Joined: Wed Apr 16, 2008 1:16 am Posts: 1043 Location: Sydney, Australia
Hilarious puzzle! Had to use a shortcut technique.... was going completely bonkers. Must have missed something important. It gets a SudokuSolver score of 1.40. [Code now fixed for JS and SumoCue. Thanks Afmob!]
That was quite an interesting Assassin, Ed! It started really easy but it suddenly came to a halt and even in the last stages it proved to be quite stubborn. Furthermore my first walkthrough contained a false move but I was able to fix it using step 6b.
A285 Walkthrough:
1. N12346 a) Innies N236 = R3C4 = 3 b) Innies N14 = R5C3 = 9 c) 3(2) = {12} locked for R2+N1 d) 3 locked in 9(2) @ N1 = {36} locked for R1+N1 e) 42(7) = {3456789} -> 9 locked for R3+N1 f) 13(2) = {58} locked for C1+N1 g) 8(3) = {134} locked for C1+N4 h) 9(2) @ N4 = {27} locked for R6+N4 i) 42(7) = {3456789} -> 4,7 locked for R3
2. N7 a) 2,6 locked in R789C1 @ C1 for N7 b) 16(4) = 13{48/57} -> 1,3 locked for N7 c) 18(3) = 7{29/56} because R89C1 = (2679) -> 7 locked for N7 d) 16(4) = {1348} locked for N7 e) 11(2) = [29/65]
3. C789 a) 13(2) = {49} locked for R6+N6 because (58) is a Killer pair of 14(2) b) 14(2) = {68} locked for C7+N6 c) Innies C9 = 13(2) = {49} locked for C9 d) Outies N6 = 14(2) = {68} locked for R3+N3 e) 9(2) = {27} -> R2C9 = 7, R1C9 = 2 f) 21(5) = {12459} because R3C567 = (125) -> R2C57 = {49} locked for R2 g) Hidden Single: R2C8 = 3 @ N3 h) 12(3) @ N9 = 1{29/47} because R7C9 = (49), {345} blocked by Killer pair (35) of 11(2) @ C9 and {246} blocked by R7C1 = (26) -> 1 locked for R7+N9 i) 11(2) @ C8 <> 8 j) 8 locked in 11(2) @ R8C9 @ N9 = {38} locked for C9+N9 k) 6 locked in 11(2) @ R8C8 @ N9 = {56} locked for C8+N9
4. R789 ! a) 25(5) = {12589/12679/13579/14578/23479} since all other combos blocked by R9C8 = (56) and R9C9 = (38) b) Innies N9 = 11(2) = {29/47} c) 25(5) <> {13579} since Innies N9 belong to 25(5) d) ! Hidden Killer quad (1348) in 25(5) + R9C39 @ R9 -> 25(5) must have at least two of (1348) -> 25(5) <> {12679} e) 25(5) = {12589/14578/23479} <> 6 f) Killer pair (38) locked in 25(5) + R9C9 for R9
5. N4789 ! a) 18(3): R9C1 <> 6 since [765] blocked by R9C8 = (56) b) Hidden Killer triple (279) in R8C456 @ R8 c) ! 25(5): R8C7 <> 7 because 7{158}4 blocked by R9C3 = (14) and 7{239}4 blocked by Killer triple (279) in R8C456 d) Innies N9 = 11(2): R9C7 <> 4 e) 18(3) = {279} locked for N7 since [675] blocked by Killer pair (57) of 25(5) f) R7C1 = 6, R7C2 = 5 g) Naked triple (279) locked in R9C127 for R9 h) Outies N9 = 14(3) = {158} locked for R9+N8 i) 11(2) @ N8 = {38} -> R7C5 = 3, R6C5 = 8
6. C456+N9 ! a) Outies N89 = 6(2) = {15} locked for R6+N5 b) 20(3) = {479} -> 4,7 locked for R5+N5 c) 14(3) = {149/257} because {167} blocked by Killer pair (67) of 27(5) d) ! Hidden Killer pair (47) in R1C6 for C6 since 14(3) can only have one of them -> R1C6 = (47) e) 16(3) = 1{69/78} because {457} blocked by R1C6 = (47) -> 1 locked for R1+N2 f) 14(3) = {149} because {257} blocked by R3C6 = (25) -> R6C6 = 1; 4,9 locked for C6+N8 g) R1C6 = 7 h) 27(5) = {34578} -> R1C8 = 4, R1C7 = 5, R2C6 = 8 i) R6C8 = 9, R6C9 = 4, R7C9 = 9 j) 12(3) = {129} -> 2 locked for R7+N9
7. Rest is singles.
Rating:
Hard 1.25. I used a Hidden Killer quad and a Hidden Killer triple combined with combo analysis.
Edit: I optimised the start and merged some steps which were in the same region.
Last edited by Afmob on Wed Oct 29, 2014 9:19 pm, edited 1 time in total.
Thanks Ed for another excellent Assassin. As Afmob said, it starts easily and then becomes stubborn. It leads to some interesting steps in both my original walkthrough and alternative continuation.
My original walkthrough for Assassin 285:
Thanks Ed for correcting a typo and for your comments about steps 20a and 21a.
Prelims
a) R12C1 = {49/58/67}, no 1,2,3 b) R1C23 = {18/27/36/45}, no 9 c) R12C9 = {18/27/36/45}, no 9 d) R2C23 = {12} e) R56C7 = {59/68} f) R6C23 = {18/27/36/45}, no 9 g) R67C5 = {29/38/47/56}, no 1 h) R6C89 = {49/58/67}, no 1,2,3 i) R7C12 = {29/38/47/56}, no 1 j) R89C8 = {29/38/47/56}, no 1 k) R89C9 = {29/38/47/56}, no 1 l) 8(3) cage at R4C1 = {125/134} m) 20(3) cage at R5C3 = {389/479/569/578}, no 1,2 n) 42(7) cage at R3C1 = {3456789}, no 1,2
Steps resulting from Prelims 1a. Naked pair {12} in R2C23, locked for R2 and N1, clean-up: no 7,8 in R1C23, no 7,8 in R1C9 1b. 8(3) cage at R4C1 = {125/134}, 1 locked for C1 and N4, clean-up: no 8 in R6C23
2. 45 rule on R12 2 innies R2C57 = 13 = {49/58/67}, no 3 2a. 45 rule on R12 3 outies R3C567 = 8 = {125/134}, 1 locked for R3
3. 45 rule on N14 1 innie R5C3 = 1 outie R3C4 + 6 -> R3C4 = 3, R5C3 = 9, clean-up: no 5 in R6C7 3a. R3C567 (step 2a) = {125} (only remaining combination), locked for R3, 5 also locked for 21(5) cage at R2C5, no 5 in R2C57, clean-up: no 8 in R2C57 (step 2)
4. 3 in N1 only in R1C23 = {36}, locked for R1 and N1, clean-up: no 7 in R12C1, no 3,6 in R2C9 4a. R2C8 = 3 (hidden single in N3), clean-up: no 8 in R89C8
5. 9 in 42(7) cage at R3C1 only in R3C12, locked for R3 and N1, clean-up: no 4 in R12C1 5a. Naked pair {58} in R12C1, locked for C1 and N1, clean-up: no 3,6 in R7C2
6. 8(3) cage at R4C1 = {134} (only remaining combination), locked for C1 and N4, clean-up: no 5,6 in R6C23, no 7,8 in R7C2 6a. Naked pair {27} in R6C23, locked for R6 and N4, clean-up: no 6 in R6C89, no 4,9 in R7C5 6b. R3C89 = {68} (hidden pair in R3), locked for N3, clean-up: no 1 in R1C9, no 7 in R2C5 (step 2) 6c. 2,6 in C1 only in R789C1, locked for N7, clean-up: no 9 in R7C1
7. R56C7 = {68} (cannot be [59] which clashes with R6C89), locked for C7 and N7, clean-up: no 5 in R6C89 7a. Naked pair {49} in R6C89, locked for R6 and N6, clean-up: no 2,7 in R7C5
8. 45 rule on N9 2 innies R89C7 = 11 = {29/47}, no 1,3,5 8a. 1 in N9 only in 12(3) cage at R7C7, locked for R7
9. R3C9 = {68} -> 12(3) cage at R3C9 = {138/156}, no 2,7, 1 locked for C9 and N6
10. 45 rule on R789 3 outies R6C456 = 14 = {158/356}, 5 locked for N5 10a. R5C3 = 9 -> R5C45 = 11 = {47} (only remaining combination, cannot be [83] which clashes with R6C456), locked for R5 and N5 10b. R4C1 = 4 (hidden single in C1)
11. 45 rule on C9 2 innies R67C9 = 13 = {49} (only possible combination because R6C9 only contains 4,9), locked for C9, clean-up: no 5 in R12C9, no 2,7 in R89C9
12. R12C9 = [27], clean-up: no 6 in R2C5 (step 2) 12a. Naked pair {49} in R2C57, locked for R2 12b. Killer pair 4,9 in R2C7 and R89C7, locked for C7
13. 1 in N9 only in 12(3) cage at R7C7 = {129/147} (cannot be {138/156} because R7C9 only contains 4,9), no 3,5,6,8 13a. R7C9 = {49} -> no 4,9 in R7C8
14. 3 in N9 only in R89C9 = {38}, locked for C9 -> R3C9 = 6 14a. Naked pair {15} in R45C9, locked for N6 -> R45C8 = [72], R4C7 = 3, R7C8 = 1 14b. R89C8 = {56} (hidden pair in N9), locked for C8
15. 16(3) cage at R1C4 = {169/178/457} 15a. R2C4 = {568} -> no 5,8 in R1C45
16. 27(5) cage at R1C6 contains 3 = {13689/34569/34578} 16a. R1C7 = {15} -> no 1,5 in R12C6
17. 18(3) cage at R8C1 = {279/369/567} (cannot be {189/378/459/468} because 1,3,4,5,8 only in R9C2), no 1,4,8 17a. 2 in C1 only in R7C12 = [29] or 18(3) cage = {279} -> 18(3) cage = {279/567} (cannot be {369}, locking-out cages), no 3, 7 locked for N7, clean-up: no 4 in R7C2 17b. 6 of {567} must be in R8C1 (R9C12 cannot be [65] which clashes with R9C8) -> no 6 in R9C1
18. 16(4) cage at R7C3 = {1348} (hidden quad in N7)
19. R4C3 = 5 (hidden single in C3), R45C9 = [15] 19a. Naked pair {68} in R45C2, locked for C2 -> R1C23 = [36] 19b. Naked pair {68} in R5C27, locked for R5
20. 45 rule on N9 3 outies R9C456 = 14 = {158/167/239/347} (cannot be {149/248/257} which clash with R89C7, cannot be {356} which clashes with R9C8) 20a. R9C456 = {158/167/347} (cannot be {239} because R9C456 “see” all 2,9 in N9 except for R7C79 and 2,9 cannot both be in R8C1), no 2,9 [I first saw this elimination as R9C456 cannot be {239} because R7C12 and R7C89 cannot both be [29] Ed pointed out that step 20a would be simpler as R9C456 = {158/167/347} (cannot be {239} because R9C456 “see” all 2,9 in N8 except for R8C1), no 2,9]
[With hindsight the killer ALS block, which I eventually found in step 30, could have been used instead of step 21a to reduce R9C456 to one remaining combination. See alternative continuation below.] 21. 18(3) cage at R8C1 (step 17a) = {279/567}, R9C456 (step 20a) = {158/167/347} 21a. Hidden killer pair 5,6 in 18(3) cage, R9C456 and R9C8 for R9, R9C8 = {56} -> 5 in 18(3) cage = [675] or R9C456 contains one of 5,6 -> R9C456 = {158/167}, no 3,4, 1 locked for R9 and N8 [Ed pointed out that 18(3) cage = {279} (only remaining combination, cannot be {567} = [675] which clashes with R9C456), locked for N7, followed by hidden killer pair 5,6 on R9 would have been simpler.] 21b. Killer pair 5,6 in R9C456 and R9C8, locked for R9 21c. 18(3) cage = {279} (only remaining combination), locked for N7 -> R7C12 = [65], clean-up: no 5,6 in R6C5
22. Naked pair {38} in R67C5, locked for C5 22a. R6C456 (step 10) = {158/356} 22b. R6C5 = {38} -> no 3,8 in R6C46
23. 14(3) cage at R6C6 = {149/158/167/257/356} (cannot be {239/248/347} because R6C6 only contains 1,5,6) 23a. 3,8 of {158/356} must be in R7C6 -> no 3,8 in R8C6 23b. 3 in N8 only in R7C56, locked for R7
24. 27(5) cage at R1C6 contains 3 = {13689/34569/34578} -> R12C6 = [46/78/86/96] 24a. 14(3) cage at R6C6 (step 23) = {149/158/167/257/356} 24b. 4 in C6 only in R12C6 = [46] or 14(3) cage = {149} -> R12C6 = [46/78/86] (cannot be [96], locking-out cages, no 9 in R1C6, 14(3) cage = {149/158/257} (cannot be {167/356}, locking-out cages), no 3,6
25. R7C5 = 3 (hidden single in N8), R6C5 = 8, R6C7 = 6 25a. R5C6 = 3 (hidden single in N5)
26. 20(4) cage at R6C4 = {1289/1469/2459/2567} (cannot be {1478/1568} which clash with R9C456, cannot be {2468} because R6C4 only contains 1,5) 26a. R6C4 = {15} -> no 5 in R8C45
27. Hidden killer triple 7,8,9 in 20(4) cage at R6C4, 14(3) cage at R6C6 and R9C456 for N8, 14(3) cage (step 24b) contains one of 7,8,9, R9C456 (step 21a) contains one of 7,8 -> 20(4) cage (step 26) must contain one of 7,8,9 = {1469/2459/2567} (cannot be {1289} which contains both of 8,9), no 8
28. 14(3) cage at R6C6 (step 24b) = {149/158/257} 28a. Consider combinations for 16(3) cage at R1C4 (step 15) = {169/178/457} 16(3) cage = {169/178}, 1 locked for N2 => R3C6 = {25} => 14(3) cage = {149/158} (cannot be {257} which clashes with R3C6) or 16(3) cage = {457}, 4 locked for N2 => 4 in C6 only in 14(3) cage = {149} -> 14(3) cage = {149/158}, no 2,7 -> R6C6 = 1, R6C4 = 5
29. 16(3) cage at R1C4 (step 15) = {169/178}, no 4, 1 locked for R1 and N2 -> R1C7 = 5, R12C1 = [85]
[I ought to have spotted this earlier …] 30. R89C7 (step 8) = {29/47} 30a. R9C456 (step 21) = {158} (only remaining combination, cannot be {167} which clashes with R9C12 + R89C7 = {29}, killer ALS block), locked for R9 and N8 30b. Naked pair {49} in R78C6, locked for C6 and N8 -> R1C6 = 7
31. Naked pair {19} in R1C45, locked for R1 and N2, R2C4 = 6 (cage sum), R1C8 = 4, R6C89 = [94], R7C9 = 9, R7C7 = 2 (cage sum)
and the rest is naked singles.
I don't optimise my walkthroughs but this time I realised that my original step 30 could have been used to simplify my step 21, so ...
Alternative continuation after step 20:
If you are using solver software, set up the diagram using the code string, then import the position after step 20 by using Import/Candidates to copy and paste this position.
Joined: Wed Apr 16, 2008 1:16 am Posts: 1043 Location: Sydney, Australia
Afmob and Andrew both found much purer ways than me into this gritty puzzle. Really enjoyed both their WTs but not really surprised I couldn't find their ways. I worked quite differently in the key areas. [Thanks Andrew for some corrections and good suggestions]
I've started with Afmob's beginning and shown my way from there. Download the attached file and open with SudokuSolver on your computer.
I realised this is my 80th V1 Assassin so a really good one to pass that milestone.
4. Hidden single 5 in c3 -> r4c3 = 5 4a. r45c9 = [15]
5. Naked pair {68} in r45c2: both locked for c2 5a. r1c23 = [36]
6. Naked pair {27} in r45c8: both locked for c8 and n6 6a. r4c7 = 3, r4c1 = 4
7. 12(3)r7c7 = {129/147}: can't have both 4 & 9 -> no 4,9 in r7c78 7a. r7c8 = 1
8. "45" on n9, 2 innies r89c7 = 11 = {29/47} = [4/9..] 8a. Killer pair 4,9 in r2c7 & r89c7: both locked for c7
My shortcut step 9. r89c39 can't be {38/38} since the puzzle will not have one solution -> r89c3 must have 1 or 4 -> no 4 in r7c3 (Killer Unique Rectangle: Note Afmob and Andrew would not use this step since they don't believe in principle in UR as a valid technique. For me, it was a sanity saver!)
10. r8c7 sees all of n8 except for r7c456 so must repeat there 10a. "45" on r7: 4 innies r7c3456 = 22 10b. Must have 3 & 8 for r7 10c. but {3568} blocked since no 2,4,7,9 from r8c7 10d. = {2389/3478}(no 5,6)
11. Hidden pair 5,6 in r7 -> r7c12 = [65]
12. 11(2)r6c5 = {38} only valid combination: both locked for c5
13. r5c3 = 9 -> r5c45 = 11 = {47} only combination: both locked for r5 and n5 13a. r45c8 = [72]
14. "45" on n89: 3 outies r6c456 = 14 and must have 5 for n5 14a. = {158/356} 14b. can't have both 3 & 8 -> no 3,8 in r6c46
15. Naked pair {38} in r7c35: both locked for r7
16. 14(3)r6c6; {158/239/248/347/356} all blocked by r6c6 must have (156) and r7c6 from (2479) 16a. = {149/167/257}(no 3,8)
17. 27(5)r1c6 = {13689/34569/34578} = 6/7 in r12c6 (no eliminations yet) 17a. -> {167} blocked from 14(3)r6c6 17b. = {149/257}(no 6) 17c. can't have both 1 & 5 -> no 1,5 in r8c6
18. 14(3)r6c6 = {149/257}; r3c6 = (125) -> 1 in 14(3) or r3c6, locked for c6
19. 20(4)n5 = {2369} only -> r5c6 = 3 and 6 locked for n5 and r4 19a. r67c5 = [83], r7c3 = 8, r45c2 = [86], r56c7 = [86]
20. 20(4)r6c4; {1568} blocked by r7c4 = (2479); {2468} blocked by r6c4 = (15) 20a. = {1289/1469/1478/2459/2567} 20b. Can't have both 1 & 5 -> no 1,5 in r8c45
21. "45" on n9: 3 outies r9c456 = 14 and must have 1 & 5 for n8 = {158} only: all locked for r9 and 8 for n8
22. 14(3)r6c6 = {149/257}: ie, can't have both 4 & 7. The only other place in c6 for 4 & 7 is r1c6 -> r1c6 = (47) (Hidden killer pair)
23. 16(3)n2: {457} blocked by r1c6 = (47) 23a. = {169/178}(no 4,5) 23b. Must have 1: 1 locked for n2 and r1 23c. r1c7 = 5
24. 14(3)r6c6: {257} blocked by r3c6 = (25) 24a. 14(3)r6c6 = {149} only; r6c6 = 1, r78c6 = {49} only: both locked for n8 and c6 [Andrew suggested "Or r6c6 = 1 (Hidden single), r78c6 = {49}]
25. 27(5)r1c6 = {34578}(no 6,9) only valid combination on from there. Finally cracked.
I realised this is my 80th V1 Assassin so a really good one to pass that milestone.
Congratulations! Only Ruud has posted more V1 Assassins.
Your comment gave me an idea. I'll add puzzle creators' names as an extra column in the rating columns for Archive D onward. I've already done that for the TJK Archive in the Other Variants forum.
Killer Unique Rectangle: Note Afmob and Andrew would not use this step since they don't believe in principle in UR as a valid technique.
Just to avoid confusion: I know that UR is a valid technique if one knows that there is only one solution prior to solving the puzzle. I just think that it is the task of the solver the prove the unicity of the solution.
My view is fairly similar. While I don't doubt that UR is a valid technique if one knows that there a unique solution, it seems to me that it's bypassing solving the whole puzzle.
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