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Assassin 370 http://www.rcbroughton.co.uk/sudoku/forum/viewtopic.php?f=3&t=1477 |
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Author: | Ed [ Fri Feb 15, 2019 5:21 am ] |
Post subject: | Assassin 370 |
Attachment: a370.JPG [ 64.89 KiB | Viewed 6191 times ] Nice hard one for a milestone! Took me a long, long time to work out the weak area in this puzzle so was very satisfying to find a decent way to unlock it. SudokuSolver gives it 2.40 and "uses simple trial & error" (which usually means the sort of thing we do all the time). JSudoku has a very hard time too but no T&E. code: 3x3::k:3840:3840:3840:0000:3330:4867:4867:4867:4867:6678:0000:0000:0000:3330:4357:3078:4359:4359:6678:6678:0000:4357:4357:4357:3078:4359:2824:6678:5897:5897:5897:3338:3083:3083:4108:2824:6678:5897:5897:3853:3338:3083:4108:4108:3854:4367:4367:5897:3853:3853:3853:7696:3601:3854:6674:6674:6674:7696:1811:1811:7696:3601:3601:1044:6674:6165:7696:7696:7696:7696:3588:3588:1044:6165:6165:6165:5633:5633:5633:5633:3588: solution: Code: +-------+-------+-------+ | 6 4 5 | 2 9 8 | 7 1 3 | | 2 7 1 | 5 4 3 | 8 6 9 | | 9 3 8 | 1 6 7 | 4 2 5 | +-------+-------+-------+ | 5 1 4 | 7 8 9 | 2 3 6 | | 7 6 2 | 3 5 1 | 9 4 8 | | 8 9 3 | 6 2 4 | 1 5 7 | +-------+-------+-------+ | 4 5 9 | 8 1 6 | 3 7 2 | | 3 8 6 | 4 7 2 | 5 9 1 | | 1 2 7 | 9 3 5 | 6 8 4 | +-------+-------+-------+ Ed |
Author: | Andrew [ Thu Feb 21, 2019 7:27 am ] |
Post subject: | Re: Assassin 370 |
Thanks Ed for a very stubborn Assassin. I'll be interested to see which part you found to be the weak area. Here's my walkthrough for Assassin 370: Prelims a) R12C5 = {49/58/67}, no 1,2,3 b) R23C7 = {39/48/57}, no 1,2,6 c) R34C9 = {29/38/47/56}, no 1 d) R45C5 = {49/58/67}, no 1,2,3 e) R56C9 = {69/78} f) R6C12 = {89} g) R7C56 = {16/25/34}, no 7,8,9 h) R89C1 = {13} i) 26(4) cage at R7C1 = {2789/3689/4589/4679/5678}, no 1 j) 23(6) cage at R4C2 = {123458/123467}, no 9 Steps resulting from Prelims and Initial Placement 1a. Naked pair {89} in R6C12, locked for R6 and N4, clean-up: no 6,7 in R5C9 1b. Naked pair {13} in R89C1, locked for C1 and N7 1c. 45 rule on N7 1 outie R9C4 = 9 2. 45 rule on N5 1 innie R4C4 = 1 outie R4C7 + 5 -> R4C4 = {678}, R4C7 = {123} 2a. 23(6) cage at R4C2 = {123458/123467}, 2,4 locked for N4 2b. 45 rule on N4 2 innies R45C1 = 1 outie R4C4 + 5, IOU no 5 in R5C1 3a. 45 rule on N89 2 outies R6C78 = 6 = {15/24} 3b. 45 rule on N689 2 innies R4C79 = 8 = [17/26/35], R4C7 = {123} -> R4C9 = {567}, R3C9 = {456} 3c. Killer pair 6,7 in R34C9 and R6C9, locked for C9, 7 also locked for N6 3d. 45 rule on N3 2(1+1) outies R1C6 + R4C9 = 14 = [77/86/95], R4C9 = {567} -> R1C6 = {789} 3e. 45 rule on N2 3 innies R1C46 + R2C4 = 15 which can only contain one of 7,8,9 -> no 7,8 in R12C4 3f. 15(4) cage at R5C4 cannot be 7{125}/7{134}/8{124} which clash with R6C78 -> no 7,8 in R5C4 4. 15(4) cage at R5C4 = {1257/1347/1356/2346} 4a. 45 rule on N5 3 innies R4C46 + R5C6 = 17 = {179/269/278/368} (cannot be {359/458/467} which clash with 15(4) cage), no 4,5 in R45C6 4b. 6 of {269/368} must be in R4C4 (R4C46 + R5C6 cannot be 8{36} because 12(3) cage at R4C6 cannot be {36}3), no 6 in R45C6 4c. R45C5 = {49/58} (cannot be {67} which clashes with R4C46 + R6C5), no 6,7 5. 26(5) cage at R2C1 = {14579/14678/23579/23678/24569/24578/34568} (cannot be {13589/13679} because 1,3 only in R3C2, cannot be {12689/23489} because must contain two of 5,6,7 for R45C1) 5a. 26(5) cage only contains two of 5,6,7 which must be in R45C1 -> no 5,6,7 in R2C1 + R3C12 6. 16(3) cage at R4C8 = {169/349/358} (cannot be {259} which clash with R6C78, cannot be {268} which clashes with R56C9), no 2 7. 45 rule on R9 2 outies R8C13 = 1 innie R9C9 + 5 7a. Max R8C13 = 11 -> no 8 in max R9C9 7b. Min R8C13 = 6 -> no 2 in R8C3 8. 45 rule on R1 2 innies R1C45 = 11 = [29/38/47]/{56}, no 1 in R1C4, no 4 in R1C5, clean-up: no 9 in R2C5 8a. 15(3) cage at R1C1 = {159/168/258/267/357/456} (cannot be {249/348} which clash with 26(5) cage at R5C1) 8b. R1C45 = [29/38/47] (cannot be {56} which clashes with 15(3) cage), no 5,6, clean-up: no 7,8 in R2C5 8c. R1C46 + R2C4 = 15 (step 3e) = {249/258/267/348/357} (cannot be {159/168} because R1C4 only contains 2,3,4, cannot be {456} because R1C6 only contains 7,8,9), no 1 in R2C4 8d. R1C45 = 11 -> R1C46 cannot be 11 (CCC) -> no 4 in R2C4 8e. R1C46 + R2C4 = {249/258/267/348} (cannot be {357} = [375] which clashes with R1C45 + R2C5 = [385]) 8f. 4 of {348} must be in R1C4 -> no 3 in R1C4, clean-up: no 8 in R1C5, no 5 in R2C5 9. Consider placement for 8 in R1 9a. 8 in 15(3) cage at R1C1, locked for N1 => 26(5) cage at R2C1 (step 5) = {14579/23579/24569} => R4C1 = 5 or 8 in 19(4) cage at R1C7 which cannot contain both of 8,9 => no 9 in R1C6, no 5 in R4C9 (step 3d) -> no 5 in R4C9, clean-up: no 9 in R1C6 (step 3d), no 6 in R3C9, no 3 in R4C7 (step 3b), no 8 in R4C4 (step 2) [The first breakthrough, thanks to the elimination of 8 from R1C5 in step 8f.] 9b. Naked pair {67} in R4C49, locked for R4 -> R4C1 = 5, clean-up: no 8 in R5C5 9c. Naked pair {67} in R46C9, 6 locked for N6 9d. 3 in N6 only in 16(3) cage at R4C8 (step 6) = {349/358}, no 1 9e. R4C46 + R5C6 (step 4a) = {179/269/368} (cannot be {278} = 7{28} because 12(3) cage at R4C6 cannot be {28}2) 9f. 7 of {179} must be in R4C4 -> no 7 in R5C6 9g. R1C46 + R2C4 (step 8e) = {258/267/348} 9h. 2 of {258/267} must be in R1C4 -> no 2 in R2C4 9i. 19(4) cage at R1C6 = {1378/1468/1567/2368} (cannot be {1279} which clashes with R1C5, cannot be {2458/2467} which clash with R1C4, cannot be {1459/3457} which clash with R3C9, cannot be {1369/2359} because R1C6 only contains 7,8), no 9 9j. 15(3) cage at R1C1 (step 8a) = {159/357/456} (cannot be {168/258/267} which clash with 19(4) cage), no 2,8, 5 locked for R1 and N1 9k. 7,9 of {159} must be in R1C1 -> no 7,9 in R1C23 9l. R1C45 = 11 (step 8b) = [29/47], R12C5 = [76/94] -> R1C45 + R2C5 = [294/476], 4 locked for N2 9m. Killer triple 3,4,5 in 19(4) cage at R1C6, R23C7 and R3C9, locked for N3 10. R1C6 + R4C9 (step 3d) = 14 = [77/86] 10a. R1C46 + R2C4 (step 9g) = {258/348} (cannot be {267} = [276] which clashes with R4C49 = [67], no 6,7 [The second breakthrough.] 10b. R1C6 = 8 -> R4C9 = 6, R3C9 = 5, R4C7 = 2 (step 3b), R4C4 = 7, R6C9 = 7 -> R5C9 = 8, clean-up: no 7 in R23C7, no 4 in R6C78 (step 3a) 10c. R4C7 = 2 -> R45C6 = 10 = {19}, locked for C6 and N5, clean-up: no 4 in R45C5, no 6 in R7C5 10d. R45C5 = [85], clean-up: no 2 in R7C6 10e. Naked pair {15} in R6C78, locked for R6 and N6 10f. 30(7) cage at R6C7 must contain 2, locked for N8, clean-up: no 5 in R7C6 10g. R7C56 = [16] (cannot be {34} because 30(7) cage at R6C7 must contain both of 3,4 and R7C56 ‘sees’ all its cells except for R68C7 and R6C7 only contains 1,5) [I’d been aware of this type of ‘sees all except’ step for a while, realising that R678C7 had to contain one of 1,2,3, but this was the first time I found it useful.] 10h. 30(7) cage at R6C7 must contain 1 in R68C7, locked for C7 11. 8 in C4 only in 30(7) cage at R6C7 = {1234578}, no 6,9, no 8 in R78C7 12. R5C1 = 7 (hidden single in N4) 12a. 15(3) cage at R1C1 (step 9j) = {159/456}, no 3 12b. 3 in R1 only in R1C789, locked for N3, clean-up: no 9 in R23C7 12c. Naked pair {48} in R23C7, locked for C7 and N3 12d. R5C7 = 9 (hidden single in C7) -> naked pair {34} in R45C8, locked for C8, R45C6 = [91] 12e. 30(7) cage at R6C7 must contain 4, locked for N8 12f. 22(4) cage at R9C5 = {3568} (only possible combination, cannot be {1678/2578} because 1,2,8 only in R9C8) = [3568], R89C1 = [31] 12g. 7 in N8 only in R8C56, locked for R8 and 30(6) cage at R6C7 12h. Naked pair {15} in R68C7 -> R17C7 = [73] 12i. R1C67 = [87] = 15 -> R1C89 = 4 = [13], R1C5 = 9 -> R2C5 = 4, R1C4 = 2 (step 8b), R23C7 = [84], R6C78 = [15] 12j. Naked pair {37} in R23C6, locked for C6 and N2 -> R3C45 = [16] 12k. Naked pair {48} in R78C4, locked for N8 -> R8C56 = [72] 12l. Naked pair {29} in R2C29, locked for R2 -> R2C8 = 6 12m. R8C8 = 9 -> R89C9 = 5 = [14] 12n. Naked pair {27} in R9C23, locked for N7, R9C4 = 9 -> R8C3 = 6 (cage sum) and the rest is naked singles. Rating Comment: I'll rate my walkthrough for A370 at 1.5 I only used one forcing chain, but my final key step was a 'sees all except' step. |
Author: | Ed [ Sat Feb 23, 2019 9:03 pm ] |
Post subject: | Re: Assassin 370 |
I worked in the same key areas as Andrew. However, when I first did it, I had other areas of the grid much more sparse so felt much harder than Andrew's WT looks. Andrew is so good at finding combination clashes. I usually have to get cages reduced a lot further before I can find them. Hence, my WT is fairly different, mainly because of my steps 8 and 15 which use different "45s". a370 WT: Preliminaries from SukokuSolver Cage 4(2) n7 - cells ={13} Cage 17(2) n4 - cells ={89} Cage 15(2) n6 - cells only uses 6789 Cage 7(2) n8 - cells do not use 789 Cage 12(2) n3 - cells do not use 126 Cage 13(2) n2 - cells do not use 123 Cage 13(2) n5 - cells do not use 123 Cage 11(2) n36 - cells do not use 1 Cage 26(4) n7 - cells do not use 1 Cage 23(6) n45 - cells do not use 9 NOTE: no clean-up done unless stated. 1. "45" on n7: 1 outie r9c4 = 9 2. 17(2)n4 = {89}: both locked for n4 and r6 2a. r5c9 = (89) 3. 4(2)n7 = {13}: both locked for c1 and n7 4. "45" on n3: 2 outies r1c6 + r4c9 = 14 (no 1,2,3,4: note, could be [77]) 5. "45" on n6789: 2 innies r4c79 = 8 = [35/26/17](no 4,8,9); r4c7 = (123) 5a. no 5,6 in r1c6 (outiesn3=14) 6. "45" on n56789: 2 innies r4c49 = 13 = {67}/[85] 6a. r4c4 = (678) 7. 11(2)r3c9 = {56}/[47] = 6/7 7a. -> killer pair 6,7 with r6c9: both locked for c9 and 7 for n6 Key step to get anywhere. Like a big intersection. 8. "45" on n356789: 1 outie r1c6 - 1 = 1 innie r4c4 = [76/87/98] 8a. "45" on r1: 2 innies r1c45 = 11 (no 1: no 8 in r1c4) 8b. "45" on r1: 1 innie r1c4 + 2 = 1 outie r2c5 8c. "45" on c456789: 3 innies r124c4 = 14 8d. but [356] blocked by 5 in r2c5 (step 8b) 8e. but [536] blocked by 7 in both r1c6 and r2c5 (steps 8. & 8b) 8f. -> {356} blocked from h14(3) 8g. = {158/167/248/257/347} 8h. but {167} as [716], blocked by 7 in r1c6 (step 8.) 8i. and 1 in {167} must go in r2c4 8j. -> no 6 in r4c4 nor r2c4 8k. -> no 7 in r4c9 (h13(2)) 8l. -> no 7 in r1c6 (outiesn3=14) 8m. and no 1 in r4c7 (h8(2)r4c79) 9. hidden single 7 in n6 -> r6c9 = 7, r5c9 = 8 10. 11(2)r3c9 = {56} only: 5 locked for c9 11. 23(6)r4c4 = {123458/123467} 11a. can't have both 7,8 -> no 7 in r45c23 12. 7 in n4 only in r45c1: 7 locked for c1 and no 7 in r3c2 13. "45" on n4: 1 outie r4c4 + 5 = 2 innies r45c1 13a. 1 outie = (78) -> 2 innies = 12/13 and must have 7 = {57/67} Lots of combos involved here. 14. 26(5)r2c1: {13679} blocked by 1,3 only in r3c2 14a. must have 7 for r45c1 = {14579/14678/23579/23678/24578} 14b. can't have both 5 & 6, one of which must go in r45c1 -> no 5,6 in r23c1+r3c2 Took me a long time to look in this area. 15."45" on r4..9: 4 outies r2c1+r3c12 + r3c9 = 19 15a. 6 in r3c9 -> 3 outies in n1 = 13 = {28}[3]/{48}[1] 15b. note: must have 8 with r3c9 = 6 15c. "45" on n3: 1 outie r1c6 - 3 = 1 innie r3c9 = [85/96]: note: must have 8 with r3c9 = 5 15d. -> 8 in r1c6 or r23c1+r3c2 -> no 8 in r1c123 16. 19(4)r1c6 must have 8,9 for r1c6 -> max. other 3 = 11 16a. -> no 8,9 in r1c789 (note, can't be 8128) 17. 8 in r1 only in n2 in r1c56: locked for n2 17a. no 5 in r1c5, no 6 in r1c4 (h11(2)r1c45) 18. 8 in n2 in r1c6 -> 7 in r4c4 (iodn356789=-1) or 8 in n2 in r1c5 -> 3 in r1c4 (h11(2)) 18a. -> h14(3)r124c4 must have 3 or 7 18b. = {167/257/347}(no 8) 18c. -> r4c4 = 7, r1c6 = 8, r34c9 = [56], r4c7=2 (1 innie n6789), r45c1 = [57] 19. "45" on n789: 2 outies r6c78 = 6 = {15} only: both locked for n6 and r6 20. 30(7)r6c7 = {1234569/1234578} 20a. must have 2 which is only in n8: 2 locked for n8 20a. must have both 3 & 4 which can't both go in r8c7 20b. ->{34} blocked from 7(2)n8 20c. -> 7(2)n8 = {16} only: both locked for n8 and r7 21. hidden single 6 in c1 -> r1c1 = 6 22. 19(4)r1c6 = [8]{137} only: 1,3,7 locked for r1 and n3 23. 12(2)n3 = {48} only: both locked for n3 and c7 24. r1c1 = 6 -> r1c23 = 9 = {45} only: both locked for r1 and n1 24a. r1c45 = [29], r2c5 = 4, r2c4 = 5 (h14(3)) 25. r45c1 = 12 -> r2c1 + r3c12 = 14 = {29}[3] only: 2,9 locked for n1 and c1 26. hidden single 4 in c1 -> r7c1 = 4 27. 14(3)r6c8 = [572] only permutation 28. 8 in c4 only in 30(7)r6c7 -> = {1234578}(no 9) 28a. must have 2,4,7 which are only in n8 -> r8c456 = [4]{27}: 2 & 7 locked for r8 & n8 28b. r7c4 = 8 29. hidden single 9 in c7 -> r5c7 = 9 30. r4c7 = 2 -> r45c6 = 10 = [91/46] only singles. Ed |
Author: | wellbeback [ Sun Feb 24, 2019 9:46 pm ] |
Post subject: | Re: Assassin 370 |
Thanks Ed! This was a frustrating puzzle for me in that I didn't find a nice way to do it. Had to use some elimination chains. I really wanted to use ...: the interesting shape of the 30(7). E.g., First - if 7(2)n8 from {25}/{34} -> r68c7 = {25}/{34} Second - if 30(7) = {1234569} -> r9c56 = {78} and r78c8 = {78} Here's what I finally came up with! Assassin 370 WT: 1. Innies whole puzzle = uncaged cells in n12 = +23(5) (May have repeats). Innies r1 -> r1c45 = +11(2) 4(3)r8c1 = {13} Outies n7 -> r9c4 = 9 Outies r789 -> r6c78 = +6(2) -> Remaining Innies n6 = r4c79 = +8(2) 2. 17(2)n4 = {89} 23(6)n4 = {1234(58|67)} IOD n5 -> r4c4 = r4c7 + 5 -> r4c4 from (678), r4c7 from (123) 3. IOD n124 -> r1c6 = r4c4 + 1 -> r1c6 from (789) 5. Trying r4c4 = 8 Puts r45c1 = {67} Also puts r1c6 = 9 Puts remaining Innies n2 = r12c4 = +6(2) (No 3) -> puts 8 in r1 in r1c123 -> leaves no solution for 26(5)r2c1 -> r4c4 from (67) -> r45c1 = [56] or [57] i.e., r4c1 = 5 6. Trying r4c4 = 6 Puts r1c6 = 7 Puts remaining innies n2 = r12c4 = +8(2) -> puts r12c4 = {35} -> puts 13(2)n2 = {49} Which leaves no solution for r1c45 = +11(2) -> r4c4 = 7 7. -> r45c1 = [57] Also -> r4c7 = 2 -> r4c9 = 6 -> r3c9 = 5 Also -> 15(2)n6 = [87] Also -> r6c78 = {15} -> 16(3)n6 = {349} Also r6c3456 = {2346} -> 15(4)n5 = {2346} -> 13(2)n5 = [85] -> r45c6 = {19} Also r1c6 = 8 8. 2 in r4c7 -> 2 in 30(7) in n8 -> 7(2)n8 not {25} -> 12(2)n3 from {39} or {48} -> At least one of (34) in 30(7) in n8 -> 7(2)n8 not {34} -> 7(2)n8 = [16] 9. 26(5)n14 cannot contain all of (567) -> HS 6 in c1 -> r1c1 = 6 -> 3 in r1 in n3 -> 19(4)r1 = [8{137}] -> 12(2)n3 = {48} -> 17(3)n2 = {269} Also r1c45 = [29] -> r2c45 = [54] -> 17(4)n3 = {1367} Also 12(2)n3 = [84] 10. Also 15(3)r1 = [6{45} -> 26(5)n14 = [{29}357] -> HS r7c1 = 4 Also 17(2)n4 = [89] -> HS r7c3 = 9 Also HS r3c3 = 8 -> r2c23 = {17} 11. 8 in n8 in r78c4 -> 30(7) = {1234578} -> 9 in n9 in r8c89 -> HS 9 in c7 -> r5c7 = 9 -> r45c6 = [91] Also r45c8 = {34} 12. Only solution for 14(3)r6c8 is [572] -> r6c7 = 1 -> 19(4)r1 = [8713] Also 4 in 30(7) in r8c46 -> HS 4 in r9 -> r9c9 = 4 -> 14(3)n9 = [914] etc. |
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