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Ed
 Post subject: Assassin 260
PostPosted: Fri May 17, 2013 9:55 am 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
Really good milestone puzzle. Found a way to make big inroads from step 1 but then you realize it was just a detour (unless I missed something important)! Feels almost obligatory to find Assassins that have a hard ending......enjoy! It gets a SudokuSolver score of 1.35.

Assassin 260
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Code: paste into solver:
3x3::k:4352:4352:4352:4609:4609:2306:4099:4099:4099:3076:4869:4869:4609:7942:2306:7942:4615:4615:3076:4869:4869:4609:7942:7942:7942:4615:5128:3076:4869:5385:6922:6922:7942:5128:5128:5128:3083:3083:5385:5385:6922:2828:2828:1805:1805:6414:6414:6414:5903:6922:6922:2828:7440:5393:6414:4114:5903:5903:5903:4627:7440:7440:5393:4114:4114:5903:3604:5903:4627:7440:7440:5393:3093:3093:3093:3604:4627:4627:2326:2326:2326:
Solution: 
+-------+-------+-------+
| 2 7 8 | 1 5 6 | 9 4 3 |
| 6 9 4 | 8 2 3 | 1 7 5 |
| 5 1 3 | 4 7 9 | 8 6 2 |
+-------+-------+-------+
| 1 2 5 | 6 9 4 | 3 8 7 |
| 8 4 9 | 7 3 5 | 2 1 6 |
| 7 3 6 | 2 1 8 | 4 5 9 |
+-------+-------+-------+
| 9 5 7 | 3 4 1 | 6 2 8 |
| 3 8 1 | 5 6 2 | 7 9 4 |
| 4 6 2 | 9 8 7 | 5 3 1 |
+-------+-------+-------+
Cheerio
Ed
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Andrew
 Post subject: Re: Assassin 260
PostPosted: Sun May 19, 2013 7:56 pm 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Thanks Ed for another nice Assassin. Loved the cage pattern interactions which led to the interesting early steps! :D

At one stage I thought I might finish this Assassin in one session. Then I reached a stage where it was hard to see what to do next.
Ed wrote:
Feels almost obligatory to find Assassins that have a hard ending....
I commented to Ed that I'd rather struggle in the middle of a puzzle than toward the end. That was before I found my later steps, which were more interesting than I'd expected. Ed probably found a different way to do the ending.

Thanks Ed for pointing out a typo and a simplification.
Here is my walkthrough for A260:
Prelims

a) R12C6 = {18/27/36/45}, no 9
b) R5C12 = {39/48/57}, no 1,2,6
c) R5C89 = {16/25/34}, no 7,8,9
d) R89C4 = {59/68}
e) 21(3) cage at R4C3 = {489/579/678}, no 1,2,3
f) 21(3) cage at R6C9 = {489/579/678}, no 1,2,3
g) 9(3) cage at R9C7 = {126/135/234}, no 7,8,9
h) 11(3) cage at R5C6 = {128/137/146/236/245}, no 9 Oops! I overlooked this while solving the puzzle.

1. 45 rule on N1 2 outies R4C12 = 3 = {12}, locked for R4 and N4

2. 45 rule on N9 2 outies R6C89 = 14 = {59/68}

3. 45 rule on R9 3 innies R9C456 = 24 = {789}, locked for R9 and N8

4. 45 rule on N14 2(1+1) outies R5C4 + R7C1 = 16 = [79/88/97]

5. 45 rule on N69 2(1+1) outies R3C9 + R5C6 = 7 = {16/25/34}, no 7,8,9

6. 45 rule on N8 3 outies R6C4 + R78C3 = 10 = {127/136/145/235}, no 8,9
6a. 23(6) cage at R6C4 = {123467} (only remaining combination), no 5
6b. R6C4 + R78C3 = {127} (only remaining combination because no 7 in R7C45 + R8C5), locked for 23(6) cage, CPE no 7 in R6C3
6c. Naked triple {346} in R7C45 + R8C5 = {346}, locked for N8 -> R8C4 = 5, R9C4 = 9, clean-up: no 7 in R7C1 (step 4)
6d. Naked pair {12} in R78C6, locked for C6, clean-up: no 7,8 in R12C6, no 5,6 in R3C9 (step 5)
6e. Min R5C6 = 3 -> max R56C7 = 8, no 8,9 in R56C7

7. 45 rule on N7 3 innies R7C1 + R78C3 = 17 = {179/278}, 7 locked for C3, N7 and 23(6) cage at R6C4, no 7 in R6C4

[From the start I could see that there are interesting interactions between the 21(3) cage at R4C3 and R5C12. Now I can get something from them.]
8. 21(3) cage at R4C3 and R5C12 form a combined 33(5) cage (because their cells “see” each other) = {36789/45789}, 7 locked for R5, 9 locked for N4

9. 25(4) cage at R6C1 = {3679/4579/4678} (cannot be {3589} which clashes with R6C89), 7 locked for R6 and N4, clean-up: no 5 in R5C12
9a. Killer pair 5,6 in 25(4) cage and R6C89, locked for R6

10. R5C4 = 7 (hidden single in R5), R7C1 = 9 (step 4), clean-up: no 3 in R5C2
10a. R5C4 = 7 -> R45C3 = 14 = {59/68}, no 4
10b. Killer pair 8,9 in R45C3 and R5C12, locked for N4

11. R7C1 + R78C3 (step 7) = {179} (only remaining combination) -> R78C3 = {17}, locked for C3, N7 and 23(6) cage at R6C4 -> R6C4 = 2
11a. 1 in C4 only in R123C4, locked for N2

12. 45 rule on N4 2 remaining innies R45C6 = 9 = {36/45}
12a. Naked quad {3456} in R12C6 + R45C6, locked for C6

13. 11(3) cage at R5C6 and R5C89 form combined 18(5) cage (because their cells “see” each other) = {12456} (only remaining combination), no 3, clean-up: no 4 in R3C9 (step 5), no 6 in R4C6 (step 12), no 4 in R5C89
13a. 5,6 cannot both be in R5C789 (which would clash with R6C89) -> R5C6 = {56}, clean-up: no 3 in R3C9 (step 5), no 5 in R4C6 (step 12)
13b. Killer pair 5,6 in R5C89 and R6C89, locked for N6

14. 3 in N6 only in R4C789, locked for R4 -> R4C6 = 4, R5C6 = 5 (step 12), R3C9 = 2 (step 5), clean-up: no 2 in R5C8
14a. Naked pair {16} in R5C89, locked for R5 and N6 -> R56C7 = [24], clean-up: no 8 in R6C89 (step 2)
14b. Naked pair {59} in R6C89, locked for R6 and N6 -> R6C6 = 8, R4C45 = [69], R56C5 = [31], R9C56 = [87], R3C6 = 9
14c. R4C3 = 5 (hidden single in R4), R5C3 = 9 (cage sum)

15. Naked pair {46} in R78C5, locked for C5 and N8 -> R7C4 = 3
15a. R123C4 = {148} = 13, R1C5 = 5 (cage sum), R23C5 = [27]

16. 45 rule on N3 2 remaining innies R23C7 = 9 = {18/36}, no 5

17. 21(3) cage at R6C9 = {489/579} (cannot be {678} because R6C9 only contains 5,9), no 6, 9 locked for C9

18. 5 in N3 only in 18(3) cage at R2C8 = {459/567}, no 1,3,8
18a. 4 in {459} must be in R3C8 (R23C8 cannot be {59} which clashes with R6C8 and 9 only in R2C8), no 4 in R2C89

19. 8 in C3 only in R123C3, locked for N1

20. 2 in N1 only in 17(3) cage at R1C1 = {269/278}, no 1,3,4
20a. 9 of {269} must be in R1C2 -> no 6 in R1C2

21. 12(3) cage at R9C1 = {246/345}, 4 locked for R9 and N7
21a. 9(3) cage at R9C7 = {126/135}, 1 locked for N9

22. 1 in C1 only in 12(3) cage at R2C1 = {147/156} -> R4C1 = 1, R4C2 = 2, R23C1 = [47/56/65], no 3, no 4 in R2C1
22a. Killer pair 6,7 in 17(3) cage at R1C1 and R23C1, locked for N1
22b. 17(3) cage at R1C1 (step 20) = {269/278}
22c. R1C2 = {79} -> no 7 in R1C1

23. 16(3) cage at R1C7 = {178/349} (cannot be {169} which clashes with R23C7, cannot be {367} which clashes with R1C6), no 6

24. 5 in C7 only in R79C7, locked for N9
24a. 9(3) cage at R9C7 = {126/135}
24b. 5 of {135} must be in R9C7 -> no 3 in R9C7
24c. 2 of {126} must be in R9C8 -> no 6 in R9C8

25. 45 rule on R1 2 remaining innies R1C46 = 7 = [16/43], no 8

26. 19(5) cage at R2C2 = {12349/12358}
26a. 1,5,9 only in R23C2 -> R23C2 = {159}
26b. 19(5) cage at R2C2 = {12349/12358}, 3 locked for C3 -> R6C3 = 6

[At this stage I was struggling to make progress, then I found the next two steps; but there was still a lot of hard work after that.]
27. 4 in C9 only in R1C9 or in 21(3) cage at R6C9 = {489} -> no 8 in R1C9 (locking-out cages)

28. 5 in C1 only in R23C1 = {56} or in R9C1 -> no 6 in R9C1 (locking-out cages)

29. 12(3) cage at R9C1 (step 21) = {246/345}
29a. 6 of {246} must be in R9C2, 4 of {345} must be in R9C3 -> no 4 in R9C2

30. R5C2 = 4 (hidden single in C2), R5C1 = 8

31. Hidden killer pair 4,5 in R23C1 and R9C1, R23C1 contains one of 4,5 -> R9C1 = {45}
31a. 12(3) cage at R9C1 (step 21) = {246/345}
31b. 3,6 only in R9C2 -> R9C2 = {36}

32. 16(3) cage at R7C2 = {268/358}
32a. 2 of {268} must be in R8C1 -> no 6 in R8C1
32a. R8C1 = {23} -> no 3 in R8C2

33. 29(5) cage at R6C8 = {24689/25679/34589} (cannot be {23789/34679/35678} which clash with 9(3) cage at R9C7)
33a. Consider combinations for 29(5) cage
29(5) cage = {24689/34589}, 4 locked for N9
or 29(5) cage = {25679} must have 5 in R6C8 (because 21(3) cage at R6C9 is 9{48}) and 6 in R7C78 (R7C78 cannot be [72] which clashes with R7C36, ALS block) => R7C5 = 4 => no 4 in R7C9
-> no 4 in R7C9

34. 21(3) cage at R6C9 (step 17) = {489/579}
34a. R7C9 = {78} -> no 7,8 in R8C9

35. R23C7 (step 16) = {18/36}, R23C1 (step 22) = [47/56/65]
35a. Consider combinations for 18(3) cage at R2C8 (step 18) = {459/567}
18(3) cage = {459} = [954] => R23C1 = [65], R2C6 = 3 => R23C7 = {18}
or 18(3) cage = {567}, locked for N3 => R23C7 = {18}
-> R23C7 = {18}, locked for C7 and N3

36. 16(3) cage at R1C7 (step 23) = {349} (only remaining combination), locked for R1 and N3 -> R1C4 = 1, R12C6 = [63], 17(3) cage at R1C1 = [278], R23C3 = [43], R8C1 = 3, R9C2 = 6, R9C3 = 2, R9C7 = 5

37. 6 in C7 only in R78C7, locked for N9
37a. 29(5) cage at R6C8 (step 33) = {25679} (only remaining combination, cannot be {24689} because 2,4,8 only in R78C8), no 4,8 -> R6C8 = 5
37b. Naked triple {127} in R7C368, locked for R7 -> R7C79 = [68]

and the rest is naked singles.

Rating Comment:
I thought about 1.5 but the ending felt more than that, so I'll rate my walkthrough at Hard 1.5.


Last edited by Andrew on Sat May 25, 2013 10:37 pm, edited 1 time in total.

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Ed
 Post subject: Re: Assassin 260
PostPosted: Sat May 25, 2013 11:53 am 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
Andrew wrote:
Ed probably found a different way to do the ending.
And the beginning. Glad you enjoyed it Andrew. Really enjoyed your steps 8 & 13. I originally had to use lots of Andrew's ending steps before finding my 22b. which Andrew found much earlier in his solve. However, the big difference to Andrew's end in my optimized solution is step 19 which I saw quite early first time through.

A260
30 steps:
Prelims courtesy of SudokuSolver
Cage 14(2) n8 - cells only uses 5689
Cage 7(2) n6 - cells do not use 789
Cage 12(2) n4 - cells do not use 126
Cage 9(2) n2 - cells do not use 9
Cage 9(3) n9 - cells do not use 789
Cage 21(3) n69 - cells do not use 123
Cage 21(3) n45 - cells do not use 123
Cage 11(3) n56 - cells do not use 9
Cage 23(6) n578 - cells do not use 9

1. "45" on r9: 3 outies r8c4 + r78c6 = 8
1a. -> r8c4 = 5, r78c6 = 3 = {12} only: both locked for c6 & n8
1b. r9c4 = 9
1c. r78c6 = 3 -> r9c56 = 15 (cage sum) = {78} only: both locked for r9 and n8
1d. Naked triple {346} in r7c45+r8c5: locked for 23(5)r6c4 -> no 3,4,6 in r6c4 nor r78c3 [Andrew noticed that I could have gone a bit further with this: -> r6c4 + r78c3 = 10 = {127}, which would have made step 5 redundant]
1e. no 7,8 in 9(2)n2

2. "45" on n1: 2 outies r4c12 = 3 = {12} only: both locked for r4 and n4

3. "45" on n14: 2 outies r5c4 + r7c1 = 16
3a. but [88] blocked since 8 in n4 is only in 12(2), 21(3)r4c3 or 25(4)r6c1 and the two outies see all these cells
3b. -> r5c4 + r7c1 = [79] (only permutation)
3c. no 3 in r5c2
3d. no 5 in 12(2)n4

4. "45" on n78: 1 outie r6c4 = 2

5. "45" on n7: 2 remaining innies r78c3 = 8 = {17} only: locked for n7 & c3

6. "45" on r1234: 3 innies r4c345 = 20 = {389/569}(no 4)
6a. must have 9: 9 locked for r4

7. "45" on n9: 2 outies r6c89 = 14 and must have 9 for n6 = {59} only: both locked for n6 and r6
7a. no 2 in 7(2)n6

8. "45" on n69: 2 outies r3c9 + r5c6 = 7 (no 7,8,9: no 5,6 in r3c9)

9. Hidden single 2 in n6 -> r5c7 = 2
9a. 7(2)n6 = {16/34} = [3/6..]
9b. r5c7 = 2 -> r5c6 + r6c7 = 9
9c. but {36} blocked by 7(2) = [3/6] and r5c6 sees that cage
9c. -> r5c6 + r6c7 = 9 = [54] only permutation
9d. 7(2)n6 = {16} only: locked for r5 and n6
9e. r3c9 = 2 (outies n69 = 7)
9f. no 4 in 9(2)n2

10. Hidden single 5 in n4 -> r4c3 = 5, r5c3 = 9 (cage sum)
10a. 12(2)n4 = {48} only: locked for n4 & r5
10b. r5c5 = 3

11. 6 in n4 only in r6: 6 locked for r6
11a. r6c6 = 8, r6c5 = 1, r9c56 = [87], r4c45 = [69], r4c6 = 4

12. deleted

13. Naked pair {46} in r78c5: locked for n8 and c5, r7c4 = 3

14. naked triple {148} in r123c4 = 13 -> r1c5 = 5 (cage sum), r23c5 = [27], r3c6 = 9 (hidden single n2)

15. 8 in c3 only in n1: locked for n1

16. 2 in n1 only in 17(3) = {269/278}(no 1,3,4) = [6/7..]

17. 1 in c1 only in 12(3)r2c1 = {147/156}(no 2,3) -> r4c12 = [12]
17a. r4c1 = 1 -> r23c1 = 11 = {56}[74](no 4 in r2c1) = [6/7..]

18. Killer pair 6,7 in n1 in 17(3) (step 16) and r23c1 (step 17a): 6 & 7 locked for n1

Now ready for the key, eliminating 4 from r3c8
19. 7 in r2 only in split 11(2)r23c1 = [74] or in 18(3)n3 -> 4 in r3c8 must have 7 in r2c89 or their would be no 7 for r2: but {77}[4] not possible in an 18(3) -> no 4 in r3c8 (Locking-out cages)

20. "45" on n3: 2 remaining innies r23c7 = 9 = {18/36}(no 5) = [3/8,6/8..]

21. 21(3)r6c9 must have 5 or 9 for r6c9 = {489/579}(no 6)
21a. must have 9: 9 locked for c9

This next sub-step b. is the one that eluded me for a very long time.
22. 18(3)n3: {378/468} blocked by [3/8,6/8] in r23c7 (step 20)
22a. 18(3) = {189/369/459/567}
22b. but 4 cannot be in r2c9 since {59} in r23c8 is blocked by r6c8 = (59)
22c. {459} blocked since 4 & 9 are only in r2c8
22c. 18(3) = {189/369/567}(no 4)

23. 4 in n3 only in 16(3) = {349/457}(no 1,6,8)
23a. 4 locked for r1

24. "45" on r1: 2 remaining innies r1c46 = 7 = [16] only permutation
24a. r2c6 = 3

25. 17(3)n1 = [278] (only permutation), r23c3 = [43], naked pair {56} in r23c1: locked for c1 and n1

26. h9(2)r23c7 = {18} only: both locked for c7 and n3

27. r6c123 = [736], 12(3)n7 = [462] (only permutation), r8c12 = [38], r7c2 = 5

28. Naked triple {135} in r9c789: locked for n9

29. 6 in c7 only in r78c7 in 29(5)r6c8: no 6 in r78c8

30. {24689} in 29(5)r6c8 blocked since 2,4,8 only in r78c8
30a. = {25679} only (no 4,8)
30b. Hidden single 8 in n9 -> r7c9 = 8 -> r68c9 = 13 = [94] only permutation

On from there.
Cheerio
Ed
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