SudoCue Users

This one gave me some headache until I realized that I had missed an elimination.

The walkthrough is the way I figured it out, no cleanups or shortcuts, unnecessary steps included and, as always, in tiny font. Please feel free to comment.

Edit: Ed gave me some corrections and additions, they are included in blue.

Walkthrough Assassin 31

1. r12c1 = 16(2) = {79} -> 7,9 locked in N1 and c1
2. r567c3 = 6(3) = {123} -> 1,2,3 locked in c3
3. r23c4 = 6(2) = {15|24}
4. r23c6 = 15(2) = {69|78}
5. r89c4 = 10(2) = {19|28|37|46}
6. r89c6 = 13(2) = {49|58} ({67} not possible, one is needed for step 5
7. -> 8,9 locked for c6 in 15(2) and 13(2)
8. N12 : 19(3) = {469|478|568} -> r1c4 = {456789} -> no 7 or 9 in r12c3 -> no 4 in r1c4 possible
9. 45 on c5: r56c5 = 10(2) = {19|28|37|46} -> no 5
10. 45 on N7 : r7c23 = 6(2) = [42]|[51] -> 3 locked in r56c3 for N4
11. 45 on N9 : r7c78 = 15(2) = {69|78}
12. 45 on N8 : r7c46 = 9(2) = {27|36|[81]} ({45} not possible, one is needed for 6(2) in r7) -> 6 locked in 9(2) or 15(2) for r7
13. 45 on r89 : r7c159 = 15(3) = {159|249|258|357} -> {258} blocked by r7c23 (step 10) which eliminates 8 for 15(3)
14. 45 on c12 : r89c3 = 16(2) = {79} -> 7,9 locked for c3 and N7
15. 45 on c89 : r89c7 = 10(2) = {19|28|37|46} -> no 5
16. 45 on c123 : r145c4 = 16(3)
17. 45 on c1234 : r67c4 = 13(2) = {67|[58]} -> no 6,7 in r7c6 (step 12)
18. 45 on c789 : r145c6 = 9(3) = {126|135|234}
19. 45 on c6789 : r67c6 = 8(2) = [53]|[62]|[71]
20. using steps 12, 17, 19 : r6c46 = 12{2} = {57} -> 5,7 locked for r6 and N5
21. -> no 7 in r7c4 and no 2 in r7c6 -> no 3,7 in 10(2) in c5
22. 6,8 locked in r7c478 for r7
23. N7 : 13(3) = {139|157|247} -> r9c12 = {12345}
24. N7 : 26(4) = {3689|5678} -> no 2,4 -> 6,8 locked in N7 and r8 -> r8c12 = {68}
25. -> no 2,4 in r9c47 and no 5 in r9c6
26. N9 : 17(4) = {1259|1349|1457|2357} = [7/9..] -> Killer pair with r7c78 for n9 -> no 7,9 in 13(3) -> no 1,3 in r8c7
27. c6 : r7c6 = {13} -> {135} not possible for 9(3) -> no 5
28. step 13 : r7c1 = {35} -> 15(3) = {159|357} -> r7c59 = {13579}
29. -> single in r7 : r7c3 = 2, r7c2 = 4
30. r9 : 1 locked in r9c12 -> no 9 in r8c47
31. N4 : 1 locked in r56c3
32. N47 : 21(4) = 4{269|278} -> 2 locked in N4 -> no 8 in r5c2
33. c1 : 15(3) : must have one but can't have both 6 and 8 -> {168} not possible -> no 1 -> r9c1 = 1 -> r6c1 = 2 -> no 8 in r5c5 -> 8 not possible in r3c1
To clarify step 33: c1 : 6,8 locked in 15(3) and r8c1 -> no 6,8 in r6c1 -> rc61 =2
34. c2 : 6,8 locked in r568c2
35. -> c2 : 15(4) = {1239|1257} -> r4c2 = {79}
36. 8 locked in r123c3 -> no 8 in r4c3
37. N58 : 31(6) = 567{139|148|238} -> no 6 possible in r45c4 and r9c5 -> 6 locked in r79c4 -> no 6 in r1c4
38. N9 : 13(3) = {238|247|256|346} -> no 9 (now unnecessary due to addition in step 26)
39. N145 : 20(4) = {1469|1568|2459|2468|3458} -> r34c3 = {4568}, min: 9, max: 14 -> r45c4 = {123489}, min: 6, max: 11 (8 not possible) -> (step 16) r1c4 = {5679} -> r45c4 : min: 7 -> combination {68} not possible in r34c3
To clarify step 39: r45c4 = {123489}, so r45c4 = 8 not possible (5,7 removed by step 20) -> no 8 possible in r1c4
40. 45 on N2 (2 innies, 1 outie) : r1c46 - 2 = r4c5
40a. r1c46 : min: 6, max: 11
40b. r4c5 : min: 4, max: 9
41. 45 on N1 (2 innies, 2 outies) : r3c13 + 5 = r1c4 + r4c2
41a. r1c4 + r4c2 : min: 12, max: 18 (doubles possible)
41b. r3c13 : min: 7, max: 13
42. 45 on N3 (2 innies, 2 outies) : r3c79 - 3 = r1c6 + r4c9
42a. r1c6 + r4c9 : min: 2, max: 14 (doubles possible)
42b. r3c79 : min: 5, max: 17
43. N69 : 22(4) : {2578} not possible
44. 45 on r6789 : r5c1469 = 23(4)
45. N8 : 13(3) : can't have both 3 and 8 (9(2)), can't have both 4 and 8 (13(2)) -> 13(3) = {139|157|247} -> no 8 in 13(3)
46. N12 : r1c4 = {579} -> no 5 in r12c3 for 19(3)
47. (step 39) 20(4) has 5 -> 20(4) = 5{168|249|348}
48. N9 : 17(4) = 1{259|349|457} -> has 7 or 9 -> 7,9 locked in r78c789 -> no 7 in 13(3) -> no 3 in r8c7 (this is now unnecessary, it was done before in addition to step 26)
49. -> N9 : 17(4) : 2 not possible in r8c89
50. c7 : 17(3) : {368} not possible, one is needed in r9c7
51. c5 : 22(4) = {2389|2569|2578|3469|3568|4567} -> no 1 -> {2569} also blocked by 13(3)
52. c5 : 13(3) can't have both 1 and 3 -> {139} not possible -> no 3,9 -> 7 locked in 13(3) for c5 and N8 (this is the key to unlock the whole puzzle, should have gotten here earlier)
53. -> N8 : {37} not possible in 10(2) -> r7c6 = 3 -> r7c4 = 6 -> r7c1 = 5 -> r9c2 = 3 -> r9c3 = 9 -> r8c3 = 7 -> r9c4 = 8 -> r8c4 = 2 -> r9c6 = 4 -> r8c6 = 9 -> r9c5 = 7 -> r7c5 = 1 -> r8c5 = 5 -> r9c7 = 6 -> r8c7 = 4 -> r7c9 = 9
54. N58 : 31(6) : r5c5 = 2, r6c5 = 8
55. singles in c6 : r1c6 = 2, r6c6 = 5 -> r6c4 = 7
56. c6 : 15(2) = {78}
57. N356 : 14(4) : r45c6 = {16} locked in N5 -> r34c7 = {25} locked in c7
58. c4 : 6(2) = {15} -> r1c4 = 9 -> r12c3 = {46} locked in N1 and c3 -> r3c1 = 3 -> r3c3 = 8 -> r1c1 = 7 -> r2c1 = 9 -> r3c6 = 7 -> r2c6 = 8
59. combination eliminations: r4c2 = 7, r4c3 = 5 -> r4c7 = 2 -> r3c7 = 5 -> r3c4 = 1 -> r2c4 = 5 -> r3c2 = 2 -> r2c2 = 1 -> r1c2 = 5
60. r45c1 = {48} -> r8c1 = 6 -> r8c2 = 8
61. r12c7 = [83] -> r7c78 = [78]
The rest is simple cleanup.

Greetings,
Peter

I found this a really tricky Assassin - took 3 attempts to get it properly.

Here is a condensed version of Peter's walk-through: with the un-necessary steps left out. The step numbers match Peter's. I've made a few little adjustments to clean up - so any mistakes are mine.

Peter's Walkthrough: Assassin 31, Condensed version

1. r12c1 = 16(2) = {79} -> 7,9 locked in N1 and c1

2. r567c3 = 6(3) = {123} -> 1,2,3 locked in c3

3. r23c4 = 6(2) = {15|24}

4. r23c6 = 15(2) = {69|78}

5. r89c4 = 10(2) = {19|28|37|46}

6. r89c6 = 13(2) = {49|58} ({67} not possible, one is needed for step 5

7. -> 8,9 locked for c6 in 15(2) and 13(2)

8. N12 : 19(3) = {469|478|568} -> r1c4 = {456789} -> no 7 or 9 in r12c3 -> no 4 in r1c4 possible

9. 45 on c5: r56c5 = 10(2) = {19|28|37|46} -> no 5

10. 45 on N7 : r7c23 = 6(2) = [42]|[51] -> 3 locked in r56c3 for N4

11. 45 on N9 : r7c78 = 15(2) = {69|78}

12. 45 on N8 : r7c46 = 9(2) = {27|36|[81]} ({45} not possible, one is needed for 6(2) in r7) -> 6 locked in 9(2) or 15(2) for r7

13. 45 on r89 : r7c159 = 15(3) = {159|249|357} (no 8) (since {258} blocked by r7c23 -step 10)

14. 45 on c12 : r89c3 = 16(2) = {79} -> 7,9 locked for c3 and N7

15. 45 on c89 : r89c7 = 10(2) = {19|28|37|46} -> no 5

16. 45 on c123 : r145c4 = 16(3)

17. 45 on c1234 : r67c4 = 13(2) = {67|[58]} -> no 6,7 in r7c6 (step 12)

18. 45 on c789 : r145c6 = 9(3) = {126|135|234} (no 7)

19. 45 on c6789 : r67c6 = 8(2) = [53]|[62]|[71]

20. using steps 12, 17, 19 : r6c46 = 12{2} = {57} -> 5,7 locked for r6 and N5

21. -> no 7 in r7c4 and no 2 in r7c6 -> no 3,7 in 10(2) in c5

22. 6,8 locked in r7c478 for r7

23. N7 : 13(3) = {139|157|247} -> r9c12 = {12345}

24. N7 : 26(4) = {3689|5678} ({2789/4679} blocked by 13(3),{4589} blocked by r7c2) -> no 2,4 -> 6,8 locked in N7 and r8 -> r8c12 = {68}

25. -> no 2,4 in r9c47 and no 5 in r9c6

26. N9 : 17(4) = {1259|1349|1457|2357} = [7/9..] -> Killer pair with r7c78 for n9 -> no 7,9 in 13(3) -> no 1,3 in r8c7

27. c6 : r7c6 = {13} -> {135} not possible for 9(3) (step 18) ={126|234} -> no 5
28. step 13 : r7c1 = {35} -> 15(3) = {159|357} -> r7c59 = {13579}

29. -> single in r7 : r7c3 = 2, r7c2 = 4

30. r9 : 1 locked in r9c12 -> no 9 in r8c47

31. N4 : 1 locked in r56c3

32. N47 : 21(4) = 4{269|278} (no 5) -> 2 locked in N4 -> no 8 in r5c2

33. c1 : 15(3) : must have one but can't have both 6 and 8 -> {168} not possible -> no 1 -> r9c1 = 1 -> r6c1 = 2 -> no 8 in r5c5 -> 8 not possible in r3c1
To clarify step 33: c1 : 6,8 locked in 15(3) and r8c1 -> no 6,8 in r6c1 -> rc61 =2

34. c2 : 6,8 locked in r568c2


35. -> c2 : 15(4) = {1239|1257} -> r4c2 = {79}

36. 8 locked in r123c3 -> no 8 in r4c3

37. N58 : 31(6) = 567{139|148|238} -> no 6 possible in r45c4 and r9c5 -> 6 locked in r79c4 -> no 6 in r1c4

52. c5 : 13(3) can't have both 1 and 3 (blocked by 9(2), 4 and 8 (blocked by 13(2) -> {139/148} not possible -> no 3,8,9 -> =7{15/24} ->7 locked for c5 and N8 (this is the key to unlock the whole puzzle)

53. -> N8 : {37} not possible in 10(2) -> r7c6 = 3 -> r7c4 = 6 -> r7c1 = 5 -> r9c2 = 3 -> r9c3 = 9 -> r8c3 = 7 -> r9c4 = 8 -> r8c4 = 2 -> r9c6 = 4 -> r8c6 = 9 -> r9c6 = 6 -> r9c89 = {25} -> r9c5 = 7 -> r7c5 = 1 -> r8c5 = 5 -> r8c7 = 4 -> r7c9 = 9

54. N58 : 31(6) : r5c5 = 2, r6c5 = 8

55. r45c6 = {16} -> r1c6 = 2, r6c6 = 5 (single c6) -> r6c4 = 7

56. c6 : 15(2) = {78}

57. N356 : 14(4) : r45c6 = {16} locked in N5 -> r34c7 = {25} locked in c7

58. c4 : 6(2) = {15} -> r1c4 = 9 -> r12c3 = {46} locked in N1 and c3 -> r3c1 = 3 -> r3c3 = 8 -> r1c1 = 7 -> r2c1 = 9 -> r3c6 = 7 -> r2c6 = 8

59. combination eliminations: r4c2 = 7, r4c3 = 5 -> r4c7 = 2 -> r3c7 = 5 -> r3c4 = 1 -> r2c4 = 5 -> r3c2 = 2 -> r2c2 = 1 -> r1c2 = 5

60. r45c1 = {48} -> r8c1 = 6 -> r8c2 = 8

61. r12c7 = [83] -> r7c78 = [78], r4c5 = 9, r56c7 = {19}:locked for n6, r3c8 = 9, 22(4):n67 = 3{47/56} with r5c8 = {57} and 3 locked for n6 and r6 -> r56c3 = [31], r45c4 = [34], r45c1 = [48]
The rest is simple cleanup.

As I commented in the A34 and A71 threads, I didn't manage to solve three of Ruud's Assassins when they first appeared. Now having caught up with my backlog of other walkthroughs I'm having another go at them.

This time I found A31 a lot easier although on checking my original partial walkthrough I found that I'd come fairly close to the breakthrough, only missing the clash in step 8 and step 12 which I felt was the key breakthrough for this puzzle.

In the introduction to A31, Ruud wrote:A tough Assassin that stumps SumoCue. Activate grey matter to continue.

SumoCue probably missed step 12.

Here is my walkthrough. The hardest moves are step 12 and the two-directional clash in step 18; I'm not sure if that clash was necessary but it made the solution quicker.

Prelims

a) R12C1 = {79}, locked for C1 and N1
b) R23C4 = {15/24}
c) R23C6 = {69/78}
d) R12C9 = {17/26/35}, no 4,8,9
e) R89C4 = {19/28/37/46}, no 5
f) R89C6 = {49/58} (cannot be {67} which clashes with R23C6)
g) 19(3) cage at R1C3 = {289/379/469/478/568}, no 1
h) R345C9 = {289/379/469/478/568}, no 1
i) R567C3 = {123}, locked for C3
j) 14(4) cage at R3C7 = {1238/1247/1256/1346/2345}, no 9

1. Killer pair 8,9 in R23C6 and R89C6, locked for C6

2. Max R12C3 = 14 -> min R1C4 = 5

3. 45 rule on C12 2 outies R89C3 = 16 = {79}, locked for C3 and N7

4. 45 rule on N7 2 innies R7C23 = 6 = [51/42]
4a. 3 in C3 locked in R56C3, locked for N6

5. 45 rule on N9 2 innies R7C78 = 15 = {69/78}

6. 45 rule on C89 2 outies R89C7 = 10 = {19/28/37/46}, no 5

7. 45 rule on C1234 2 innies R67C4 = 13 = {49/58/67}, no 1,2,3
7a. 45 rule on C5 2 innies R56C5 = 10 = {19/28/37/46}, no 5
7b. 45 rule on C6789 2 innies R67C6 (or from cage sum) = 8 = {17/26/35}, no 4

8. 45 rule on N8 2 innies R7C46 = 9 = [63/72/81] (cannot be [45] which clashes with R7C2), clean-up: no 4,8,9 in R6C4, no 1,2,3 in R6C6

9. 45 rule on C789 3 outies R145C6 = 9 = {126/135/234}, no 7

10. R9C3 = {79} -> R9C12 = 4,6 = {13/15/24}, no 6,8
10a. Killer pair 1,2 in R7C3 and R9C12, locked for N7

11. 45 rule on C1 4 innies R6789C1 = 14 = {1238/1256/1346} (cannot be {2345} which clashes with R7C2 which “sees” all of R6789C1), 1 locked for C1
[In my original start I’d eliminated 1 from R345C1 which cannot be {168} because 26(4) cage in N7 must contain at least one of 6,8 in R78C1]
11a. 1 in N1 locked in R123C2, locked for C2, clean-up: no 3,5 in R9C1 (step 10)

12. R67C4 = 13 (step 7), R67C6 = 8 (step 7b), R7C46 = 9 (step 8) -> R6C46 = 12 = {57}, locked for R6, N5 and 31(5) cage at R5C5, clean-up: no 3 in R56C5 (step 7a), no 2 in R7C6 (step 7b)
12a. R7C46 = [63/81]
12b. Killer pair 6,8 in R7C4 and R7C78, locked for R7
12c. R145C6 (step 9) = {126/234} (cannot be {135} which clashes with R7C6), no 5
[Alternatively for step 12, 45 rule on N8 4 outies R5C5 + R6C456 = 22, R56C5 = 10 (step 7a) -> R6C46 = 12 …]

13. R789C5 = {157/247/256/346} (cannot be {139} which clashes with R7C6, cannot be {148} which clashes with R89C6, cannot be {238} which clashes with R7C46), no 8,9
13a. Killer pair 4,5 in R789C5 and R89C6, locked for N8, clean-up: no 6 in R89C4

14. R8C12 = {68} (hidden pair in N7), locked for R8, clean-up: no 2 in R9C4, no 5 in R9C6, no 2,4 in R9C7 (step 6)
14a. 26(4) cage in N7 = {3689/5678}, no 4

15. R6789C1 (step 11) = {1238/1256/1346}
15a. 1,2,4 only in R69C1 -> R69C1 = {124}

16. 21(4) cage at R5C2 = {1479/1569/1578/2469/2478/2568}
16a. R7C2 = {45} -> no 4,5 in R5C2 + R6C12
16b. Naked triple {123} in R5C3 + R6C13, locked for N4
16c. Min R45C1 = 9 -> max R3C1 = 6

17. Hidden killer pair 6,8 in R7C78 and R9C789 for N9 -> R9C789 must contain one of 6,8 = {238/256/346} (cannot be {139/157/247} which don’t contain 6 or 8, cannot be {148} which clashes with R9C12), no 1,7,9, clean-up: no 1,3,9 in R8C7 (step 6)

18. 45 rule on R9 3 innies R9C456 = 19 = {289/379/478} (cannot be {469} which clashes with R89C6 = {49}, cannot be {568} because 5,6 only in R9C5), no 1,5,6 clean-up: no 9 in R8C4
[I ought to have spotted this 45 a lot earlier. Fortunately it’s only important now.]

19. R9C1 = 1 (hidden single in R9), R6C1 = 2, R7C3 = 2, R7C2 = 4 (step 4), clean-up: no 8 in R5C5 (step 7a)
19a. R7C4 = 6 (hidden single in N8), R7C6 = 3 (step 8), R6C4 = 7 (step 7), R6C6 = 5, R7C1 = 5, R8C3 = 7 (step 14a), R9C23 = [39], R9C4 = 8, R8C4 = 2, R9C6 = 4, R8C6 = 9, R9C5 = 7, R78C5 = [15], R89C7 = [46], clean-up: no 4 in R23C4, no 6 in R23C6, no 4,9 in R56C5 (step 7a), no 9 in R7C78 (step 5)
19b. R56C5 = [28]
19c. R7C9 = 9 (hidden single in R7)
19d. R3C1 = 3 (hidden single in C1)

20. Naked pair {16} in R45C6, locked for C6, N5 and 14(4) cage at R3C7 -> R1C6 = 2, clean-up: no 6 in R2C9
20a. R1C6 = 2 -> R12C7 = 11 = {38}, locked for C7 and N3 -> R7C78 = [78], clean-up: no 5 in R12C9
20b. R56C7 = {19} (hidden pair in C7), locked for N6

21. Naked pair {15} in R23C4, locked for C4 -> R1C4 = 9, R12C1 = [79], clean-up: no 1 in R2C9
21a. R4C5 = 9 (hidden single in C5)

22. 21(4) cage at R5C2 (step 16) = {2469} (only remaining combination, cannot be {2478} because 7,8 only in R5C2) -> R56C2 = {69}, locked for C2 and N4 -> R8C12 = [68]

23. R4C2 = 7 (hidden single in C2), R4C3 = 5 (hidden single in N4), R34C7 = [52], R23C4 = [51], R3C2 = 2, R12C2 = [51]

24. R4C3 = 5, R45C4 = {34} -> R3C3 = 8 (cage sum), R23C6 = [87]

25. R1C7 = 8 (hidden single in R1), R2C7 = 3, R1C5 = 3 (hidden single in R1)
25a. Naked pair {46} in R2C35, locked for R2
25b. R3C8 = 9 (hidden single in R3)
25c. R4C6 = 1 (hidden single in R4), R5C6 = 6, R56C2 = [96], R56C7 = [19], R56C3 = [31], R45C4 = [34], R45C1 = [48], R4C89 = [68]

26. R34C8 = [96] = 15 -> R12C8 = 6 = [42]

and the rest is naked singles