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Andrew
PostPosted: Wed Aug 03, 2011 4:42 am 
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Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Puzzle rating table, with links to archive entries; each of these has a link to the puzzle thread.

Abbreviations used in Rating Table:
Est = Estimated rating by puzzle maker
E = Easy
Score = SudokuSolver v3.3 score, rounded to nearest 0.05
+------------------------+-----------+-------+-------+-------+-----------------------+-------+
| Puzzle                 |  Made By  |  Est  | Afmob | Andrew|     Other Raters      | Score |
+------------------------+-----------+-------+-------+-------+-----------------------+-------+
| Assassin 150           | Ronnie G  |       | E1.25 | E1.25 |                       |  1.05 |
| Assassin 150V2         | Ronnie G  |       | E1.75 | E1.75 |                       |  1.65 |
| Assassin 150V1.25      | Ronnie G  |       |       |  1.25 |                       |  1.30 |
+------------------------+-----------+-------+-------+-------+-----------------------+-------+


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 12:54 am, edited 1 time in total.

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Andrew
PostPosted: Wed Aug 03, 2011 9:20 pm 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Assassin 150 by Ronnie G (April 2009) here
Puzzle Diagram:
Image
Images with "udosuk style Killer Cages" by Børge: 
Image     Image
Code: Select, Copy & Paste into solver:
3x3::k:1792:2561:2561:4099:4099:4099:3078:3078:2824:1792:3338:3851:3851:4099:1038:1038:4624:2824:4882:3338:3338:3861:4630:5399:4624:4624:2586:4882:3356:3861:3861:4630:5399:5399:2338:2586:4882:3356:2086:2086:4630:1577:1577:2338:2586:1069:4398:7215:7215:4145:7986:7986:4660:3381:1069:4398:7215:4145:4145:4145:7986:4660:3381:4398:4398:7215:7215:3395:7986:7986:4660:4660:5704:5704:5704:5704:3395:4685:4685:4685:4685:
Solution: 
+-------+-------+-------+
| 5 9 1 | 3 2 7 | 8 4 6 |
| 2 6 7 | 8 4 1 | 3 9 5 |
| 8 4 3 | 5 6 9 | 2 7 1 |
+-------+-------+-------+
| 7 5 9 | 1 3 8 | 4 6 2 |
| 4 8 6 | 2 9 5 | 1 3 7 |
| 1 3 2 | 4 7 6 | 5 8 9 |
+-------+-------+-------+
| 3 7 8 | 6 1 2 | 9 5 4 |
| 6 1 5 | 9 8 4 | 7 2 3 |
| 9 2 4 | 7 5 3 | 6 1 8 |
+-------+-------+-------+
Quote:
Ronnie G: Another milestone for us... the big 1-5-0
Thought this was a good time to return to our roots, with a simple(r) puzzle, to entice the newer members and our guests!
I wanted to use a traditional cage pattern, no diagonals or remote cages, and lots of I/O's that may or may not be useful, just like Ruud's early Assassins.
Many regulars will no doubt find this puzzle too easy, so I plan to post a V2 soon. Enjoy!
SS Score 1.03.
Happy Easter everyone!

Afmob: I found this one harder than SudokuSolver's rating suggested since it took me some time to find the breakthrough move. I hope someone finds an easier way to crack it.
Rating: Easy 1.25.

Joe Casey: Agreed - on the Casey scale this was "no pushover". Is your middle name Ruud? It looks as if it's going to be as easy as you said but then it jams up. Sorry I haven't kept track of how I got it as I was listening to Jimi Hendrix at the same time.

Ronnie G: Well, first off let me apologize if I was misleading about the difficulty of V1. The last thing I wanted to do was scare away newbies or wannabes :oops:
When I solved it, I did use sort of a "trick" move, (actually more like a one-two punch), but the rest of the puzzle was straightforward, or at least seemed so to me. I assumed from the SS score that there was an easier way. I've never offered a personal "score" for any Assassin, and now I probably never will! Obviously I don't know how to properly rate a puzzle!

manu: Thanks for this assassin, Ronnie. It offers ... No way don't worry too much about the rating, Ronnie ; it is only an indication about the techniques needed, which is slightly different of the difficulty felt by a(n?) human solver.

Andrew: From these comments (by Afmob and Ronnie G) and my walkthrough I'll assume there probably isn't an easier way that we would consider to be a 1.0 solving path. When I've occasionally commented to Ed that I've looked for easier moves because of a SS score, he's replied that sometimes SS has used a harder step than one would expect from the score. This can happen if there's only one harder step and the solution is fairly short; that may have happened for A150.

See also discussion about the rating for this puzzle, including how SudokuSolver and JSudoku solved it, after the posted walkthroughs.

Walkthrough by Afmob:
I found this one harder than SudokuSolver's rating suggested since it took me some time to find the breakthrough move. I hope someone finds an easier way to crack it.

A150 Walkthrough:

1. R789
a) Innie R9 = R9C5 = 5
b) Cage sum: R8C5 = 8
c) 4(2) = {13} locked for C1
d) Innies C1 = 15(2) = [69/78/96]

2. R123
a) 7(2) = {25} locked for C1+N1
b) 4(2) = {13} locked for R2
c) Innies N3 = 4(2) = {13} locked for N3
d) 12(2) <> 9
e) 11(2) = {29/56} since (47) is a Killer pair of 12(2)
f) Outies R1 = 11(3) = {245} -> R2C5 = 4; 2,5 locked for R2
g) 13(3) = 4{18/36} because {139} blocked by R3C9 = (13); R3C23 = 4{1/3} -> 4 locked for R3+N1

3. C123 !
a) 19(3) = 4{69/78} -> 4 locked for N4
b) 13(2) <> 9
c) Killer pair (68) locked in R2C2 + 13(2) for C2
d) 17(4): R678C2 <> 9 because R8C1 >= 6
e) ! Innies+Outies C12: -7 = R13C3 - R9C12: R9C2 <> 9 because R9C12 = [69] clashes with Innies C1 = 15(2)
and R9C12 = [89] implies R3C13 = 10 which clashes with 10(2) @ N1 (Double IOU?)
f) Hidden Single: R1C2 = 9 @ C2 -> R1C3 = 1
g) 13(3) = {346} -> R2C2 = 6; 3 locked for R3
h) 13(2) = {58} locked for C2+N4
i) 19(3) = {478} since R3C1 = (78) -> R3C1 = 8; 7 locked for C1+N4
j) 17(4) = {1367} because {1349} blocked by R3C2 = (34) -> R8C1 = 6; 1,3 locked for C2 and 7 locked for N7

4. C789
a) 11(2) = {56} -> R2C9 = 5, R1C9 = 6
b) 13(2) = {49} locked for C9
c) Innies C9 = 11(2) = {38} -> R8C9 = 3, R9C9 = 8
d) Innie R12 = R2C8 = 9
e) R3C9 = 1, R2C7 = 3
f) 3 locked in 9(2) @ N6 = {36} locked for C8+N6
g) 18(4) @ R6C8 = {2358} -> R6C8 = 8; 2,5 locked for C8+N9

5. C456
a) 16(4) @ N2 = {2347} -> 2,3,7 locked for R1+N2
b) Innies C1234 = Innies C6789 = 9(2): R7C46 = (267)
c) 22(4) = 49{27/36} -> R9C1 = 9; R9C4 = (67)
d) Hidden Single: R5C5 = 9 @ R5
e) R3C5 = 6 -> R4C5 = 3, R4C8 = 6, R5C8 = 3
f) 8(2) = {26} locked for R5
g) Hidden Single: R1C4 = 3 @ C4
h) Innie C1234 = R7C4 = 6

6. Rest is singles.

Rating: Easy 1.25. I used small IOD combo analysis.
Walkthrough by manu:
Thanks for this assassin, Ronnie. It offers some interesting dependences between cells and cages, that are difficult to explain in a WT. I have tried to avoid hard combinations analysis and have prefered a short forcing chain that seems to me easier whereas it increases the puzzle rating. No way don't worry too much about the rating, Ronnie ; it is only an indication about the techniques needed, which is slightly different of the difficulty felt by a(n?) human solver. Combo analysis employed by SSolver are sometimes very hard to follow and could be viewed as a kind of contradiction step.

Edit : thanks to Ed for helpful comments
Walkthrough Assassin 150 V1

I have used a killer pair (step 10b), a kind of "cloning cell" technique (step 5c) and a short forcing chain (step 7b) that can be viewed as a kind of a killer XY-wing.

1)4(2) at n4={13} locked for c1 → 7(2) at n1={25} locked for c1 and n1

2)Innie for r9 : r9c5=5 → r8c5=8

3)a) Innies for n1 : r3c1+r2c3=15 : (6789) for these cells
b) Innies for n3 : r2c7+r3c9=4 → r2c7=(13), r3c9=(13), {13} locked for n3
c) Deduce from b) and cage 4(2) at n2 that r2c6=r3c9, and that digit at r2c6=r3c9 is locked for r1 and n1 at cage 10(2) : combinations = {19/37} : no 4
d) Cage 12(3) at n3={48/57} since combinations of cage 10(2) blocks combination {39} (alt. : a consequence of step 3)b)e) Combinations of cage 11(2) at n3 : {29/56} no {47} because {47} is blocked by combinations of cage 12(2)

4)a) Innies for r12 : r2c2+r2c8=15 : naked quad {6789} locked at r2c2348 for r2
b) cage 4(2) at n2={13} locked for r2 → r2c5=4 (HS).
c) 4 is locked for r1 at cage 12(2)={48} locked for n3 and r1.
d) r2c8<>8 → r2c2<>7 (step a)
e) 4 is locked for r3 and n1 at cells at r3c23 → 13(3)={148/346} : r2c2=(68), r2c8=(79)

5)a) Innies for c1 : r89c1 totals 15 : r89c1=(6789)
b) 4 is locked for c1 and n4 at r45c1 → 13(2) at n4={58/67}
c) 19(3) at c1 contains 4 : the two remaining cells (r3c1 and one of r45c1) total 15.
From step 3a) r3c1 and r2c3 also total 15, so r2c3 is equal to one of r45c1 (cloning cell).
We conclude that cage 13(2) at n4 sees both cells r2c2 and r2c3 (alt., suggested by Ed : "45" on n1: 2 outies r45c1 - 4 = r2c3.
Since 4 is locked at r45c1 and this equals the IOD -> the other cell at r45c1 = r2c3.Nice piece of logic ! )
d) r2c2+r2c3<>15 (since it would clash with h15(2) at r2c3 + r3c1 step 3a) : combinations of r2c23 : [67/68/86/89]
e) Using step b and c, cage 13(2) blocks combinations [68] and [86]. We deduce r2c23=[67/89] and r3c1=(86), r2c4=(86)

6)a) Innies for c1234 : r1c4+r7c4=9 : no 9
b) Innies for c6789 : r1c6+r7c6=9 : no 9
c) r7c46<>8 → r1c46<>1. Deduce that cage 16(4) at n2 cannot contain both 1 and 9 : combination {1249} is no valid. Deduce that 9 is locked at r3c456 for r3 and n2.

7)a) Combinations of cage 18(3) at n3 : [9{27}] or [7{56}]
b) Short forcing chain (in fact a killer XY-Wing)
(i) r2c8=9 → r2c2=6 (step 4a)
(ii) r2c8=7 → r3c78={56} (step a)
We deduce that r3c1 must be different of 6

8)a) r3c1=8, r2c2=6, r2c4=8, r2c3=7, r2c8=9.
b) Last combinations : r3c23={34} locked for n1 and r3 ->r3c9=1 and r2c67=[13],
r1c23={19} locked for r1, r3c78={27} locked for r3 and n3, r12c9=[65], r12c1=[52].
c) Last combinations : r45c1={47} locked for c1 and n4, 13(2) at n4 = {58} locked for n4 and c2, cage 13(2) at c9 = {49} locked for c9, r45c9={27} locked for c9 and n6
d) Naked pair : r89c1={69} locked for n7, r89c9=[38]

9)3 is locked for c8 and n6 at cage 9(2) : combination {36}, 6 locked for n6 and c8.

10)a) 7 is locked for r6 at r6c456 : locked also for n5. No 7 for cage 8(2) at n4.
b) Killer pair {25} for r5 at cages 6(2) and 8(2) : deduce r45c2=[58], r45c9=[27], r45c1=[74]
c) cage 6(2) at r5 = [51], cage 8(2) at r5 = {26} locked for r5, r45c8=[63].
d) NS : r5c5=9 → r34c5=[63], r3c6=9, r3c4=5
e) Last combination : r4c34=[91].

11)a) HS for c5 : r7c5=1
b) r67c1=[13]

12)Innies for c8 : r1c8+r3c8+r9c8=12 : only combination r139c8=[471] → r134c7=[824] r4c6=8.

13)r6c9=9, r6c7=5 and r6c8=8, all naked singles

14)a) r8c1<>9 since r6c2+r7c2+r8c2 <> 8 ( combination {134} blocked by r3c2=(34) ) → r89c1=[69]
b) last combination for cage 17(4) at n4 : {1367} → r678c2=[371], r1c23=[91], r3c23=[43]
c) NS : r9c2=2, last combination of cage 22(4) at n7 : [9247]
d) Last combination for the two innies of c1234 (step 6a) : r17c4=[36]

15) Rest is only naked singles
Walkthrough by Andrew:
Afmob wrote:
I found this one harder than SudokuSolver's rating suggested since it took me some time to find the breakthrough move. I hope someone finds an easier way to crack it.

Ronnie G wrote:
When I solved it, I did use sort of a "trick" move, (actually more like a one-two punch), but the rest of the puzzle was straightforward, or at least seemed so to me. I assumed from the SS score that there was an easier way.
From these comments and my walkthrough I'll assume there probably isn't an easier way that we would consider to be a 1.0 solving path. When I've occasionally commented to Ed that I've looked for easier moves because of a SS score, he's replied that sometimes SS has used a harder step than one would expect from the score. This can happen if there's only one harder step and the solution is fairly short; that may have happened for A150. See also Ed's message later in this thread.

I took an overnight break after reaching innie-outie combo analysis. When I returned to the puzzle I found a better innie-outie but still needed combo analysis. Then after going through Afmob's walkthrough I found a simplified version of the key step which I've given after my walkthrough.

I'll rate A150 at Easy 1.25; that also applies to the simplified version because it still uses a combo overlap.

Here is my walkthrough.

Prelims

a) R12C1 = {16/25/34}, no 7,8,9
b) R1C23 = {19/28/37/46}, no 5
c) R1C78 = {39/48/57}, no 1,2,6
d) R12C9 = {29/38/47/56}, no 1
e) R2C34 = {69/78}
f) R2C67 = {13}, locked for R2, clean-up: no 4,6 in R1C1, no 8 in R1C9
g) R45C2 = {49/58/67}, no 1,2,3
h) R45C8 = {18/27/36/45}, no 9
i) R5C34 = {17/26/35}, no 4,8,9
j) R5C67 = {15/24}
k) R67C1 = {13}, locked for C1, clean-up: no 4,6 in R2C1
l) R67C9 = {49/58/67}, no 1,2,3
m) R89C5 = {49/58/67}, no 1,2,3
n) R345C1 = {289/379/469/478/568}, no 1
o) 21(3) cage at R3C6 = {489/579/678}, no 1,2,3
p) R345C9 = {127/136/145/235}, no 8,9

1. 45 rule on R9 1 innie R9C5 = 5, R8C5 = 8

2. Naked pair {25} in R12C1, locked for C1 and N1, clean-up: no 8 in R1C23

3. 45 rule on C1 2 innies R89C1 = 15 = [69/78/96]

4. 45 rule on C9 2 innies R89C9 = 11 = {29/47}/[38/56], no 1, no 6 in R8C9, no 3 in R9C9

5. 45 rule on N1 2 innies R2C3 + R3C1 = 15 = {69/78}, no 4
5a. 4 in C1 locked in R56C1, locked for N4, clean-up: no 9 in R45C2

6. 45 rule on N3 2 innies R2C7 + R3C9 = 4 = {13}, locked for N3, clean-up: no 9 in R1C78, no 8 in R2C9
6a. R12C9 = {29/56} (cannot be {47} which clashes with R1C78), no 4,7

7. 45 rule on R12 2 innies R2C28 = 15 = {69/78}
7a. Naked quad {6789} in R2C2348, locked for R2, clean-up: no 2,5 in R1C9
7b. R2C5 = 4 (hidden single in R2)

8. Min R2C2 = 6 -> max R3C23 = 7, no 6,7,8,9 (because cannot repeat 6 in cage)
8a. Naked triple {134} in R3C23 and R3C9, locked for R3
8b. 4 in R3 locked in R3C23, locked for N1, clean-up: no 6 in R1C23
8c. R3C23 = {14/34} = 5,7 -> R2C2 = {68}, clean-up: no 6,8 in R2C8 (step 7)
8d. Killer pair 6,8 in R2C2 and R45C2, locked for C2

9. 4 in R1 locked in R1C78 = {48}, locked for R1 and N3

10. 45 rule on C5 3 remaining innies R167C5 = 10 = {127/136}, no 9, 1 locked for C5

11. 45 rule on C1234 2 innies R17C4 = 9 = {27/36}/[54], no 1,9

12. 45 rule on C6789 2 innies R17C6 = 9 = {27/36}/[54], no 1,9

13. 17(4) cage at R6C2 = {1259/1367/1457/2357/2456} (cannot be {1349} which clashes with R3C2)
13a. 9 of {1259} must be in R8C1 -> no 9 in R678C2

[See at end for simplified version of step 14]
14. 45 rule on C12 3(1+2) innies R1C2 + R9C12 = 1 outie R3C3 + 17, IOU R9C12 cannot be [89] = 17
14a. Max R9C12 = 16 -> R1C2 must be greater than R3C3 -> no 1 in R1C2, clean-up: no 9 in R1C3
14b. R9C12 cannot be 15 (because of overlap clash with R89C1 = 15, step 3) -> R1C2 cannot be 2 greater than R3C3 -> no 3 in R1C2, clean-up: no 7 in R1C3

15. 45 rule on C12 2 innies R9C12 = 2 outies R13C3 + 7
15a. Min R13C3 = 4 -> min R9C12 = 11, no 1 in R9C2
15b. R13C3 = {13/14} (cannot be [34] because R9C12 cannot total 14), 1 locked for C3 and N1, clean-up: no 7 in R5C4
15c. R13C3 = 4,5 -> R9C12 = 11,12, no 6 in R9C1, no 7,9 in R9C2, clean-up: no 9 in R8C1

16. R1C2 = 9 (hidden single in C2), R1C3 = 1, R1C9 = 6, R2C9 = 5, R12C1 = [52], clean-up: no 6 in R2C3 + R3C1 (step 5), no 6,9 in R2C4, no 7,8 in R67C9

17. R345C9 = {127} (only remaining combination) -> R3C9 = 1, R45C9 = {27}, locked for C9 and N6, R2C67 = [13], clean-up: no 4 in R5C6, no 5 in R5C7

18. R89C9 = [38] (hidden pair in C9), R9C1 = 9, R8C1 = 6 (step 3)
18a. Naked pair {78} in R2C34, locked for R2 -> R2C2 = 6, R2C8 = 9, clean-up: no 7 in R45C2

19. Naked triple {237} in R1C456, locked for N2 -> R2C4 = 8, R2C3 = 7, R3C1 = 8, clean-up: no 1 in R5C4

20. Naked pair {58} in R45C2, locked for C2 and N4, clean-up: no 3 in R5C4

21. 7 in C2 locked in R678C2 -> 17(4) cage at R6C2 (step 13) = {1367} (only remaining combination), 3 locked for C2 -> R3C23 = [43], R9C2 = 2, R9C3 = 4, R9C4 = 7 (cage sum), R78C3 = [85], clean-up: no 5 in R5C4

22. Naked pair {26} in R5C34, locked for R5 -> R45C9 = [27], R45C1 = [74], R5C67 = [51], R45C2 = [58], R5C8 = 3, R4C8 = 6, R345C5 = [639], R9C78 = [61], R9C6 = 3, R4C3 = 9, R3C4 = 5, R4C4 = 1 (cage sum), R3C6 = 9

23. 16(4) cage at R6C5 = {1267} (only remaining combination) -> R6C5 = 7, R7C5 = 1, R7C46 = {26}, locked for R7 and N8 -> R8C6 = 4, R8C4 = 9

24. R7C3 + R8C34 = [859] = 22 -> R6C34 = 6 = [24]

25. Naked pair {27} in R8C78, locked for R8 and N9

and the rest is naked singles and a cage sum.

Simplified version of step 14; in my original walkthrough I hadn’t spotted that steps 14 and 14b eliminate 9 from R9C2.

14. 45 rule on C12 3(1+2) innies R1C2 + R9C12 = 1 outie R3C3 + 17, IOU R9C12 cannot be 17 = [89]
14a. R9C12 cannot be [69] (because of overlap clash with R89C1 = 15, step 3)
14b. R9C12 not [69/89] -> no 9 in R9C2, R1C2 = 9 (hidden single in C2), R1C3 = 1, clean-up: no 7 in R5C4

Steps 15 and 16 are then simplified because of the placements in R1C23.
Discussion of the Puzzle Rating, with how SudokuSolver and JSudoku solved it:
Ed

I found this puzzle (A150) really tricky. I solved it using Andrew's alternate step 14 at the end of his WT. My first reaction on finding that way was, "Hmm - a composite move like that feels like at least a 1.50 rating" but then spend lots of frustration time trying to find an easier alternative. Wish I'd had manu's attitude with this puzzle and just been content with an interesting solution (and his has plenty of interest in it!!) and be "so-what" about the score and others' ratings.

I know SudokuSolver can't do that sort of composite move so thought I'd find out how it did it. I've explained everything out to make it so humans can follow how it works.

From here (at Afmob's step 3d or Andrew's step 13)
Code:
.-------------------------------.-------------------------------.-------------------------------.
| 25        1379      1379      | 23567     12367      23567     | 48        48        69        |
| 25        68        6789      | 6789      4         13        | 13        79        25        |
| 6789      134       134       | 256789    2679      56789     | 25679     25679     13        |
:-------------------------------+-------------------------------+-------------------------------:
| 46789     5678      12356789  | 123456789 23679     456789    | 456789    12345678  1234567   |
| 46789     5678      123567    | 123567    23679     1245      | 1245      12345678  1234567   |
| 13        12357     12356789  | 123456789 12367     123456789 | 123456789 123456789 456789    |
:-------------------------------+-------------------------------+-------------------------------:
| 13        123457    123456789 | 23467     12367     23467     | 123456789 123456789 456789    |
| 679       123457    12345679  | 1234679   8         1234679   | 12345679  12345679  234579    |
| 689       123479    12346789  | 1234679   5         1234679   | 12346789  12346789  246789    |
'-------------------------------.-------------------------------.-------------------------------'

1. "45" on c12: innies r9c12 - 7 = 2 outies r13c3
1a. min. r13c3 = {13} = 4 -> min. r9c12 = 11 (no 1)

2. "45" on c2: 2 outies r3c3 + r8c1 + 2 = 2 innies r19c2
2a. 2 outies = [16] = 7 -> 2 innies = 9 = [72]
2b. 2 outies = [17] = 8 -> 2 innies = 10 = [73] ([19] blocked by 1 in r3c3; [37] blocked by 7 in r8c1)
2c. 2 outies = [19] = 10 -> 2 innies = 12 = [93] ([39] blocked by 9 in r8c1)
2d. 2 outies = [36] = 9 -> 2 innies = 11 = [74/92]
2e. 2 outies = [37] = 10 -> 2 innies = 12 = [93] ([39] blocked by 3 in r3c3)
2f. 2 outies = [39] = 12 -> 2 innies = 14 blocked
2g. 2 outies = [46] = 10 -> 2 innies = 12 = {39}
2h. 2 outies = [47] = 11 -> 2 innies = 13 = [94]
2i. 2 outies = [49] = 13 -> 2 innies = 15 blocked
2j. In summary, no 1 in r1c2, no 7 in r9c2 (this is the crucial one)
2k. -> No 9 in r1c3

3. "45" on c2: 3 outies r13c3 + r8c1 - 8 = 1 innie r9c2
3a. Looking at the 3 outies: with 9 in r8c1 and min. r13c3 = 4 which means a min. of 13 in the outies -> min. in r9c2 = 5. However, 9 is not available in r9c2 because it's in r8c1. -> no 9 in r8c1
3b. no 6 in r9c1 (h15(2))

4. "45" on c12: 3 innies r1c2 + r9c12 - 17 = 1 outie r3c3
4a. Now Andrew's nice 4-cell IOU move works in a simple way. r9c12 cannot equal the IOD of 17 since that would force r1c2 & r3c3 to be equal -> no 9 in r9c2 since r9c12 could only be [89] = 17.

Step 2 looks very much like hypotheticals so we'd probably give it a rating of 2.00. Can anyone see a pattern method to get rid of the 7 from r9c2?

How did SS get such a low score?
1) Unlike humans, it's "45" routines don't just work on IOU and max./min. but all permutations. Unfortunate in this case that it found the key one (no 7 in r9c2) so early in it's solution.
2) The SSscore is just the sum of the step count with weightings given to each step type. It found step 4 above by step 60 which is unusually early for most Assassins.
3) The first key placement at r1c2 has an unusual property. It basically reduces the whole puzzle to singles in one stroke. This reduces the step count even further and hence, gives a lower score. This type of placement is apparently called a "backdoor single". udosuk mentions this here and was well known in vanilla sudoku circles at that time (Sept '06).

It would be interesting to see what would happen to the overall correlation for all Assassins of the SSscore if the main "45" routines just did IOU and max/min. eliminations. Worth a try Richard?

So the moral is, the SSscore and human ratings can be quite different!

Another interesting week. Thanks Ronnie!


Andrew

Just tidying up my files for A150 and I realised that I hadn't commented on Ed's interesting post about how SS solved A150.

Ed wrote:
I found this puzzle (A150) really tricky. I solved it using Andrew's alternate step 14 at the end of his WT. My first reaction on finding that way was, "Hmm - a composite move like that feels like at least a 1.50 rating" but then spend lots of frustration time trying to find an easier alternative.
As I said to Ed at the time, I didn't see my alternate step 14 as a composite move; to me there are two separate and independent parts in this step, each of which eliminates one permutation. I don't see that as being any different to gradually eliminating combinations/permutations from a fixed cage. I'm therefore surprised that SS can't do what I did as two steps.

Ed wrote:
Step 2 looks very much like hypotheticals so we'd probably give it a rating of 2.00. Can anyone see a pattern method to get rid of the 7 from r9c2?

How did SS get such a low score?
1) Unlike humans, it's "45" routines don't just work on IOU and max./min. but all permutations. Unfortunate in this case that it found the key one (no 7 in r9c2) so early in it's solution.
I'll agree that SS's step 2 looks very much like hypotheticals, which I'd rate at least 1.75 and possibly 2.0; in this case more likely 2.0 because some of the I-O permutation analysis involved tricky blocking.

It's interesting that the elimination of 7 from r9c2 was the key in SS's solving path. I felt that eliminating 9 from r9c2, which made r1c2 = 9 a hidden single in c2, was the key elimination.


Ed

I know it's way out of date but been meaning to have a look at how JSudoku does A-1-5-0. For another reason (to be revealed in about a week :) ), I've finally taken an interest in how JSudoku solves killers.

Code:
+----------------------------------+----------------------------------+----------------------------------+
| 25         1379       1379       | 23567      1237       23567      | 48         48         69         |
| 25         68         6789       | 6789       4          13         | 13         79         25         |
| 6789       134        134        | 256789     2679       56789      | 25679      25679      13         |
+----------------------------------+----------------------------------+----------------------------------+
| 46789      5678       12356789   | 123456789  23679      456789     | 456789     12345678   1234567    |
| 46789      5678       123567     | 123567     23679      1245       | 1245       12345678   1234567    |
| 13         12357      12356789   | 123456789  12367      123456789  | 123456789  123456789  456789     |
+----------------------------------+----------------------------------+----------------------------------+
| 13         123457     123456789  | 23467      12367      23467      | 12456789   123456789  456789     |
| 679        123457     12345679   | 1234679    8          1234679    | 12345679   12345679   234579     |
| 689        123479     12346789   | 123479     5          1234679    | 12346789   12346789   246789     |
+----------------------------------+----------------------------------+----------------------------------+


From marks above (copy and "Paste Into" A150 in SudokuSolver)
1. 3 of n1 locked in cage 10(2) in r1c23 or h16(4) in r3c2378 -> 7 also locked in Cage 10(2) or h16(4) -> no 7 in r3c1 (Locked cages)
1a. no 8 in r2c3 (h15(2)n1)
1b. no 7 in r2c4 (cage sum)

2. 19(3)n1 = {469/478}
2a. 8 of {478} must be in r3c1 -> no 8 in r45c1

3. Grouped XY-Chain -> no 6 in r2c3. Like this
3a. if r2c2 is not 6 it is 8 -> 8 in c1 is in r9c1 in h15(2)r89c1 (no 6) -> 6 in n7 in c789c3 -> no 6 in r2c3
3b. if r2c2 = 6 -> no 6 in r2c3
3c. no 9 in r2c4
3d. no 9 in r3c1 (h15(2)n1)

4. XY-X Chain -> no 6 in r3c78. Like this.
4a. If r1c9 is not 6 it is 9 -> r2c8 = 7 -> r1c3 = 9 -> r3c1 = 6 (h15(2)n1) -> no 6 in r3c78
4b. if r1c9 = 6 -> no 6 in r3c78

5. r1c9 = 6 (hsingle n3)

Now it's cracked.

Some nice moves in there.
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Andrew
PostPosted: Wed Aug 03, 2011 9:56 pm 
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Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Assassin 150 V2 by Ronnie G (April 2009) here
Puzzle Diagram:
Image
Images with "udosuk style Killer Cages" by Børge: 
Image     Image
Code: Select, Copy & Paste into solver:
3x3::k:1792:4097:4097:4099:4099:4099:2310:2310:3336:1792:2826:2827:2827:4099:2830:2830:2832:3336:5394:2826:2826:5653:4118:6167:2832:2832:4634:5394:3868:5653:5653:4118:6167:6167:4130:4634:5394:3868:3868:5653:4118:6167:4130:4130:4634:5394:3886:5935:5935:4145:6962:6962:4404:4634:3886:3886:5935:4145:4145:4145:6962:4404:4404:2623:2623:5935:5935:3395:6962:6962:1606:1606:4424:4424:4424:4424:3395:6221:6221:6221:6221:
Solution: 
+-------+-------+-------+
| 2 7 9 | 5 8 1 | 3 6 4 |
| 5 6 8 | 3 2 4 | 7 1 9 |
| 3 1 4 | 9 7 6 | 2 8 5 |
+-------+-------+-------+
| 8 5 7 | 2 6 9 | 1 4 3 |
| 6 9 1 | 4 3 8 | 5 7 2 |
| 4 2 3 | 1 5 7 | 6 9 8 |
+-------+-------+-------+
| 9 4 5 | 7 1 3 | 8 2 6 |
| 7 3 6 | 8 9 2 | 4 5 1 |
| 1 8 2 | 6 4 5 | 9 3 7 |
+-------+-------+-------+
Quote:
Ronnie G: Moving on, here's the V2 I promised. I didn't really like this puzzle and searched for something better but I've run out of time. I had to resort to some fairly heavy combo-crunching to solve it, which I find tedious, but others might enjoy. It has a slightly altered cage pattern from V1 and also a different solution.
SS score: 1.67.

Afmob: That was a tough Killer! Like V1 I hope that someone finds an easier way to solve it.
Rating: (Easy?) 1.75.

Andrew (in 2010): It certainly was tough! I don't think my way was any easier ...
I'll also rate A150 V2 at (Easy?) 1.75 because I think Afmob's solving path and my one have similar levels of difficulty.

Walkthrough by Afmob:
That was a tough Killer! Like V1 I hope that someone finds an easier way to solve it. Maybe by using a small forcing chain?

A150 V2 Walkthrough:

1. R6789
a) Innie R9 = R9C5 = 4
b) Cage sum: R8C5 = 9
c) Innies R6789 = 12(2) <> 1,2,6

2. R123 !
a) 16(2) = {79} locked for R1+N1
b) Innies N1 = 11(2) = {38/56}
c) 9(2) <> 2
d) Innies N3 = 12(2) <> 1,2,6
e) 11(2) @ N1 = {38/56}
f) 2 locked in 11(3) @ N3 = 2{18/36/45} <> 7
g) ! Hidden Killer pair (79) in Innies N3 + R2C9 since Innies N3 can only have one of them
-> R2C9 = (79) and Innies N3 = {39/57}
h) 13(2) = [49/67]
i) 11(2) @ N3: R2C6 = (2468)

3. R123
a) Outies R1 = 16(3): R2C5 <> 7 since R2C9 = (79)
b) 7,9 locked in R3C456 @ N2 for R3
c) Innies N3 = 12(2) = [79/35]
d) 11(2) @ N3 = [29/47]

4. C456
a) Innies C6789 = 4(2) = {13} locked for C6
b) Innies C1234 = 12(2) = [48/57]
c) 16(4) @ N8 = 1{258/267/357} because R7C4 = (78) -> R67C5 <> 7,8
d) 7 locked in 16(3) @ C5 = 7{18/36}

5. R123
a) 9(2) = {18/36} since (45) blocked by R1C4 = (45)
b) Killer pair (13) locked in R1C6 + 9(2) for R1
c) 7(2): R2C1 <> 4,6
d) Outies R1 = 16(3) = {169/178/259} <> 3 because R2C9 = (79) and {367} blocked by Killer pair (36) of 11(2) @ N1
e) 7(2) <> 4
f) 4 locked in 11(3) @ N1 = 4{16/25}
g) 3,8 locked in Innies N1 = 11(2) = {38}
h) 11(2) @ N1 = {38} locked for R2
i) Innies R12 = 7(2) <> 4

6. R123
a) Hidden Single: R2C6 = 4 @ R2 -> R2C7 = 7
b) R2C9 = 9 -> R1C9 = 4, R1C4 = 5
c) Innie N3 = R3C9 = 5
d) 18(4) = {2358} -> 2,3,8 locked for C9+N6
e) R8C9 = 1 -> R8C8 = 5
f) 16(4) = 25{18/36} -> 2 locked for C5+N2; R2C5 <> 1 because R1C6 = (13)
g) Killer pair (38) locked in 16(4) + R2C4 for N2

7. R6789
a) 16(4) = {1357} -> R7C4 = 7
b) R7C9 = 6, R9C9 = 7
c) 17(3) = [74/92]6
d) Innies R6789 = 12(2) = [48/93]
e) 24(4) = 7{269/359/368} -> R9C6 = (56)

8. R456
a) 16(3) @ N6 = {169/457}: R5C7 <> 4 since R45C8 <> 5
b) Killer pair (79) locked in 16(3) @ N6 + R6C8 for N6
c) 24(4) <> {4569} since it's blocked by R9C6 = (56)

9. C123
a) Innies C1 = 17(3) = {179/278/359/458/467} because 6{29/38} blocked by R1C1 = (26) and R1C3 = (38)
b) Innies C1 = 17(3): R79C1 <> 3 since R8C1 <> 5,9 and R8C1 <> 2,6 because 7 only possible there
c) 10(2): R8C2 <> 4,8

10. R6789 !
a) 27(5): R6C6 <> 2,6 because 7 only possible there and 39{168/258/456} with R78C7 = {39} blocked by Killer pair (39) of 24(4) @ N9
b) 27(5): R6C6 <> 8 since 7 only possible there, 389{16/25} with R78C7 = {39} blocked by Killer pair (39) of 24(4) @ R9 and R8C6 <> 1,4,5,9
c) ! Outies N9 = 29(3+2): R6C68 must have 9 because
- R6C678 <> [517] = 13 since R89C6 <= 14
- R6C678 <> [547] = 16 since it clashes with R89C6 = 13 = [85]
- R6C678 <> [567] = 18 since it clashes with R89C6 = 11 = [65]
-> 9 locked in R6C68 for R6
d) Innies R6789 = 12(2) = {48} -> R6C1 = 4, R6C9 = 8
e) Innies C1 = 17(3): R8C1 <> 8 since R79C1 <> 4,7
f) 10(2) = {37} locked for R8+N7
g) 15(3) <> 7 since R7C23 <> 3,6,7

11. C456+N6
a) 4,9 locked in 22(4) @ C4 for 22(4) -> 22(4) = 49{18/27/36} <> 5
b) Innies N6 = 16(3): R4C7 <> 5 since 4 only possible there
c) 24(4) @ N6 = {1689/2679/4578} because R4C7 = (146)
d) Hidden Killer pair (28) in R8C6 for C6 since 24(4) @ N6 can only have one of (28) -> R8C6 = (28)

12. C123+R8 !
a) 6 locked in 23(5) @ R8 for 23(5)
b) Innies N14 = 20(3+1) = 3+8{27/36} / 8+{138/156/237} -> 8 locked in R24C3 for C3
c) ! Innies N14 = 20(3+1) <> 3+{368} since R6C3 = 3 sees R2C3 = 3
d) ! Innies N14 = 20(3+1) <> 8+{138} since R4C3 = 8 sees R2C3 = 8
e) 15(3) @ R4C2 <> 3,7 because 7{26/35} are blocked by Killer pairs (57,67) of Innies N14
f) ! Killer pair (12) locked in 15(3) @ R4C2 + Innies N14 for N4
g) 21(4) = 34{59/68} -> 3 locked for C1
h) R8C1 = 7, R8C2 = 3
i) Hidden Single: R1C2 = 7 @ C2 -> R1C3 = 9
j) Hidden triple (378) locked in R246C3 @ C3 -> R46C3 = (378)
k) Innies N14 = 20(3+1) = {378}+2 -> R6C2 = 2

13. N69
a) Hidden Single: R6C7 = 6 @ R6
b) 16(3) = {457} -> R5C7 = 5; 4,7 locked for C8+N6
c) R4C7 = 1
d) 24(4) @ N6 = {1689} -> 6,8,9 locked for C6; 8 also locked for N5
e) 24(4) @ R9 = {3579} -> R9C6 = 5; 3,9 locked for R9+N9

14. Rest is singles.

Rating: (Easy?) 1.75. I used combo analysis of large Outies.
Walkthrough by Andrew (in 2010):
In the A154 thread I wrote:
Having caught up with my backlog of unfinished V1s (A161 and A165) last month, I had a look to see if there were any other of Ronnie's puzzles that I hadn't yet done. I found that I'd got stuck on A154 V1.5 and hadn't yet started A150 V2 so I had a go at both of them in the last few days.
Now that I've gone through Afmob's walkthrough, here is my one. The critical area was N9 and the 27(5) cage which we looked at in different ways. Afmob first looked at the 27(5) and then outies for N9. I found innies-outies for N9 easier to think about although now that I've gone through Afmob's walkthrough his way seems to be more direct, particularly in finding the critical 9 locked in R6C68 for R6.

Afmob wrote:
That was a tough Killer! Like V1 I hope that someone finds an easier way to solve it. Maybe by using a small forcing chain?
It certainly was tough! I don't think my way was any easier; I didn't spot any forcing chains.

Rating Comment. I'll also rate A150 V2 at (Easy?) 1.75 because I think Afmob's solving path and my one have similar levels of difficulty. My hardest steps were 28b, 29a and 30a.

Here is my walkthrough for A150 V2. Thanks Afmob for the clarification to step 24b.

Prelims

a) R12C1 = {16/25/34}, no 7,8,9
b) R1C23 = {79}
c) R1C78 = {18/27/36/45}, no 9
d) R12C9 = {49/58/67}, no 1,2,3
e) R2C34 = {29/38/47/56}, no 1
f) R2C67 = {29/38/47/56}, no 1
g) R8C12 = {19/28/37/46}, no 5
h) R89C5 = {49/58/67}, no 1,2,3
i) R8C89 = {15/24}
j) 11(3) cage in N1 = {128/137/146/236/245}, no 9
k) 11(3) cage in N3 = {128/137/146/236/245}, no 9

1. 45 rule on R9 1 innie R9C5 = 4, R8C5 = 9, clean-up: no 1 in R8C12

2. Naked pair {79} in R1C23, locked for R1 and N1, clean-up: no 2 in R1C78, no 2,4 in R2C4, no 4,6 in R2C9

3. 45 rule on C1234 2 innies R17C4 = 12 = [48/57]
3a. R1C78 = {18/36} (cannot be {45} which clashes with R1C4)
3b. 16(4) cage at R6C5 cannot contain both of 7,8 -> no 7,8 in R6C5 + R7C56

4. 45 rule on C6789 2 innies R17C6 = 4 = {13}, locked for C6, clean-up: no 8 in R2C7
4a. Killer pair 1,3 in R1C6 and R1C78, locked for R1, clean-up: no 4,6 in R2C1

5. 45 rule on R12 2 innies R2C28 = 7 = {16/25/34}, no 7,8

6. 45 rule on R6789 2 innies R6C19 = 12 = {39/48/57}, no 1,2,6

7. 45 rule on N1 2 innies R2C3 + R3C1 = 11 = {38/56}, no 1,2,4, clean-up: no 7,9 in R2C4

8. 45 rule on N3 2 innies R2C7 + R3C9 = 12 = {39/57}/[48], no 1,2,6, no 4 in R3C9, clean-up: no 5,9 in R2C6

9. 11(3) cage in N1 = {128/146/245} (cannot be {236} which clashes with R2C3 + R3C1), no 3, clean-up: no 4 in R2C8 (step 5)

10. 2 in N3 only in 11(3) cage = {128/236/245}, no 7

11. 7,9 in N3 only in R2C9 and R2C7 + R3C9
11a. Hidden killer pair 7,9 in R2C9 and R2C7 + R3C9 for N3, R2C7 + R3C9 cannot contain both of 7,9 -> R2C9 = {79} and R2C7 + R3C9 must contain one of 7,9 -> R2C7 + R3C9 = {39/57}, no 4,8, clean-up: no 5,8 in R1C9, no 7 in R2C6

12. 45 rule on R1 3 outies R2C159 = 16 = {169/178/259} (cannot be {268/358} because R2C9 only contains 7,9, cannot be {367} which clashes with R2C34), no 3, clean-up: no 4 in R1C1
12a. 1 of {169/178} must be in R2C1 -> no 1 in R2C5
12b. 7 of {178} must be in R2C9 -> no 7 in R2C5

13. R2C79 = {79} (hidden pair in R2), locked for N3, clean-up: no 6,8 in R2C6

14. 16(4) cage in N2 = {1258/1348/1456/2356}
14a. Killer pair 2,4 in 16(4) cage and R2C6, locked for N2

15. 3 in N1 only in R2C3 + R3C1 (step 7) = {38} (only remaining combination), locked for N1, clean-up: no 5,6 in R2C4
15a. Naked pair {38} in R2C34, locked for R2, clean-up: no 4 in R2C2 (step 5)

16. R2C6 = 4 (hidden single in R2), R2C7 = 7, R2C9 = 9, R1C9 = 4, R1C4 = 5, R7C4 = 7 (step 3), clean-up: no 2 in R2C1, no 3,8 in R6C1 (step 6), no 2 in R8C8
16a. 2 in N2 only in R12C5, locked for C5
16b. 16(4) cage in N2 (step 14) = {1258/2356}
16c. Killer pair 3,8 in 16(4) cage and R2C4, locked for N2

17. 45 rule on N3 1 remaining innie R3C9 = 5, clean-up: no 2 in R2C2 (step 5), no 7 in R6C1 (step 6), no 1 in R8C8

18. 16(4) cage at R6C5 = {1357} (only remaining combination), no 6, 5 locked for C5

19. 18(4) cage at R3C9 = {2358} (only remaining combination), locked for C9 -> R8C9 = 1, R8C8 = 5, R7C9 = 6, R9C9 = 7, clean-up: no 5 in R6C1 (step 6)
19a. Naked triple {238} in R456C9, locked for N6

20. R7C9 = 6 -> R67C8 = 11 = [74/92]

21. 24(4) cage at R9C6 = {2679/3579/3678}
21a. 5,6 only in R9C6 -> R9C6 = {56}

22. 16(3) cage in N6 = {169/457}
22a. 5 of {457} must be in R5C7 -> no 4 in R5C7
22b. Killer pair 7,9 in 16(3) cage and R6C8, locked for N6

23. 45 rule on C1 3 innies R789C1 = 17 = {179/278/359/458/467} (cannot be {269} which clashes with R1C1, cannot be {368} which clashes with R3C1)
23a. 7 of {278/467} must be in R8C1 -> no 2,6 in R8C1, clean-up: no 4,8 in R8C2
23b. 3 of {359} must be in R8C1 -> no 3 in R79C1

24. 45 rule on N9 2 outies R6C8 + R9C6 = 2 innies R78C7 + 2, R6C8 + R9C6 = 12,13,14,15 -> R78C7 = 10,11,12,13 = {28/29/38/39/48/49}
[After going through Afmob’s walkthrough I realised that this should have been R78C7 = {28/29/38/48/49} (cannot be {39} which clashes with 24(4) cage at R9C6). As a result some of the steps after this may be a bit longer than necessary.]
24a. 27(5) cage at R6C6 = {12789/13689/14589/14679/23589/23679/24579/24678} (cannot be {15678} because R78C7 must contain one of 2,3,4, cannot be {34569} because {39} must be in R78C7 and {456} clashes with R9C6, cannot be {34578} because {38} must be in R78C7 and R8C6 doesn’t contain 4,5 or 7)
24b. {49} of {14589/14679} must be in R78C7, {49} of {24579} must be in R78C7 (because 2 must be in R8C6), {48} of {24678} must be in R78C7 (R78C7 cannot be {28} because R6C67 = [74] clashes with R6C18, ALS block) -> no 4 in R6C7

25. 45 rule on N6 3 innies R4C7 + R6C78 = 16 = {169/457}
25a. 4 of {457} must be in R4C7 -> no 5 in R4C7

26. 45 rule on C789 3 remaining outies R689C6 = 1 innie R4C7 + 13
26a. R4C7 = {146} -> R689C6 = 14/17/19 = {257/269/289/568}(cannot be {278} because R9C6 only contains 5,6)
26b. 7,9 of {257/269/289} must be in R6C6 -> no 2 in R6C6

27. 45 rule on R8 4 innies R8C3467 = 20 = {2378/2468/3467}
27a. 7 of {2378/3467} must be in R8C3 -> no 3 in R8C3

28. 24(4) cage at R3C6 = {1689/2679/4578} (cannot be {2589} because R4C7 only contains 1,4,6, cannot be {4569} which clashes with R9C6)
28a. R689C6 (step 26a) = {257/269/568} (cannot be {289} which clashes with 24(4) cage)
28b. 7 in C6 only in 24(4) cage at R3C6 or in R6C6 -> 24(4) cage = {2679/4578} or 24(4) cage = {1689}, R6C6 = 7, R4C7 = 1, R6C7 = 6 (step 25) -> either R6C67 = [76] or R6C6 not 7 and R6C7 = {15} (step 25, because R4C7 = {46} when 7 in 24(4) cage at R3C6) -> 27(5) cage at R6C6 must contain both of 6,7 or not contain 7
28c. 27(5) cage at R6C6 (step 24a) = {13689/14589/23589/23679/24678} (cannot be {12789/24579} which contain 7 but not 6, cannot be {14679} because R6C67 cannot be [76] and also contain 1)
28d. 3,4 of {23589/23679/24678} must be in R78C7 = {38/39/48}, no 2 in R78C7

29. 4 in C7 only in R4C7 and R78C7, R46C7 = {16/45} (step 25) -> R6C7 can only contain 1 or 6 when R78C7 contains 4 (a sort of variable hidden killer pair)
29a. 27(5) cage at R6C6 (step 28c) = {14589/23589/24678} (cannot be {13689/23679} which must have 1 or 6 in R6C7 but don’t contain 4)
29b. 7 of {24678} must be in R6C6 -> no 6 in R6C6

30. 27(5) cage at R6C6 (step 29a) = {14589/23589/24678}
30aa. {14589} => R6C7 = 1, R4C7 + R6C8 = [69] (step 25)
30ab. {23589} => R8C6 = 2 => R6C6 = 9 (step 28a)
30ac. {24678} => R6C6 = 7 => R6C8 = 9
30b. -> 9 must be in R6C68, locked for R6 -> R6C1 = 4, R6C9 = 8 (step 6), clean-up: no 6 in R8C2

31. R789C1 (step 23) = {179/278/359}, no 6
31a. 3,7 only in R8C1 -> R8C1 = {37} -> R8C12 = {37}, locked for R8 and N7

32. 21(4) cage at R3C1 = {2478/3459/3468} (cannot be {1479/2469} because R3C1 only contains 3,8), no 1

33. 9 in C4 only in R345C4, locked for 22(4) cage at R3C4, no 9 in R4C3
33a. 4,9 in C4 only in 22(4) cage at R3C4 = {1489/2479/3469}, no 5
33b. 7 of {2479} must be in R4C3 -> no 2 in R4C3

34. 15(3) cage at R6C2 = {159/168/249/258/348/456} (cannot be {267/357} because 3,6,7 only in R6C2), no 7

35. R689C6 (step 28a) = {257/269/568}
35a. 2,8 only in R8C6 -> R8C6 = {28}

36. 6 in R8 only in R8C34, locked for 23(5) cage at R6C3, no 6 in R6C34
36a. 23(5) cage at R6C3 = {12569/13469/13568/14567/23468/23567}
36b. 2,6 of {12569/23567} must be in R8C34, 2,3 of {23468} must be in R6C34 -> no 2 in R7C3

37. 45 rule on N4 3 innies R4C3 + R6C23 = 1 outie R3C1 + 9
37a. R3C1 = {38} -> R4C3 + R6C23 = 12,17 = {138/156/237/278/368}
37b. 15(3) cage at R4C2 = {159/168/267} (cannot be {258/357} which clash with R4C3 + R6C23), no 3
37c. R4C3 + R6C23 = {138/237/278/368} (cannot be {156} which clashes with 15(3) cage), no 5

38. 15(3) cage at R6C2 (step 34) = {159/168/249/258/348/456}
38a. 2 of {249/258} must be in R6C2 -> no 2 in R7C12

39. R7C8 = 2 (hidden single in R7), R6C8 = 9 (step 20), clean-up: no 1,6 in 16(3) cage in N6 (step 22)
39a. R5C7 = 5, R45C8 = {47}, locked for N6
39b. Naked pair {16} in R46C7, locked for C7, clean-up: no 3,8 in R1C8

40. Naked pair {16} in R12C8, locked for N3
40a. R3C7 = 2 (hidden single in N3)

41. R1C1 = 2 (hidden single in N1), R2C1 = 5
41a. R2C5 = 2 (hidden single in N2)

42. 21(4) cage at R3C1 (step 32) = {3468} (only remaining combination), locked for C1, 6 locked for N4 -> R8C12 = [73]
42a. Naked pair {19} in R79C1, locked for N7

43. 15(3) cage at R6C2 (step 34) = {159/249} (cannot be {258/348} because R7C1 only contains 1,9) -> R7C1 = 9, R67C2 = [15/24], R9C1 = 1
43a. Killer triple 1,4,6 in R23C2 and R67C2, locked for C2
43b. 6 in C2 only in R23C2, locked for N1

44. R9C7 = 9 (hidden single in R9)
44a. 24(4) cage at R9C6 (step 21) = {3579} (only remaining combination) -> R9C6 = 5, R9C8 = 3

45. Naked pair {48} in R78C7, locked for C7 and 27(5) cage at R6C6 -> R8C6 = 2, R1C7 = 3, R1C6 = 1, R12C8 = [61], R3C8 = 8, R1C5 = 8, R2C2 = 6, R2C34 = [83], R3C1 = 3, R7C56 = [13], R6C5 = 5, R6C6 = 7, R6C7 = 6 (step 28b, or hidden single in R6), R4C7 = 1

46. R6C3 = 3 (hidden single in R6), R4C3 = 7, R1C23 = [79], R45C8 = [47]

47. Naked pair {68} in R89C4, locked for C4 -> R3C4 = 9

and the rest is naked singles.
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Andrew
PostPosted: Wed Aug 03, 2011 10:10 pm 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Assassin 150 V1.25 by Ronnie G (posted by Andrew) (March 2010) here
Puzzle Diagram:
Image
Images with "udosuk style Killer Cages" by Børge: 
Image     Image
Code: Select, Copy & Paste into solver:
3x3::k:1792:4097:4097:4099:4099:4099:2310:2310:3336:1792:2826:2827:2827:4099:2830:2830:2832:3336:5394:2826:2826:5653:4118:6167:2832:2832:4634:5394:3868:5653:5653:4118:6167:6167:4130:4634:5394:3868:3868:5653:4118:6167:4130:4130:4634:5394:2350:5935:5935:4145:6962:6962:4148:4634:4150:2350:5935:4145:4145:4145:6962:4148:1854:4150:2350:5935:5935:3395:6962:6962:4148:1854:4424:4424:4424:4424:3395:6221:6221:6221:6221:
Solution: 
+-------+-------+-------+
| 2 7 9 | 5 8 1 | 3 6 4 |
| 5 6 8 | 3 2 4 | 7 1 9 |
| 3 1 4 | 9 7 6 | 2 8 5 |
+-------+-------+-------+
| 8 5 7 | 2 6 9 | 1 4 3 |
| 6 9 1 | 4 3 8 | 5 7 2 |
| 4 2 3 | 1 5 7 | 6 9 8 |
+-------+-------+-------+
| 9 4 5 | 7 1 3 | 8 2 6 |
| 7 3 6 | 8 9 2 | 4 5 1 |
| 1 8 2 | 6 4 5 | 9 3 7 |
+-------+-------+-------+
Quote:
Ronnie G: While searching for a better V2, I did stumble across a fun puzzle, SS 1.31, which I will gladly send to anyone who asks!

Andrew: After finishing A150 V2 I asked Ronnie for this puzzle; I've no idea whether anyone else did. I enjoyed solving it and asked Ronnie for permission to post it after the next Assassin had appeared. We now have A188 :D so here is A150 V1.25.
Enjoy!

Andrew: Thanks Ronnie for the enjoyable A150 V1.25, particularly the breakthrough in C8 (step 30) which I think you intended to be the key to this puzzle.
I'll rate my walkthrough for A150 V1.25 at 1.25.

Walkthrough by Andrew:
Thanks Ronnie for the enjoyable A150 V1.25, particularly the breakthrough in C8 (step 30) which I think you intended to be the key to this puzzle.

Rating Comment. I'll rate my walkthrough for A150 V1.25 at 1.25. I used a hidden killer triple. It's some time since I solved this puzzle but I don't remember any particular difficulties.

Here is my walkthrough for A150 V1.25.

Prelims

a) R12C1 = {16/25/34}, no 7,8,9
b) R1C23 = {79}
c) R1C78 = {18/27/36/45}, no 9
d) R12C9 = {49/58/67}, no 1,2,3
e) R2C34 = {29/38/47/56}, no 1
f) R2C67 = {29/38/47/56}, no 1
g) R78C1 = {79}
h) R78C9 = {16/25/34}, no 7,8,9
i) R89C5 = {49/58/67}, no 1,2,3
j) 11(3) cage in N1 = {128/137/146/236/245}, no 9
k) 11(3) cage in N3 = {128/137/146/236/245}, no 9
l) 9(3) cage at R6C2 = {126/135/234}, no 7,8,9

1. 45 rule on R9 1 innie R9C5 = 4, R8C5 = 9, R78C1 = [97]

2. Naked pair {79} in R1C23, locked for R1 and N1, clean-up: no 2 in R1C78, no 2,4 in R2C4, no 4,6 in R2C9

3. 45 rule on C1 1 innie R9C1 = 1, clean-up: no 6 in R12C1

4. 45 rule on C9 1 innie R9C9 = 7, clean-up: no 6 in R1C9

5. 1 in N1 only in 11(3) cage = {128/146}, no 3,5
5a. Killer pair 2,4 in R12C1 and 11(3) cage, locked for N1, clean-up: no 7,9 in R2C4

6. 45 rule on C1234 2 innies R17C4 = 12 = [48/57]
6a. R1C78 = {18/36} (cannot be {45} which clashes with R1C4)
6b. 16(4) cage at R6C5 cannot contain both of 7,8 -> no 7,8 in R6C5 + R7C56

7. 45 rule on C6789 2 innies R17C6 = 4 = {13}, locked for C6, clean-up: no 8 in R2C7
7a. Killer pair 1,3 in R1C6 and R1C78, locked for R1, clean-up: no 4 in R2C1

8. 7,9 in R9 only in 24(4) cage at R9C6 = {2679/3579}, no 8
8a. 5 of {3579} must be in R9C6 -> no 5 in R9C78

9. 45 rule on R12 2 innies R2C28 = 7 = [16/25/43/61], no 7,8, no 2,4 in R2C8

10. 45 rule on R6789 2 innies R6C19 = 12 = [39/48/84], no 1,2,5,6, no 3 in R6C9

11. 45 rule on N3 2 innies R2C7 + R3C9 = 12 = [39/48/75/93], no 1,2,6, no 5 in R2C7, no 4 in R3C9, clean-up: no 5,6,9 in R2C6

12. 2 in N3 only in R3C78, locked for R3
12a. 11(3) cage = {128/236/245}, no 7

13. R2C7 = 7 (hidden single in N3), R2C6 = 4, R3C9 = 5 (step 11), R1C4 = 5, R7C4 = 7 (step 6), clean-up: no 8 in R12C9, no 2 in R2C1, no 2 in R2C2, no 6 in R2C3, no 3 in R2C8, no 2 in R78C9

14. R12C9 = [49], R1C1 = 2, R2C1 = 5, R6C9 = 8, R6C1 = 4 (step 10), clean-up: no 6 in R2C4, no 3 in R78C9

15. Naked pair {16} in R78C9, locked for C9 and N9
15a. Naked pair {23} in R45C9, locked for N6
15b. 24(4) cage at R9C6 (step 8) = {2679/3579}
15c. 5,6 only in R9C6 -> R9C6 = {56}

16. R2C5 = 2 (hidden single in R2)

17. 11(3) cage in N1 = {146} (only remaining combination), locked for N1
17a. 6 in C1 only in R45C1, locked for N4

18. 16(4) cage at R6C5 = {1357} (only remaining combination), no 6, 5 locked for C5

19. 9(3) cage at R6C2 = {135/234} (cannot be {126} which clashes with R2C2), no 6, 3 locked for C2
19a. 1 of {135} must be in R6C2 -> no 5 in R6C2

20. Hidden killer pair 7,9 in R1C2 and R45C2 for C2, R1C2 = {79} -> R45C2 must contain one of {79}
20a. 15(3) cage in N4 = {159/357} (only remaining combinations containing 7 or 9), no 2,8
20b. R45C2 must contain one of 7,9 -> no 7,9 in R5C3

21. R9C2 = 8 (hidden single in C2)
21a. R9C12 = [18] = 9 -> R9C34 = 8 = [26/53/62], no 3 in R9C3
21b. 8 in R7 only in R7C78, locked for N9

22. 2,3 in C2 only in 9(3) cage at R6C2 (step 19) = {234} (only remaining combination), locked for C2, 4 locked for N9

23. Naked pair {16} in R23C2, locked for C2 and N1 -> R3C3 = 4

24. 5 in C2 only in R45C2, locked for N4

25. 16(4) cage in N2 = {1258/2356}
25a. Killer pair 3,8 in 16(4) cage and R2C4, locked for N2

26. Naked quad {1679} in R3C2456, locked for R3

27. 16(3) cage at R6C8 = {259/268/349/358/457} (cannot be {169/178/367} because 1,6,7 only in R6C8), no 1

28. 45 rule on N6 3 innies R4C7 + R6C78 = 16 = {169/457}
28a. 5 of {457} must be in R6C7 -> no 5 in R4C7 + R6C8

29. 4 in C4 only in R45C4 -> 22(4) cage at R3C4 = {1489/2479/3469} (cannot be{3478} because R3C4 only contains 1,6,9)
29a. 7 of {2479} must be in R4C3 -> no 2 in R4C3
29b. 2 in N4 only in R6C23, locked for R6

30. 4,5,7 in C8 only in R45678C8
30a. Hidden killer triple 4,5,7 in R45C8 and 16(3) cage at R6C8 for C8, R45C8 cannot contain more than two of 4,5,7 -> 16(3) cage at R6C8 must contain at least one of 4,5,7
30b. 16(3) cage at R6C8 (step 27) = {259/349/457} (cannot be {268} which doesn’t contain any of 4,5,7, cannot be {358} because 3,5,8 only in R78C8), no 6,8

31. R7C7 = 8 (hidden single in N9), clean-up: no 1 in R1C8
31a. R8C4 = 8 (hidden single in N8), R2C34 = [83], R3C1 = 3, R3C78 = [28], R2C8 = 1 (step 12a), R23C2 = [61], R1C6 = 1, R1C5 = 8 (step 25), R7C6 = 3, clean-up: no 5 in R9C3 (step 21a)
31b. R7C5 = 1 (hidden single in N8), R6C5 = 5, R78C9 = [61]

32. Naked pair {26} in R9C34, locked for R9 -> R9C6 = 5
32a. Naked pair {39} in R9C78, locked for N9

33. 2 in N9 only in R78C8 -> 16(3) cage at R6C8 (step 30b) = {259} (only remaining combination) -> R6C8 = 9, R78C8 = {25}, locked for C8 and N9 -> R8C7 = 4, R9C78 = [93], R1C78 = [36]

34. R5C7 = 5 (hidden single in C7)

35. Naked pair {16} in R6C47, locked for R6 -> R6C6 = 7
35a. Naked pair {36} in R45C5, locked for C5 and N5 -> R6C4 = 1

and the rest is naked singles.
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