C7 = 2, R9C6 = 7, R7C7 = 7

22. R2C6 = 6 (hidden single in N2), R5C56 = [68], R8C6 = 3

23. R6C5 = 5 -> R78C5 = 11 = [29]

24. Naked pair {58} in R8C49, locked for R8 -> R8C1 = 7, R8C3 = 1
24a. Naked pair {58} in R7C13, locked for R7 and N7 -> R7C9 = 3, R9C13 = [23], R9C4 = 5 (prelim m)

25. Naked pair {13} in R23C5, locked for C5 and N2

and the rest is naked singles.


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PostPosted: Fri Jun 17, 2011 10:20 pm 
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Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Assassin 119 V2 by Afmob (September 2008) here
Puzzle Diagram:
Image
Images with "udosuk style Killer Cages" by Børge:
Image     Image
Code: Select, Copy & Paste into solver:
3x3:d:k:5376:5376:3842:3842:5124:6661:6661:4103:4103:5376:3842:3842:5124:6413:5124:6661:6661:4103:5376:8467:5124:6413:6413:6413:5124:6937:4103:3867:4636:8467:7198:7198:7198:6937:5922:3107:3867:4636:4636:8467:7198:6937:5922:5922:3107:3867:4636:8467:7198:7198:7198:6937:5922:3107:4406:8467:7224:4409:4409:4409:7224:6937:6718:4406:2880:2880:7224:4409:7224:2373:2373:6718:4406:4406:1354:1354:7224:3405:3405:6718:6718:
Solution:
+-------+-------+-------+
| 9 5 8 | 4 2 6 | 3 7 1 |
| 4 2 1 | 5 7 3 | 9 8 6 |
| 3 7 6 | 9 8 1 | 4 5 2 |
+-------+-------+-------+
| 6 4 3 | 7 1 2 | 8 9 5 |
| 2 1 5 | 8 3 9 | 7 6 4 |
| 7 8 9 | 6 4 5 | 2 1 3 |
+-------+-------+-------+
| 8 6 7 | 2 5 4 | 1 3 9 |
| 1 9 2 | 3 6 8 | 5 4 7 |
| 5 3 4 | 1 9 7 | 6 2 8 |
+-------+-------+-------+
Quote:
Afmob: Since Ed's Assassin won't be an X-Killer I thought that at least I should make one. :ok:
This Killer should be more challenging at least that's what SudokuSolver and JSudoku think but they both missed something very important.
SS Score: 1.64. Estimated rating: 1.25.

udosuk: Estimated Rating: 1.5 (easy) - 1.5 (hard).
I probably have missed some easier paths with what indicated by Afmob. If that's the case I'd love to hear from him. :study: (Added later: Afmob has informed me that's indeed the case. Good luck to everybody else trying to find that route.)

Afmob: Here is the easier path I've found with step 6a being the most important move. I usually don't look for these moves, so I guess I was lucky.
Rating: 1.25.

Andrew: Many thanks Afmob for a really challenging V2. I can recommend anyone who hasn't yet done so to try it!
udosuk's walkthrough has some very impressive ... After going through the walkthrough, but skipping ..., it looked like 1.5 (Hard) rather than 1.5 (Easy) to me.
Thanks udosuk for giving eliminations along the diagonals! I've also done that. It makes it much easier for those of us who do manual eliminations.
Afmob wrote:
Here is the easier path I've found with step 6a being the most important move.
IMHO step 7a is equally important. I missed that in my solution path and had to work really hard before my first placement.
Before that my path was very similar to Afmob's. After my step 14 I noticed the first part of Afmob's step 6a but missed ... However I got the same result, and a bit more, with my step 15. :)
I'll rate A119 V2 at 1.5 the way I solved it.

Walkthrough by udosuk:
This is my walkthrough for v2:

1.
5/2 @ r9c3={14|23}
Innies @ n7: r7c23+r9c3=17
=> r7c23 can't have {1234}, must be from {56789}
Innies @ r789: r7c28=9=[54|63|72|81]
Innies @ n5: r5c46={89} (NP @ r5,n5)
Outies @ n6: r37c8+r5c6=17
=> r3c8 can't be from {123489}, must be from {567}

2.
Innies @ r123: r3c28=12={57} (NP @ r3)
Outies @ n4: r37c2+r5c4=21 from {56789}={579|678}
=> r37c2=[57|75|76] (7 @ c2,33/5 locked)
Innies @ n4: r46c3 from {12345689}=12={39|48}
Outies @ c1: r19c2=8 from {12345689}={26|35}

3. (!)
Now r37c2+r46c3+r5c4=33=[57{48}9|75{48}9|76{39}8]
=> r7c23+r9c3=17 can't be [692|782|683|584|764]
=> r7c23+r9c3=17=[791|593|674]
=> r7c2 from {567}, r7c3 from {79}, r9c3 from {134}
=> r46c3 & r79c3 form KNP {49} @ c3

4. (!!)
Innie-outies @ n1: r3c23=r1c4+9
r3c2 from {57}, r3c3 from {12368}
Since r37c2+r46c3+r5c4=33=[57{48}9|75{48}9|76{39}8]
=> r1c4+r3c23 can't be [458]
Also r19c2={26|35}
=> r1c4+r3c23 can't be [256]
=> r3c2 can't be 5, must be 7

5.
Now r3c28=12=[75]
=> r7c23+r9c3=17=[593|674]
=> r46c3 & r9c3 form KNP {34} @ c3
Innie-outies @ n1: r3c3=r1c4+2
=> r1c4+r3c3=[46|68]
=> Pointing pair: r1c123 & r2c23 can't have 6

6. (!)
Now r1c4 from {46}
=> 15/4 @ r1c3: r1c3+r2c23=11 or 9 can't have 9
Also r12c3 from {1258} can't sum to 5
=> r1c4+r2c2 can't be [64]
=> r2c2 can't be 4
=> r1c3+r2c23 must be from {12358}
=> r1c3+r2c23+r1c4=15=[{128}4|{135}6]
=> r1c3+r2c23+r3c3=15+2=17=[{128}6|{135}8]

7. (!!)
Now r19c2+r7c2+r46c3=[265{48}|{35}6{39}]
In particular r1c2+r46c3=[2{48}|3{39}|5{39}]
=> r1c3+r2c23+r3c3 can't be [{135}8], must be [{128}6]

8. (Big mop up)
r1c4+r3c2=[46], r1c3+r2c23={128} (NT @ n1)
=> r19c2=8 from {356}={35} (NP @ c2)
=> r7c23+r9c3=17=[674]
=> 5/2 @ r9c3=[41], r5c4=21-6-7=8
=> 11/2 @ r8c2 from {12589}=[92]
=> r12c3={18} (NP @ c3,n1)
=> r2c2=2, r5c3=5, r5c6+r7c8=17-5=12=[93] (NE @ 27/5)
d\: r2c2+r3c3=[26] (NE @ d\)
d/: r7c3+r8c2=[79] (NE @ d/)

13/2 @ r9c6 from {2356789}={58|67}
Innies @ n9: r79c7=7 from {1456789}=[16]
=> 13/2 @ r9c6=[76], 9/2 @ r8c7 from {4578}=[54]
d\: r7c7+r8c8=[14] (NE @ d\)
=> d\: \14569=[97358] (3 NE @ d/)

Innies @ n6: r46c7=10 from {2478}={28} (NP @ c7,n6)
=> r3c7=4
Outies @ n3: r1c6=6 (NE @ 26/4)
=> 26/4 @ r1c6: r1c7+r2c78=26-6=20 from {13789}=[398]
=> r2c346=[153]
20/5 @ r1c5: r1c5=20-5-3-6-4=2

All naked singles from here.

Estimated Rating: 1.5 (easy) - 1.5 (hard)

I probably have missed some easier paths with what indicated by Afmob. If that's the case I'd love to hear from him. :study: (Added later: Afmob has informed me that's indeed the case. Good luck to everybody else trying to find that route.)
Walkthrough by Afmob:
Here is the easier path I've found with step 6a being the most important move. I usually don't look for these moves, so I guess I was lucky.

A119V2 Walkthrough:

1. R456
a) Innies N4 = 12(2) <> 6
b) Innies N5 = 17(2) = {89} locked for R5
c) Innies N6 = 10(2) <> 5
d) Outies N4 = 21(3) <> 3
e) Outies N6 = 17(3): R37C8 <> 8,9 because R5C6 = (89)

2. R37
a) Innies R123 = 12(2) = [57/75/84/93]
b) Innies R789 = 9(2) <> 9; R7C8 <> 6,7
c) Outies N4 = 21(3): R7C2 <> 8 because R3C2 <> 4
d) Innies R789 = 9(2) <> 1

3. R789
a) Innies N9 = 10(3) <> 8,9
b) Innies N7 = 17(3) can only have one of (1234) -> R7C23 <> 1,2,3,4
c) Innies R789 = 9(2): R7C8 <> 5
d) Innies N9 = 10(3): R79C7 <> 4 because R7C8 <> 1,5
e) 13(2) = [67/76/85]
f) Innies N9 = 10(3) can only have one of (567) -> R7C7 <> 5,6,7

4. R123 !
a) ! Outies N6 = 17(3) must have 5 xor 7 -> R3C8 = (57)
b) Innies R123 = 12(2) = {57} locked for R3
c) Outies N4 = 21(3) = 7{59/68} -> 7 locked for C2+33(5)

5. C123
a) Outies C1 = 8(2) = {26/35}
b) Killer triple (567) locked in Outies C1 + R37C2 for C2
c) Innies N4 = 12(2) <> 5
d) 18(4) <> {1368/2349/2358/3456} because of Killer pairs (34,38) of Innies N4
e) 18(4) must have one of (567) -> R5C3 = (567)
f) 18(4) = 1{269/278/359/458} because (567) only possible @ R5C3
-> 1 locked for C2+N4
g) Killer pair (89) locked in 18(4) + Innies N4 for N4
h) 11(2): R8C3 <> 4,5,6

6. R789 !
a) ! Innies+Outies R89: 19 = R7C1379 - R8C5: R8C5 <> 9 because R7C7 <= 3
b) R7C3 <> 9 because it sees all 9 of N8
c) Innies N7 = 17(3) = {278/368/458/467} <> 1
d) 5(2): R9C4 <> 4

7. C123 !
a) ! Innies N4 = 12(2) = {39} since (48) is a Killer pair of Innies N7
-> 3,9 locked for C3+N4+33(5)
b) Outies N4 = 21(3) = {678} -> R3C2 = 7, R5C4 = 8, R7C2 = 6
c) Innies N7 = 11(2) = {47} -> R7C3 = 7, R9C3 = 4
d) Cage sum: R9C4 = 1
e) Outies C1 = 8(2) = {35} locked for C2
f) 11(2) = {29} -> R8C3 = 2, R8C2 = 9
g) 17(4) = {1358} -> 1,8 locked for C1
h) 21(4) = {3459} locked for N1 because R1C2 = (35); 4 also locked for C1
i) 15(4) = {1248} because R12C3+R2C2 = (1268) -> R1C4 = 4, R2C2 = 2; 1,8 locked for C3
j) R3C3 = 6, R3C8 = 5, R5C6 = 9

8. R789 + D\
a) Innie R789 = R7C8 = 3
b) R7C7 = 1
c) Innie N9 = R9C7 = 6
d) Cage sum: R9C6 = 7
e) 9(2) = {45} -> R8C8 = 4, R8C7 = 5
f) Hidden Single: R4C4 = 7 @ D\, R9C9 = 8 @ D\, R1C1 = 9 @ D\

9. R789
a) Outies C9 = 9(2) = {27} -> R9C8 = 2, R1C8 = 7
b) Innies+Outies N3: 2 = R1C6 - R3C7: R1C6 = (56) and R3C7 = (34)
c) 26(4) can only have one (56) -> R2C8 <> 6
d) R2C8 = 8
e) Innies N6 = 10(2) = {28} locked for C7+N6

10. N2
a) 20(5) = {23456} because (28) only possible @ R1C5
-> R1C5 = 2, R3C7 = 4; {35} locked for R2+N2

11. Rest is singles without considering diagonals.

Rating: 1.25
Walkthrough by Andrew:
Many thanks Afmob for a really challenging V2. I can recommend anyone who hasn't yet done so to try it!

udosuk's walkthrough has some very impressive permutation analysis. After going through the walkthrough, but skipping some of the detail in the analysis, it looked like 1.5 (Hard) rather than 1.5 (Easy) to me.

Thanks udosuk for giving eliminations along the diagonals! I've also done that. It makes it much easier for those of us who do manual eliminations.

Afmob wrote:
Here is the easier path I've found with step 6a being the most important move.
IMHO step 7a is equally important. I missed that in my solution path and had to work really hard before my first placement.

Before that my path was very similar to Afmob's. After my step 14 I noticed the first part of Afmob's step 6a but missed the implication of R7C3 being {123}. However I got the same result, and a bit more, with my step 15. :)

I'll rate A119 V2 at 1.5 the way I solved it because there were times when it was very difficult to find the next move; however none of my steps are harder than 1.25. Maybe there's too much tendency to rate puzzles by hardest move. Mike's original rating definitions appear to me to refer more to puzzle difficulty than to hardest move.

Having said that, Afmob's walkthrough using both important steps 6a and 7a, is definitely 1.25 assuming that he didn't find it hard to spot those two steps.

If Ed's internet problems hadn't delayed him posting A120 I might not have been able to finish this puzzle yesterday evening. It took me some time to find steps 23a and 24a.

Here is my walkthrough for A119 V2. I'll leave it in TT for a couple of days. Step 37 was a fun move, the only one where I managed to use the diagonals for other than eliminations.

Thanks Afmob for pointing out the omission in step 25a and that step 15 needed better explanation; I've added a preliminary part for step 15. While checking this feedback I also found an omission in step 10a.

Prelims

a) R8C23 = {29/38/47/56}, no 1
b) R8C78 = {18/27/36/45}, no 9
c) R9C34 = {14/23}
d) R9C67 = {49/58/67}, no 1,2,3
e) 26(4) cage at R1C6 = {2789/3689/4589/4679/5678}, no 1
f) 26(4) cage in N9 = {2789/3689/4589/4679/5678}, no 1
g) 28(7) cage in N5 = {1234567}, locked for N5
h) 33(5) cage at R3C2 = {36789/45789}, no 1,2

1. Naked pair {89} in R5C46, locked for R5

2. 45 rule on N4 2 innies R46C3 = 12 = {39/48/57}, no 6
2a. 45 rule on N4 3 outies R37C2 + R5C4 = 21 = {489/579/678}, no 3
2b. 33(5) cage at R3C2 = {36789/45789}, CPE no 7 in 18(4) cage in R456C2

3. 45 rule on N6 2 innies R46C7 = 10 = {19/28/37/46}, no 5
3a. 45 rule on N6 3 outies R37C8 + R5C6 = 17 = {179/269/278/359/368/458} (cannot be {467} because R5C6 only contains 8,9)
3b. R5C6 = {89} -> no 8,9 in R37C8

4. 45 rule on R123 2 innies R3C28 = 12 = [57/75/84/93], no 6, no 4 in R3C2, no 1,2 in R3C8

5. 45 rule on R789 2 innies R7C28 = 9 = [45/54/63/72/81], no 9 in R7C2, no 6,7 in R7C8
5a. R37C2 + R5C4 (step 2a) = {489/579/678}
5b. 4,6 of {489/678} must be in R7C2 -> no 8 in R7C2, clean-up: no 1 in R7C8 (step 5)

6. 45 rule on N9 3 innies R7C78 + R9C7 = 10 = {127/136/145/235}, no 8,9, clean-up: no 4,5 in R9C6
6a. 1 of {127/136/145} must be in R7C7 and 5 of {235} must be in R9C7 -> no 4,5,6,7 in R7C7

7. 45 rule on C1 2 outies R19C2 = 8 = {17/26/35}, no 4,8,9

8. 45 rule on C9 2 outies R19C8 = 9 = {18/27/36/45}, no 9, no 8 in R1C8
8a. 9 in N9 locked in R789C9, locked for C9

9. 45 rule on N7 3 innies R7C23 + R9C3 = 17 = {179/269/278/359/368/458/467}
9a. R9C3 = {1234} -> no 1,2,3,4 in R7C23, clean-up: no 5 in R7C8 (step 5)
9b. 5 of {359/458} must be in R7C2 -> no 5 in R7C3
9c. R7C78 + R9C7 (step 6) = {127/136/145/235}
9d. 5,6,7 only in R9C7 -> R9C7 = {567}, clean-up: no 9 in R9C6

10. R37C2 + R5C4 (step 2a) = {579/678}, 7 locked in R37C2 for C2 and for 33(5) cage at R3C2, clean-up: no 1 in R19C2 (step 7), no 5 in R46C3 (step 2), no 4 in R8C3
10a. 8,9 of {579/678} must be in R5C4 -> no 8,9 in R3C2, clean-up: no 3,4 in R3C8 (step 4)
10b. Naked pair {57} in R3C28, locked for R3
10c. Killer pair 5,6 in R19C2 and R37C2, locked for C2, clean-up: no 5,6 in R8C3

11. 18(4) cage in N4 = {1269/1278/1359/1458} (cannot be {1368/2349/3456} which clash with R46C3, cannot be {1467/2367/2457} because 5,6,7 only in R5C3, cannot be {2358} which clashes with R19C2), 1 locked in R456C2, locked for C2 and N4
11a. 5,6,7 only in R5C3 -> R5C3 = {567}
11b. Killer pair 8,9 in R46C2 and R46C3, locked for N4

12. 45 rule on N1 2 innies R3C23 = 1 outie R1C4 + 9
12a. Max R3C23 = 16 -> max R1C4 = 7
12b. Min R1C4 = 1 -> min R3C23 = 10, no 1,2 in R3C23
12c. R3C23 cannot total 12 -> no 3 in R1C4

13. 45 rule on N3 2 innies R3C78 = 1 outie R1C6 + 3
13a. Min R3C78 = 6 -> min R1C6 = 3
13b. R3C78 cannot total 12 -> no 9 in R1C6
13c. Max R1C6 = 8 -> max R3C78 = 11, no 8,9 in R3C7

14. 45 rule on R12 4 outies R3C1379 = 1 innie R2C5 + 8
14a. Min R3C1379 = 10 -> min R2C5 = 2

15. R7C78 = {12/13/14/23} (steps 9c and 9d)
15a.
R7C456 cannot total 8,9 (because {125/134/126/135/234} clash with R7C78) -> no 8,9 in R8C5

16. 9 in N8 locked in R7C456 + R8C46 + R9C5, CPE no 9 in R7C3, clean-up: no 1 in R9C3 (step 9), no 4 in R9C4
16a. 1 in N7 locked in R789C1, locked for C1

17. 1 in N1 locked in R12C3, locked for 15(4) cage at R1C3, no 1 in R1C4
17a. R3C23 = R1C4 + 9 (step 12), min R1C4 = 2 -> min R3C23 = 11, min R3C3 = 4

18. R7C23 + R9C3 (step 9) = {368/458/467} (cannot be {278} which clashes with R8C23), no 2, clean-up: no 3 in R9C4
18a. Killer pair 3,4 in R46C3 and R9C3, locked for C3, clean-up: no 8 in R8C2

19. Hidden killer pair 8,9 in C1, 21(4) cage in N1 and 17(4) cage can each only contain one of 8,9 -> R123C1 and R789C1 must each contain one of 8,9

20. 17(4) cage in N7 = {1259/1358} (cannot be {1349} which clashes with R9C3, cannot be {1268} which clashes with R7C23 + R9C3, cannot be {1367/1457} which don’t contain 8 or 9), no 4,6,7, 5 locked for N7, clean-up: no 2 in R1C2 (step 7), no 4 in R7C8 (step 5)
20a. 6 in N7 locked in R7C23, locked for R7

21. R37C8 + R5C6 (step 3a) = {278/359}
21a. R46C7 (step 3) = {19/28/46} (cannot be {37} which clashes with R37C8 + R5C6), no 3,7

22. 17(4) cage in N8 = {1349/1358/1367/1457/2348/2357/2456} (cannot be {1259/1268} which clashes with R9C4)
22a. Killer pair 1,2 in 17(4) cage and R9C4, locked for N8

23. 45 rule on C123 3 outies R159C4 = 2 innies R37C3
23a. Min R37C3 = 13 -> min R159C4 = 13 cannot be [292] -> no 2 in R1C4

24. Min R1C4 = 4 -> max R1C3 + R2C23 = 11, no 9
24a. 15(4) cage at R1C3 = {1248/1257/1347} (cannot be {1356} which clashes with R1C2 which “sees” all cells of the 15(4) cage), no 6
24b. 4 of {1248} must be in R1C4, 3 of {1347} must be in R2C2 -> no 4 in R2C2

25. 4 in N1 locked in R123C1, locked for C1
25a. R456C1 = {267/357}, 7 locked for C1 and N4

26. 1 in N2 locked in R1C5 + R2C46 + R3C456, CPE no 1 in R3C7
26a. R3C78 = R1C6 + 3 (step 13), min R3C78 = 7 -> min R1C6 = 4

27. R3C1379 = R2C5 + 8 (step 14), min R3C1379 = 12 -> min R2C5 = 4
27a. 2,3 in N2 locked in R1C5 + R2C46 + R3C456, CPE no 2,3 in R3C7

28. R3C78 = R1C6 + 3 (step 13)
28a. Min R3C78 = 9 -> min R1C6 = 6
28b. R3C78 cannot total 10 (it must be an odd number) -> no 7 in R1C6
28c. R1C6 = {68} -> R3C78 = 9,11 = [45/47/65]

29. 1 in N3 locked in 16(4) cage = {1258/1267/1348} (cannot be {1357} which clashes with R3C8, cannot be {1456} which clashes with R3C7)
29a. Killer pair 4,5 in 16(4) cage and R3C78, locked for N3
[Note that when 16(4) cage = {1267}, R3C78 = [45] provides both candidates for the killer pair.]

30. Min R3C37 = 10 -> max R1C5 + R2C46 = 10, no 8,9

31. 9 in N2 locked in 25(4) cage = {1789/3589/3679} (cannot be {2689} which clashes with R1C6, cannot be {4579} because 5,7 only in R2C5), no 2,4
31a. 5,7 only in R2C5 -> R2C5 = {57}
31b. Killer pair 6,8 in 25(4) cage and R1C6, locked for N2
31c. 9 in N2 locked in R3C456, locked for R3

32. R3C1379 = R2C5 + 8 (step 14)
32a. 2,4 in R3 locked in R3C179
32b. R2C5 = {57} -> R3C1379 = 13,15 = {1246/1248/2346}
32c. R3C3 = {68} -> no 6,8 in R3C179 -> R3C7 = 4, locked for D/, clean-up: no 6 in R46C7 (step 3), no 7 in R8C3, no 5 in R8C8
32d. R1C4 = 4 (hidden single in N2), R2C1 = 4 (hidden single in R2), R1C1 = 9 (hidden single in N1), locked for D\

33. 16(4) cage in N3 (step 29) = {1258/1267}, no 3, 2 locked for N3
33a. Killer pair 5,7 in 16(4) cage and R3C8, locked for N3

34. 17(4) cage in N7 (step 20) = {1358}, locked for N7 -> R9C3 = 4, R9C4 = 1, clean-up: no 6 in R1C2 (step 7), no 8 in R46C3 (step 2)

35. R1C12 = [94] = 13 -> R1C2 + R3C1 = 8 = [53], R9C2 = 3, R3C2 = 7, R7C2 = 6, R7C3 = 7, locked for D/, R5C4 = 8 (step 10), R5C6 = 9, R3C8 = 5, R7C8 = 3 (step 5), clean-up: no 5 in R456C1 (step 25a), no 1 in R46C7 (step 3), no 6 in R8C78

36. Naked pair {28} in R46C7, locked for C7 and N6 -> R7C7 = 1, locked for D\, R9C7 = 6 (step 6), R9C6 = 7, R12C7 = [39], clean-up: no 7,8 in R8C8

37. 3 on D\ locked in R4C4 + R5C5 + R6C6, 3 on D/ locked in R4C6 + R5C5 + R6C4 -> R5C5 = 3

38. Naked pair {39} in R46C3, locked for C3 and N4 -> R8C3 = 2, R8C2 = 9, R8C8 = 4, locked for D\, R8C7 = 5

39. Naked pair {18} in R12C3, locked for N1 -> R2C2 = 2, R3C3 = 6, both locked for D\, R5C37 = [57], R6C6 = 5, R4C4 = 7, R9C9 = 8, R9C1 = 5, R9C58 = [92], R1C8 = 7 (step 8)

40. R2C8 = 8 (hidden single on D/), R1C6 = 6, R6C4 = 6 (hidden single on D/)

41. R3C37 = [64] = 10 -> R1C5 + R2C46 = 10 = [253], R1C9 = 1, locked for D/

and the rest is naked singles.



Assassin 119 V3 by Afmob (September 2008) here
Puzzle Diagram:
Image
Images with "udosuk style Killer Cages" by Børge:
Image     Image
Code: Select, Copy & Paste into solver:
3x3:d:k:5376:5376:3842:3842:5124:6661:6661:4103:4103:5376:3842:3842:5124:13:5124:6661:6661:4103:5376:8467:5124:21:22:23:5124:6937:4103:3867:28:8467:30:31:32:6937:34:3107:3867:37:38:8467:40:6937:42:43:3107:3867:46:8467:48:49:50:6937:52:3107:4406:8467:7224:57:58:59:7224:6937:6718:4406:4160:4160:7224:67:7224:5701:5701:6718:4406:4406:4160:4160:7224:5701:5701:6718:6718:
Solution:
+-------+-------+-------+
| 9 5 8 | 4 2 6 | 3 7 1 |
| 4 2 1 | 5 7 3 | 9 8 6 |
| 3 7 6 | 9 8 1 | 4 5 2 |
+-------+-------+-------+
| 6 4 3 | 7 1 2 | 8 9 5 |
| 2 1 5 | 8 3 9 | 7 6 4 |
| 7 8 9 | 6 4 5 | 2 1 3 |
+-------+-------+-------+
| 8 6 7 | 2 5 4 | 1 3 9 |
| 1 9 2 | 3 6 8 | 5 4 7 |
| 5 3 4 | 1 9 7 | 6 2 8 |
+-------+-------+-------+
Quote:
Afmob: By the way, if you got too much time on your hands then try to tackle this one (warning! contains minor spoilers on V2)
The only hint I can give you is that there really is only one solution but no software is going to help you solve it.

Andrew:
Afmob wrote:
By the way, if you got too much time on your hands then try to tackle this one (warning! contains minor spoilers on V2).
Having looked at both diagrams I would have thought it was the other way round. Solving V2 should be helpful to solving the puzzle in the hidden diagram. However I can't see any reason why solving the hidden one should help solving V2 since it's clearly a harder version of V2.
Afmob wrote:
The only hint I can give you is that there really is only one solution but no software is going to help you solve it.
I wonder if that's really true. At a quick glance all the missing areas can be replaced by cages in V2 using simple application of the 45 rule. Then it's just(?) a harder version of V2 by combining two pairs of cages. Solver software, which I've never used, ought then to be able to solve it.
[Edit. See my later message.]

Afmob: Well, it's only a minor spoiler because with those merged cages in R89 (5(2) + 11(2) and 9(2) + 13(2)) you know that no number can repeat in those cages, e.g. R9C4 cannot have the same value as R8C23+R9C3 and R9C6 cannot have the same value as R8C78+R9C7.

Andrew: As Afmob has pointed out to me by PM, [size=14]my "logic" about filliing the missing areas with the cages of V2 was wrong.
However if one did that anyway, it looks like it's still an extremely difficult puzzle, probably significantly more so than V2 which I'm currently finding very hard
.
Afmob has now explained what he meant by the spoiler. Of course one still has to solve V2 without relying on that since it's not part of the V2 puzzle.

udosuk: Probably won't attempt v3 now, unless there is convincing evidence that it can be solved logically.
Note I also has a v3 for my Assassin 115 with similar difficulty, but it's not a zero killer. :geek: (Archive Note. That V3 wasn't posted in the forum)


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