Assassin 27

[nd]

Nothing too fancy, though the overlap technique is needed to make things easier.

Assassin 27 walkthrough

1. 45 rule on R9 => R9C456 = 7 = {124}, R78C5 = 13 = {58|67}, 3 is locked in the 17(3) cage in R9/N9 => R9C789 = {3(59|68)}, R9C123 = {7(59|68)}. 45 rule on R8 => R8C159 = 10 => R8C159 = [154] (only valid possibility because of 20(3) cage & locking of the 3 in N9), R7C5 = 8, R8C678 = {678} (8 locked within N9), R9C789 = {359}, R67C9 = [97], R9C123 = {678}, R8C6 = 7, R7C78 = {12}, R8C234 = {239} (2 locked within N7).

2. 45 rule on R1..4 => R4C357 = 23 = {689}. Overlap rule on R19+C5 => R19C5 = 5 = {14} or [32]. 45 rule on C1..4 => R19C4 = 10 => R1C4 = {689}. 45 rule on C5 => R19C6 = 7 => R1C6 = {356}. 45 rule on R1 => R1C456 = 15, R23C5 = 8 => R1C5 cannot = 3 (no valid combos for split 15(3) cage) => R19C5 = {14}, R23C5 = {26}, R4C5 = 9, R56C5 = {37}.

3. R5C12 = {59} (because {68} contradicts R4C3 = {68}). 45 rule on C9 => R159C1 = 13 => R5C12 = [59] (otherwise R159C1 would be > 13). 45 rule on C9 => R159C9 = 9 = {135} => R5C89 = [71], R56C5 = [37], R4C1 = 7, R23C1 = {49}, R19C1 = [26] (because the cells must add to 13 - 5 = 8), R67C1 = [83].

4. Mop-up. R234C9 = {268} => R4C9 = 2. R8C4 = 3, R8C23 = [29]. R34C2 = [51], R67C2 = [34], R1C23 = {68}, R1C456 = [915], R9C456 = [142], R7C346 = [569], R6C46 = [21], and you carry on.....

[PsyMar]

Eh, I'll go ahead and post my own walkthrough anyway -- IMO, it's a bit more verbose and newbie-friendly.

Also, if you're not going to claim the naming rights, I'll call this one "Hourglass Sudoku" due to the pattern of the cages. Although if you look at the left and right quarters instead it looks kinda like a ship from "Star Wars" -- but then "X-wing sudoku" would confuse people

1. Placing pencilmarks, checking for cages with disallowed numbers:
1a. 5/2 in C7 = {14|23}
1b. 6/2 in C2 = {15|24}
1c. 7/2s in C2 and C8 both = {16|25|34}
1d. 8/2 in R5/N6 = {17|26|35}
1e. 14/2 in R5/N4 = {59|68}
1f. 19/3 in C5/N5 <> 1
1g. 20/3s in C1 and C9 <> 1|2
1h. 21/3s in R8 and R9/N7 = {489|579|678}
No maximal/minimal/near-maximal/near-minimal cages.

2. outies of R1 = R23C5 = 8 = {17|26|35}
3. Innies of R1234 = R4C357 = 23 = {689} naked triple
4. Innies of R9 = R9C456 = 7 = {124} naked triple
5. 21/3 in R9 has no 4 -> {579} or {678} -> must have 7, elim from rest of R9/N7
6. 17/3 in R9 has no 1247 -> {359} or {368} -> must have 3, elim from rest of N9
7. Outies of R9 = R78C5 = 13 = {58|67} (no 4 due to step 4)
8. Innies of C6789 = 7 = [34|52|61]
9. Innies of C1234 = 10 = [64|82|91]
10. 19/3 in C5/N5 cannot be {478} or {568} as these conflict with R78C5=13 (see step 7)
11. 19/3 must be {(28|37|46)9} -> eliminate 9 from rest of C5/N5
12. Innies of C1 = R159C1 = 13 -> [157|256|265] -> elim 5 from rest of C1
13. 20/3 in C1 does not have 5 -> 20/3 in C1 is {389} or {479} -> elim 9 from rest of C1
14. Outies-innies of R89 = R7C5-R8C19 = 3 -> only possibility is R7C5 = 8, R8C1 = 1, R8C9 = 4 -> naked single 2 in R1C1
15. outies of R9 = R8C5 = 5
16. 21/3 in R8 without 4 or 5 = {678} naked triple
17. 8 of R8 locked in N9 -> elim from rest of N9
18. 2 of R8 locked in N7 -> elim from rest of N7
19. combinations for 17/3 in R9/N9 = {359} naked triple -> naked triple {678} in R9C123
20. Hidden pair {12} in R7/N9 in R7C78
21. only combination for 20/3 in C9 with 4 in R8C9 is [974]
22. Hidden single 7 in R8/N8 in R8C6
23. Innies of N9 = 9 = {135} naked triple -> R4C9 = naked single 2 -> naked pair {68} in R23C9
24. R5C1 = hidden single 5 in C1 -> R5C2 = 9 due to sum
25. Only combination for 6/2 in C2 is [51]
26. Only combination for 8/2 in R5/N6 is [71]
27. R4C5 = hidden single 9 in R4
28. R7C12 = naked pair {34} -> 14/3 in C8 = [293] -> R7C3 = 5
29. only combination for 13/3 in R67C34 is [256] -> R7C6 = 9
30. Only combination for 12/3 in R67C67 is [192] -> 7/2 in C8 = [61] -> R4C7 = 8
31. only combination for 23/4 in R456C67 is [8645] -> a gajillion naked singles and last-digit-in-cage moves
32. only combination for 16/3 in R1/N1 is [268] -> R2C2 = 7 -> 21/3 in R9 = [687]
33. Only combination for 14/3 in R1/N3 = [743] -> naked singles and last-digit-in-cage solves it

[nd]

1a. 5/2 in C7 = {14|23}
1b. 6/2 in C2 = {15|24}
1c. 7/2s in C2 and C8 both = {16|25|34}

Quick note--actually each 7(2) has only two possibilities not three because of 1a. and 1b (5/2 blocks {34}, 6/2 blocks {25}). Not that this has much effect on the solution to the puzzle.

Yes I'm sure my solution is not that user-friendly for newbies; I try to squeeze it down as much as possible.

[PsyMar]

Yes I'm sure my solution is not that user-friendly for newbies; I try to squeeze it down as much as possible.

Didn't mean it as a criticism (if you took it that way), just thought I'd offer mine as I consider myself fairly new at this. I figure having a condensed walkthrough for people who don't like to read through what they think is obvious, plus a verbose walkthrough for newbies, isn't that bad an idea.

That, and I needed an excuse to post mine so I could claim those naming rights.

[nd]

No, not as a criticism. I just find it most interesting to try & produce a "minimal" solution, which isn't necessarily how I initially solved the puzzle--it's as efficient as I can make it, via reordering steps & omitting unnecessary ones.

[PsyMar]

I just find it most interesting to try & produce a "minimal" solution, which isn't necessarily how I initially solved the puzzle--it's as efficient as I can make it, via reordering steps & omitting unnecessary ones.

I'll try and work on that some once I'm done with school for the semester -- still have two final exams to work on, and I may take an incomplete in one class.

[Andrew]

This Assassin combines an aesthetically pleasing cage layout with an excellent package of possible solving techniques. It should be named by the first to post a walkthrough.

Yes, a pleasant cage pattern. It looked even better after I had coloured the cages in my Excel file to make it easier to distinguish between them. Hourglass is a good title from PsyMar. I'd been thinking of Flower Burst but I didn't solve it quickly enough to earn the right to name it.

A good variety of possible solving techniques. That made for the differences between the walkthroughs already posted by nd and PsyMar and my one so here goes with my walkthrough, pretty well in the order that I solved it. This is the verbose walkthrough for those of us who prefer not to use elimination solving. I know I have to use it for really difficult puzzles such as Assassins 24 and 26 but prefer not to if I can help it.

1. 45 rule on R9, 3 innies R9C456 = 7 = {124}

2. R78C5 = 13 = {58/67} (4 blocked in N8)

3. 21(3) cage cannot contain 3 -> 3 in R9 locked in 17(3) cage = 3{59/68}, 3 locked for R9, N9

4. 21(3) cage in R9 -> 7{59/68}, 7 locked for R9, N7

5. 45 rule on R1 3 innies R1C456 = 15 -> R23C5 = 8 = {17/26/35}

6. 45 rule on C5 2 innies R19C5 = 5, R9C5 = {124} -> R1C5 = {134}

7. 9 in C5 locked in 19(3) cage, also locked for N5

8. 45 rule on C1234 2 innies R19C4 = 10, R9C4 = {124} -> R1C4 = {689}

9. 45 rule on C6789 2 innies R19C6 = 7, R9C6 = {124} -> R1C6 = {356}

10. R1C5 = {14}(3 cannot form any valid 15(3) combinations with R1C4 and R1C6), the only valid combinations are [645]/[816]/[843]/[915]

11. R9C5 = {14}(step 6), 1,4 locked for C5, R23C5 = {26/35}

12. Killer pair 5/6 in R2378C5, no other 5/6 in C5 -> 19(3) cage in N5 = 9{28/37}

13. R1C456 cannot be [645] because that would clash with R23C5 -> R1C4 = {89}, R9C4 = {12} (step 8)

14. 45 rule on R1234 3 innies R4C357 = 23 = {689} with 6 blocked from R4C5, no other 6,8,9 in R4

15. 45 rule on R8 3 innies R8C159 = 10 -> max. 7 in each cell -> R8C5 = {567}, R7C5 = {678}

16. R8C19 = {12}/{13}/{14/23} -> R8C1 = {1234}, R8C9 = {124}(3 blocked in N9)

17. R8C9 = 4 (cannot have 1,2 in 20(3) cage), R67C9 = {79}, no other 7,9 in C9

18. R8C15 = [15] is only valid combination -> R7C5 = 8

19. R4C5 = 9, R56C5 = {37}, R4C37 = {68}

20. R23C5 = {26} -> R1C6 = {35}, R9C6 = {24}

21. R34C8 = {14/23}

22. R67C8 = {16/25}(cannot be {34} which would clash with R34C8)

23. Killer pair 1/2 in R34C8 and R67C8, no other 1,2 in C8

24. R5C89 = {17/26/35} but no 1,2 in R5C8 -> R5C8 = {3567}, R5C9 = {1235}

25. 45 rule on C9 3 innies R159C9 = 9 = 1{26/35} -> R9C9 = {356}, R1C9 = {1235}, 1 locked
in R15C9 for C9

26. 8 in C9 must be in R234C9 = 8{26/35}, with 8 locked in R23C9 for C9 and N3

27. 21(3) cage in R8 = {678} with the 8 in R8C78, locked for R8 and N9

28. 14(3) cage in R8 = {239} with the 2 in R8C23, locked for R8 and N7

29. 1,2 in R7 locked in R7C78 for R7 and N9 -> R7C78 = {12}, R6C8 = {56}

30. 5 in N9 must be in R9 -> R9C789 = {359}, R7C9 = 7, R6C9 = 9, R8C78 = {68}, R8C6 = 7

31. R9C9 = {35} -> R234C9 = {268}, R4C9 = 2, R23C9 = {68}, 8 in N3 locked in C9 -> 8 in N6 locked in C7 -> R8C78 = [68], R4C37 = [68], X-wing with 6 in R23C59, no other 6 in R23,
6 in R1 locked in N1

32. R1C9 = {135}, R5C9 = {135}, R5C8 = {357}

33. R9C123 = {678}, R5C12 = {59}, R5C89 = [71], R56C5 = [37], R1C9 = {35}

34. Killer pair 3/5 in R1C69, no other 3,5 in R1

35. 45 rule on C1 3 innies R159C1 = 13, min. R59C1 = 11 -> R1C1 = 2 (1 blocked in C1), R5C12 = [59], R9C1 = 6, R9C23 = {78}, R1C23 = [68]

36. R1C456 = [915], R1C9 = 3, R1C78 = [74], R9C456 = [142] (steps 8, 9 and 11)

37. R34C8 = [23], R67C8 = [61], R7C7 = 2

38. R56C7 = [45], R5C6 = 6

39. R9C8 = {59} -> R2C8 = {59}

40. 1 in N3 locked in C7, cannot be in R3C7 because 6,7 blocked from R34C6 -> R2C7 = 1, R3C7 = 9 (5 blocked in C7), R2C8 = 5, R2C6 = 8, R23C9 = [68], R9C789 = [395], R34C6 = [34], R67C6 = [19], R23C5 = [26]

41. 45 rule on R2 R2C1 = 9, R2C234 = {347}

42. R34C1 = [47], R67C1 = [83], R2C23 = {37}, R2C4 = 4, R3C4 = 7

43. R3C3 + R4C4 = 6 = [15] (1 blocked in C4), R34C2 = [51]

44. R67C2 = [34] (hidden 4 in C2), R56C3 = [24], R5C4 = 8, R6C4 = 2, R7C34 = [56] and the rest is simple elimination


Now to have another go at trying to finish Assassin 26.