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Assassin 53 V3 Revisit http://www.rcbroughton.co.uk/sudoku/forum/viewtopic.php?f=3&t=1613 |
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Author: | Ed [ Thu Apr 01, 2021 6:29 pm ] |
Post subject: | Assassin 53 V3 Revisit |
Attachment: a53v3.JPG [ 62.87 KiB | Viewed 3940 times ] Easter and killer sudoku go together in my history so hope this one is worthy! This puzzle is over the target score range (2.20) for these Revisits but JSudoku gets it out pretty easily with just 2 'complex intersections'. Also, the human raters found this one more satisfying than the misnomered v0.1 even though its score is lower (2.05). JSudoku has a very hard time with it. Code: Select, Copy & Paste into solver: 3x3::k:4096:4096:4096:5123:5123:5123:4102:4102:4102:1289:1289:5899:5123:6992:5123:4623:6737:6737:2834:5899:5899:2837:6992:6992:4623:4623:6737:2834:5899:2837:2837:3359:6992:4641:4623:6737:6948:6948:6948:6948:3359:4641:4641:4641:4641:6482:3630:6948:5711:3359:5170:5170:5428:2357:6482:3630:3630:5711:5711:5170:5428:5428:2357:6482:6482:3630:6210:5711:6210:5428:2886:2886:3912:3912:3912:6210:6210:6210:3406:3406:3406: Solution: +-------+-------+-------+ Ed |
Author: | Andrew [ Sun Apr 04, 2021 11:07 pm ] |
Post subject: | Re: Assassin 53 V3 Revisit |
Thanks Ed for this latest Revisit. My most interesting steps were 4a and 4b, although they didn't help with the later steps. Thanks Ed for pointing out that my original step 10d wasn't valid. I've reworked from step 10c, plus made a few other minor changes and a typo correction. Here's how I solved Assassin 53 V3 Revisit: Prelims a) R2C12 = {14/23} b) R34C1 = {29/38/47/56}, no 1 c) R67C9 = {18/27/36/45}, no 9 d) R8C89 = {29/38/47/56}, no 1 e) 11(3) cage at R3C4 = {128/137/146/236/245}, no 9 f) 20(3) cage at R6C6 = {389/479/569/578}, no 1,2 g) 27(4) cage at R2C5 = {3789/4689/5679}, no 1,2 h) 26(4) cage at R2C8 = {2789/3689/4589/4679/5678}, no 1 i) 14(4) cage at R6C2 = {1238/1247/1256/1346/2345}, no 9 j) 18(5) cage at R4C7 = {12348/12357/12456}, no 9 1a. 45 rule on R1 2 outies R2C46 = 7 = {16/25} (cannot be {34} which clashes with R2C12) 1b. Killer pair 1,2 in R2C12 and R2C46, locked for R2 2a. 45 rule on R1234 2 innies R4C57 = 7 = {16/25/34}, no 7,8,9 2b. 45 rule on R6789 2 innies R6C35 = 6 = {15/24} 2c. 45 rule on N7 2 outies R6C12 = 9 = {18/27/36} (cannot be {45} which clashes with R6C35), no 4,5,9 2d. 45 rule on N9 2 outies R6C89 = 9 = {18/27/36} (cannot be {45} which clashes with R6C35), no 4,5,9, clean-up: no 4,5 in R7C9 2e. Killer triple 1,2,3 in R6C12, R6C35 and R6C89, locked for R6 [Unnecessary, in view of step 2f, but step 2e follows logically from steps 2b, 2c and 2d so I’ll keep it.] 2f. 45 rule on N8 3 outies R6C467 = 21 = {489/579} (cannot be {678} which clashes with R6C12), no 6 2g. 45 rule on N8 1 outie R6C4 = 1 innie R7C6 + 1, R6C4 = {45789} -> R7C6 = {34678}, no 5,9 2h. Max R46C5 = 11 -> min R6C5 = 2 3a. 45 rule on C123 1 outie R5C4 = 1 innie R4C3 + 1, no 1 in R5C4 3b. 45 rule on C789 1 innie R6C7 = 1 outie R5C6 + 3, R6C7 = {45789} -> R5C6 = {12456} [The first interesting steps …] 4a. R4C7 ‘sees’ both R4C5 and R5C6, R4C57 (step 2a) = 7 -> R5C6 + R4C7 cannot total 7 (combination crossover clash, CCC) -> R5C789 cannot total 11 Note. This doesn’t eliminate 8 from R5C789, which can still total more than 11 4b. R6C5 ‘sees’ both R5C4 and R6C3, R6C35 (step 2b) = 6 -> R5C4 + R6C3 cannot total 6 (CCC) -> R5C123 cannot total 21 5a. 45 rule on N1 2 outies R4C12 = 10 = {28/37/46}/[91], no 5, no 9 in R4C2, clean-up: no 6 in R3C1 5b. 45 rule on N3 2 outies R4C89 = 15 = {69/78} 5c. Min R2C7 + R4C8 = 9 -> max R3C78 = 9, no 9 in R3C78 6a. R6C35 (step 2b) = {15/24}, R6C7 = R5C6 + 3 (step 3b) 6b. Consider position of 1 in N6 1 in R4C7 + R5C789, locked for 18(4) cage at R4C7, no 1 in R5C6 or 1 in R6C89, locked for R6 => R6C35 = {24}, 4 locked for R6, no 4 in R6C7 => no 1 in R5C6 -> no 1 in R5C6, clean-up: no 4 in R6C7 6c. 18(5) cage at R4C7 = {12348/12357/12456}, 1 locked for N6, clean-up: no 8 in R6C89 (step 2d), clean-up: no 1,8 in R7C9 6d. Killer pair 6,7 in R4C89 and R6C89, locked for N6, clean-up: no 1 in R4C5 (step 2a), no 4 in R5C6 6e. 18(5) cage at R4C7 = {12348/12456} 6f. 6 of {12456} must be in R5C6 -> no 5 in R5C6, clean-up: no 8 in R6C7 6g. 45 rule on C789 3 outies R567C6 = 17 = {269/278/368/467} (cannot be {359/458} because R5C6 only contains 2,6), no 5 7a. 18(5) cage at R4C7 (step 6e) = {12348/12456}, R4C89 = 15 (step 5b), R6C89 = 9 (step 2d), R6C7 = R5C6 + 3 (step 3b) 7b. Consider combinations for R6C467 (step 2f) = {489/579} R6C467 = {489} => R6C7 = 9 => R5C6 = 6 => 18(5) cage = {12456} or R6C467 = {579}, 7 locked for R6 => R6C89 = {36}, 3 locked for N6 => 18(5) cage = {12456} -> 18(5) cage = {12456}, no 3,8 -> R5C6 = 6, R6C7 = 9, clean-up: no 1 in R2C4 (step 1a), no 4 in R4C5, no 1 in R4C7 (both step 2a), no 6 in R4C89, no 5 in R4C3 (step 3a), no 7 in R6C4, no 8 in R7C6 (both step 2g) 7c. Naked pair {78} in R4C89, locked for R4, 7 locked for N6, clean-up: no 2,3 in R4C12 (step 5a), no 3,4,8,9 in R3C1, no 8,9 in R5C4 (step 3a), no 2 in R6C89, no 2,7 in R7C9 7d. Naked pair {78} in R4C89, CPE no 7,8 in R2C8 7e. Naked pair {36} in R6C89, locked for R6 7f. Naked pair {36} in R67C9, locked for C9, clean-up: no 5,8 in R8C8 7g. 1 in N6 only in R5C789, locked for R5 7h. 13(3) cage at R4C5, without 6, must contain one of 7,8,9 -> R5C5 = {789} 8a. 45 rule on N2 1 outie R4C6 = 1 innie R3C4 + 2, R4C6 = {3459} -> R3C4 = {1237} 8b. 11(3) cage at R3C4 = {137/146/236} (cannot be {245} = [245] which clashes with R4C57), no 5 8c. 6 of {146/236} must be in R4C3 -> no 2,4 in R4C3, clean-up: no 3,5 in R5C4 (step 3a) 8d. 45 rule on C123 3 outies R345C4 = 12 = {147/237}, 7 locked for C4 8e. 3 in N5 only in R4C456, locked for R4, clean-up: no 4 in R5C4 (step 3a) 8f. 9 in N5 only in R4C6 or 13(3) cage at R4C5 = [391] -> no 3 in R4C6 (locking-out cages), clean-up: no 1 in R3C4 [With hindsight I missed 9 in R4C6 + R5C5, CPE no 9 in R23C5] 8g. 11(3) cage = {137/236} (cannot be {146} because R3C4 only contains 2,3,7), no 4 8h. R345C4 = {237}, 2,3 locked for C4, clean-up: no 5 in R2C6 (step 1a) 8i. 1 in R4 only in R4C23, locked for N4, clean-up: no 8 in R6C12 (step 2d), no 5 in R6C5 (step 2b) 8j. 1 in R4 only in R4C23, CPE no 1 in R3C3 8k. Naked pair {27} in R6C12, locked for R6 and N4, clean-up: no 4 in R6C35 (step 2b) 8l. R6C35 = [51] -> R45C5 = 12 = [39/57], clean-up: no 5 in R4C7 (step 2a), no 4 in R7C6 (step 2g) 8m. 5 in R4 only in R4C56, CPE no 5 in R23C5 8n. Naked pair {48} in R6C46, 4 locked for N5, clean-up: no 2 in R3C4 8o. Naked pair {27} in R6C12, CPE no 2,7 in R8C2 8p. 45 rule on R9 2 outies R8C46 = 7 = [43/52/61] 9a. R4C12 (step 5a) = 10 9b. Consider permutations for 11(3) cage at R3C4 (step 8g) = {137/236} = [362/713] 11(3) cage = [362] => R4C12 = [91] or 11(3) cage = [713] => R4C12 = [64] -> R4C12 = [64/91], clean-up: no 7 in R3C1 9c. Max R4C2 = 4 -> min R2C3 + R3C23 = 19, no 1 in R3C2 9d. 1 in R3 only R3C78, locked for N3 9e. 18(4) cage at R2C7 contains 1 = {1278/1368/1458/1467} 9f. 1,2 of {1278} must be in R3C78, 7,8 of {1368/1458/1467} must be in R4C8 -> no 7,8 in R3C78 10a. 27(4) cage at R2C5 = {4689/5679} (cannot be {3789} = {378}9 which clashes with R3C3), no 3, 6 locked for C5 and N2, clean-up: no 1 in R2C6 (step 1a) 10b. R2C46 = [52], clean-up: no 3 in R2C12 10c. Naked pair {14} in R2C12, locked for N1, 4 locked for R2 10d. R2C46 = 7 -> R1C456 = 13 containing 1 for N2 = {139/148}, no 7 10e. 16(3) cage at R1C1 = {268/367} (cannot be {259} which clashes with R3C1, cannot be {358} which clashes with R1C456), no 5,9, 6 locked for R1 and N1 10f. 5 in R1 only in 16(3) cage at R1C7, locked for N3 10g. 16(3) cage at R1C7 = {259/457} (cannot be {358} which clashes with 16(3) cage at R1C1), no 3,8 11a. 26(4) cage at R2C8 = {2789/3689/4679}, 9 locked for N3 11b. 16(3) cage at R1C7 (step 10g) = {457} (only remaining combination), 4,7 locked for R3 and N3 11c. 4 in N2 only in 27(4) cage at R2C5 = {4689} -> R4C6 = 9, R4C1 = 6 -> R3C1 = 5, R4C3 = 1 -> R34C4 = 10 = [73], R4C2 = 4, R2C12 = [41] 11d. 16(3) cage at R1C1 = {268} (only remaining combination), 2,8 locked for N1, 8 locked for R1 11e. 14(4) cage at R6C2 = {2345} -> R6C2 = 2, R7C2 = 5, R78C3 = {34}, locked for N7, 3 locked for C3 11f. R3C23 = [39], R2C3 = 7 11g. R9C2 = 7 (hidden single in C2) -> R9C13 = 8 = [26] 11h. R8C46 (step 8p) = 7 -> R9C456 = 17 = {359/458} -> R8C46 = [61] (cannot be [43] which clashes with R9C456), R1C456 = [193], R7C6 = 7 -> R6C6 = 4 (cage sum), R3C6 = 8, clean-up: no 5 in R8C9 11i. R1C1 = 8, R8C12 = [98], clean-up: no 2,3 in R8C89 11j. R3C9 = 2 -> 26(4) cage at R2C8 = {2789} -> R2C89 = [98] and the rest is naked singles. |
Author: | Ed [ Mon Apr 12, 2021 6:40 pm ] |
Post subject: | Re: Assassin 53 V3 Revisit |
Very worthy as an Easter puzzle. Loved it! So nice to have some big cages. I did the start pretty much exactly the same way as I did on the archive WT so have borrowed that one with a different middle crack. [Thanks to Andrew for some typos and clarifications] Assassin 53 V3 WT: 1. "45" r6789: r6c35 = 6 = h6(2)r6 = {15/24} 1a. = [4/5] 2. "45" n7: r6c12 = 9 = h9(2)n4 2a. no 9 3. "45" n9: r6c89 = 9 = h9(2)n6 3a. no 9 4. "45" n8: r6c467 = 21 = h21(3)r6 4a. must have 9 for r6 4b. = 9{48/57}(no 1236) 4c. = [4/5] 5. Killer Pair 4/5 in h21(3)r6 and h5(2)r6 5a. 4 and 5 locked for r6 6. "45" n3: r4c89 = 15 = h15(2)n6 6a. = {69/78} 7. "45" n369: r5c6 + 3 = r6c7 7a. r5c6 = 1,2,4,5,6 8. 4 and 5 cannot be in r5c6. Here's how. 8a. 4 or 5 in r5c6 -> only place for 4/5 in n6 is in r6c7 8b. but this is impossible since r5c6 + 3 = r6c7 = 7/8(step 7) 8c. -> no 4 or 5 in r5c6 8d. -> no 7/8 r6c7 (step 7) 9. 1 cannot be in r5c6. Here's how. 9a. 1 in r5c6 -> 4 in r6c7 (step 7) and 1 in n6 in r6c89. 9b. -> r6c789 = {14} 9c. but this clashes with h6(2) r6 = [1/4..] 9d. no 1 r5c6 9e. no 4 r6c7 (step 7) 10. 2 cannot be in r5c6. You've probably guessed how by now. 10a. 2 in r5c6 -> r6c7 = 5 (step 7) and 2 for n6 in r6c89 10b. -> r6c789 = {25} 10c. but this clashes with h6(2)r6 = [2/5..] 10d. no 2 r5c6 11. r5c6 = 6, r6c7 = 9 (step 7) 11a. split-cage 11(2)r6c6 = [83]/{47} 11b. r6c6 = 478, r6c7 = 347 12. split-cage 12(4)r4c7 = {1245}: 1,2 locked for n6 13. h15(2)n6 = {78}: both locked for n6 & r4 13a. r2c8 sees both those so has no 7,8 14. r6c89 = {36}: both locked for r6 15. 9(2)r6c9 = {36}: both locked for c9 16. "45" r1234: r4c57 = 7 = h7(2)r4 16a. = {25}/[34], r4c5 = 235, r4c7 no 1 16b. -> 1 in n6 only in r5: 1 locked for r5 17. "45" n8: r6c46 = 12 = {48}/[57](no 7 r6c4) 17a. = [4/7..] 18. 13(3)n5 = [391/571/382] ({247} blocked by r6c46 step 17a) 18a. r4c5 = {35}, r5c5 = {789}, r6c5 = {12} 18b. r6c3 = {45} (h6(2)r6) 18c. r4c7 = {24} (h7(2)r4) 19. 5 in n6 only in r5: 5 locked for r5 20. 27(5)n4 = 5{...} (since must contain 4 or 5 for r6c3) 20a. ->r6c3 = 5 21. r6c5 = 1 (h6(2)r5) 21a. r45c5 = [39/57](no 8) 21b. 8 in r5 only in split-cage 22(4)r5c1 = 8{239/347} 22. r6c12 = h9(2) = {27}: both locked for n4, r6 22a. and not in r8c2 (CPE) 23. r6c46 = naked pair {48}: both locked for n5 23. r67c6 = [83/47] 24. "45" n147: r5c4 - 1 = r4c3 24a. r5c4 = {27}, r4c3 = {16} 25. "45" n1: r4c12 = 10 = [91]/{46} (no 3, no 9 in r4c2) 26. 2 in n5 only in c4: 2 locked for c4 27. "45" n2: 3 outies r4c346 = 13 = [139/625] 27a. r4c4={23}, r4c6 = {59} 28. "45" n2: r4c6 - 2 = r3c4 28a. r3c4 = {37} 29. naked triple {237} r345c4: 3 & 7 locked for c4 30. 5(2)n1 = {14/23} 30a. = [3/4..] 31. "45" r1: 2 outies r2c46 = 7 = h7(2)n2 31a. = [61/52] ([43] blocked by 5(2)n1 step 30a) New ending from here 32. 11(3)r3c4 = [713/362] = 7 in r3 or 6 in r4 32a. -> combined half cage r34c1+r4c2, [746] blocked 32b. -> r34c1 = [29/56] 32c. r4c2 = (14) 33. 23(4)n1 must have 1 or 4 for r4c2 33a. can't have both 1,4 since other two can't = 18 33b. -> no 1,4 in r2c3 + r3c23 34. 16(3)n1 can't have both 1,4 and make the cage sum 34a. -> 5(2) must have both = {14}(only other place in n1): both locked for n1 and r2 34b. r2c46 = [52] 35. 27(4)n2: {3789} blocked by r3c4 = (37) 35a. = {4689/5679}(no 3) 35b. must have 6: locked for c5 and n2 36. sp13(3)r1c456 = {139/148}(no 7) 36a. 1 locked for r1 37. 16(3)n1: {259} blocked by r3c1 = (25) 37a. {358} blocked by r1c456 = 3 or 8 37b. = {268/367}(no 5,9) 37c. 6 locked for n1 and r1 38. 5 in r1 only in 16(3)n3 38a. but {358} blocked by r1c456 38b. = {259/457}(no 3,8) 38c. 5 locked for n3 39. 26(4)n3: {3689} blocked by 3,6 only in r2c8 39a. = {2789/4679}(no 3) 39b. 9 locked for n3 40. 16(3)n3 = {457} only: 4,7 both locked for r1 and n3 40a. -> 7 which must be in 26(4)n3 must be in r4c9 40b. r4c8 = 8 40c. -> 18(4)r2c7: must have 3 or 6 for r2c7 = {136}[8] 40d. 6 locked for n3 40e. -> 26(4)n3 = [9827] On from there. Sorry, ran out of time for any more Ed |
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