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 Post subject: Assassin 66 v1.5 Revisit
PostPosted: Wed Sep 01, 2021 8:13 pm 
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Grand Master
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1040
Location: Sydney, Australia
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Assassin 66 v1.5 Revisit

I remember this puzzle. Gave me nightmares! Not from solving it (didn't try) but scoring it in SudokuSolver. It kept going down till now it gets a 1.35 which is a very long way from the human walkthroughs. JSudoku uses 7 'complex intersections' which suggests it is a very hard puzzle. Lets see!
Code: Select, Copy & Paste into solver:
3x3::k:3072:3072:3072:4355:4355:3589:2822:2822:2822:2825:2825:5131:4355:3589:3589:2063:5904:5904:7698:2825:5131:5131:2070:2063:2063:5904:4890:7698:4636:4636:4636:2070:4384:4384:4384:4890:7698:2853:2853:5159:5159:5159:2858:2858:4890:7698:2094:2094:2094:2865:4658:4658:4658:4890:7698:3383:2872:2872:2865:3643:3643:5693:4890:3383:3383:2872:3906:3906:3652:3643:5693:5693:4680:4680:4680:3906:3652:3652:2894:2894:2894:
Solution:
+-------+-------+-------+
| 6 2 4 | 9 5 8 | 7 1 3 |
| 1 7 9 | 3 2 4 | 5 8 6 |
| 8 3 5 | 6 7 1 | 2 9 4 |
+-------+-------+-------+
| 7 4 6 | 8 1 5 | 9 3 2 |
| 2 8 3 | 7 4 9 | 6 5 1 |
| 9 5 1 | 2 3 6 | 8 4 7 |
+-------+-------+-------+
| 4 9 2 | 1 8 7 | 3 6 5 |
| 3 1 8 | 5 6 2 | 4 7 9 |
| 5 6 7 | 4 9 3 | 1 2 8 |
+-------+-------+-------+
Cheers
Ed


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PostPosted: Fri Sep 03, 2021 3:54 am 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
I can only guess that the low SudokuSolver score is because there are several placements before one really has to start thinking.

This time it seemed easier than my first attempt, although I recognised some of my steps from then, so I hope that I've found a better way to solve it.

Start of step 4 simplified.
Here is my walkthrough for Assassin 66V1.5 Revisited:
Prelims

a) R34C5 = {17/26/35}, no 4,8,9
b) R5C23 = {29/38/47/56}, no 1
c) R5C78 = {29/38/47/56}, no 1
d) R67C5 = {29/38/47/56}, no 1
e) 11(3) cage at R1C7 = {128/137/146/236/245}, no 9
f) 11(3) cage at R2C1 = {128/137/146/236/245}, no 9
g) 20(3) cage at R2C3 = {389/479/569/578}, no 1,2
h) 8(3) cage at R2C7 = {125/134}
i) 23(3) cage at R2C8 = {689}
j) 20(3) cage at R5C4 = {389/479/569/578}, no 1,2
k) 8(3) cage at R6C2 = {125/134}
l) 11(3) cage at R7C3 = {128/137/146/236/245}, no 9
m) 22(3) cage at R7C8 = {589/679}
n) 11(3) cage at R9C7 = {128/137/146/236/245}, no 9

Steps Resulting From Prelims
1a. Naked triple {689} in 23(3) cage at R2C8, locked for N3
1b. 8(3) cage at R6C2 = {125/134}, 1 locked for R6
1c. 22(3) cage at R7C8 = {589/679}, 9 locked for N9
1d. 9 in C7 only in R456C7, locked for N6, clean-up: no 2 in R5C7

2a. 45 rule on R5 2 innies R5C19 = 3 = {12}, locked for R5, clean-up: no 9 in R5C23, no 9 in R5C7
2b. 9 in R5 only in 20(3) cage at R5C4, 9 locked for N5, clean-up: no 2 in R7C5
2c. 45 rule on R1 3 innies R1C456 = 22 = {589/679}, 9 locked for R1 and N2
2d. 45 rule on R1 3 outies R2C456 = 9 = {126/135/234}, no 7,8
2e. 45 rule on R123 3 innies R3C159 = 19 = {379/469/478/568} (cannot be {289} because 8,9 only in R3C1), no 1,2, clean-up: no 6,7 in R4C5
2f. 8,9 only in R3C1 -> R3C1 = {89}
2g. 45 rule on N1 1 innie R3C1 = 1 outie R3C4 + 2, R3C1 = {89} -> R3C4 = {67}
2h. 20(3) cage at R2C3 = {479/569/578} (cannot be {389} because R3C4 only contains 6,7), no 3
2i. R3C4 = {67] -> no 6,7 in R23C3
2j. Killer pair 8,9 in R3C1 and 20(3) cage, locked for N1
2k. 8 in R1 only in R1C456 = {589}, 5 locked for R1 and N2, clean-up: no 3 in R4C5
2l. R2C456 = 9 = {126/234}, 2 locked for R2 and N2
2m. 7 in N2 only in R3C45, locked for R3
2n. 45 rule on N3 1 innie R3C9 = 1 outie R3C6 + 3 -> R3C6 = 1, R3C9 = 4
2o. R2C456 = {234}, 3,4 locked for R2, 3 locked for N2 -> R2C7 = 5, R3C7 = 2 (cage sum), clean-up: no 5 in R4C5, no 6 in R5C8
2p. Naked pair {67} in R3C45, 6 locked for R3
2q. R3C23 = [35] (hidden pair in R3) -> R2C12 = 8 = {17}, locked for N1, clean-up: no 6 in R5C2, no 8 in R5C3
2r. 30(5) cage at R3C1 = {24789/25689} (cannot be {15789} which clashes with R2C1, cannot be {34689/35679/45678} because R5C1 only contained 1,2) -> R5C1 = 2, R3467C1 = {4789/5689}, no 1,3, 8,9 locked for C1
2s. Killer pair 4,6 in R1C1 and R3467C1, locked for C1
2t. 3 in C1 only in R89C1, locked for N7
2u. R3C9 = 4, R5C9 = 1 -> 19(5) cage at R3C9 = {12457/13456}, no 8, 5 locked for C9
2v. Killer pair 3,7 in R1C9 and 19(5) cage, locked for C9
2w. 11(3) cage at R9C7 = {128/146/236/245} (cannot be {137} because R9C9 only contains 2,6,8), no 7
2x. 45 rule on N9 3 innies R78C7 + R7C9 = 12 = {138/147/237/345} (cannot be {156/246} which clash with 11(3) cage), no 6

3a. 45 rule on N7 1 innie R7C1 = 1 outie R7C4 + 3 -> R7C4 = {123456}
3b. 45 rule on N9 1 outie R7C6 = 1 innie R7C9 + 2 -> R7C6 = {4579}
3c. 45 rule on R789 3 innies R7C159 = 17 = {269/278/359/368/458/467}
3d. R7C159 = {269/278/359/458/467} (cannot be {368} because [683] clashes with R7C14 = [63], CCC, cannot be [863] because R7C14 = [85] clashes with R7C69 = [53], CCC)
3e. 5 of {359/458} must be in R7C9 (cannot be {59}3 which clashes with R7C69 = [53], CCC) -> no 5 in R7C15, no 3 in R7C9, clean-up: no 6 in R6C5, no 2 in R7C4, no 5 in R7C6
3f. {278} must be [872] (cannot be [782] because R7C14 = [74] clashes with R7C69 = [42], CCC), 7 of {467} must be in R7C9 -> no 7 in R7C1, clean-up: no 4 in R7C4
3g. 45 rule on N8 3 innies R7C456 = 16 = {169/178/349/367/457} (cannot be {358} because R7C6 only contains 4,7,9)
3h. R7C456 = {178/349/367/457} (cannot be {169} = [169] because R7C14 = [41] blocks 14(3) cage at R7C6 = 9{14})
3i. {367} must be [637] (cannot be [367] which clashes with R7C14 = [63], CCC) -> no 6 in R7C5, clean-up: no 5 in R6C5
3j. 45 rule on N7 3 innies R7C1 + R78C3 = 14 = {149/167/248}
3k. 6 of {167} must be in R7C1 -> no 6 in R78C3
3l. 18(3) cage at R9C1 = {369/378/459/567} (cannot be {189/279/468} which clash with R7C1 + R78C3), no 1,2
3m. 13(3) cage at R7C2 = {139/157/238/256} (cannot be {148/247} which clash with R7C1 + R78C3, cannot be {346} which clash with 18(3) cage), no 4

4a. R3C1 = R3C4 + 2 (step 2g) -> R3C14 = [86/97]
4b. R7C1 = R7C4 + 3 (step 3a) -> R7C14 = [41/63/85] (cannot be [96] which clashes with R3C14), no 9 in R7C1, no 6 in R7C4
[With hindsight I ought to have seen this after step 3a but I was specifically focussed on R7 at the time.]

4c. R7C456 (step 3h) = {178/349/457}
4d. 3 of {349} must be in R7C4 -> no 3 in R7C5, clean-up: no 8 in R6C5
4e. R7C1 + R78C3 (step 3j) = {167/248}
4f. 13(3) cage at R7C2 (step 3m) = {139/157/238} (cannot be {256} which clashes with R7C1 + R78C3), no 6
4g. 18(3) cage at R9C1 (step 3l) = {369/459/567} (cannot be {378} which clashes with R7C1 + R78C3), no 8
4h. 14(3) cage at R7C6 = 4{37}/7{34}/9{14}, no 8 in R78C7
4i. R78C7 + R7C9 (step 2x) = {147/237/345}
4j. 11(3) cage at R9C7 (step 2w) = {128/236} (cannot be {146} which clashes with 18(3) cage, cannot be {245} which clashes with R78C7 + R7C9), no 4,5, 2 locked for R9 and N9, clean-up: no 4 in R7C6 (step 3b)
4k. Killer pair 5,7 in 22(3) cage at R7C8 and R7C9, locked for N9
4l. 4 in N9 only in R78C7, locked for C7, clean-up: no 7 in R5C8
4m. R7C456 = {178/349} (cannot be {457} which clashes with R7C9), no 5, clean-up: no 8 in R7C1
4n. R7C6 = {79} -> no 7,9 in R7C5, clean-up: no 2,4 in R6C5
4o. Naked pair {46} in R17C1, locked for C1
4p. Killer pair 4,6 in R7C1 and 18(3) cage, locked for N7

5a. R7C69 (step 3b) = [75/97], 7 locked for R7
5b. R7C1457 (steps 3a and 4m) = [4183/6341], 1 locked for R7
5c. 11(3) cage at R7C3 = {128} (cannot be {137} because R7C3 only contains 2,8) -> R7C4 = 1, R7C1 = 4, R7C5 = 8, R6C5 = 3, R78C3 = [28], R7C6 = 7 (step 4m) -> R7C9 = 5, R7C28 = [96], R8C89 = [79]
5d. R2C3 = 9 -> R3C4 = 6 (cage sum)
5e. R7C2 = 9 -> R8C12 = 4 = [31] -> R78C7 = [34], clean-up: no 8 in R5C8
5f. R3C5 = 7 -> R4C5 = 1
5g. 8(3) cage at R6C2 = [512] (only remaining permutation)
5h. R3C1 = 8 -> R46C1 = {79}, 7 locked for C1 and N4
5i. R5C23 = [83] (only remaining permutation)
5j. Naked pair {46} in R4C23, locked for R4, R4C4 = 8 (cage sum)
[And maybe the neatest way to finish …]
5k. 45 rule on N6 4(2+2) outies R37C9 + R46C6 = 20, R37C9 = [45] = 9 -> R46C6 = 11 = [56]
5l. R8C4 = 5, R1C45 = [95] -> R2C4 = 3 (cage sum)

and the rest is naked singles.


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