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Assassin 364 http://www.rcbroughton.co.uk/sudoku/forum/viewtopic.php?f=3&t=1464 |
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Author: | Ed [ Sat Dec 01, 2018 7:57 am ] |
Post subject: | Assassin 364 |
Attachment: a364.JPG [ 64.05 KiB | Viewed 6075 times ] code: 3x3::k:5632:5632:3585:3585:3585:5378:4099:4099:4099:7940:5632:5632:3585:3589:5378:4099:5382:5382:7940:1543:1543:4360:3589:5378:2313:2313:5382:7940:0000:0000:4360:4360:2315:2315:0000:5382:7940:7940:5645:5645:5645:5645:5645:0000:0000:4110:7940:2831:2831:3344:3344:3345:3345:0000:4110:1042:1042:5139:2324:3344:3349:3349:0000:4110:4110:6678:5139:2324:5642:3340:3340:0000:6678:6678:6678:5139:5642:5642:5642:3340:3340: solution: Code: +-------+-------+-------+ | 6 7 5 | 3 2 8 | 4 1 9 | | 3 1 8 | 4 9 6 | 2 5 7 | | 9 4 2 | 1 5 7 | 6 3 8 | +-------+-------+-------+ | 2 6 3 | 9 7 4 | 5 8 1 | | 4 8 7 | 6 1 5 | 3 9 2 | | 1 5 9 | 2 8 3 | 7 6 4 | +-------+-------+-------+ | 8 3 1 | 7 6 2 | 9 4 5 | | 5 2 4 | 8 3 9 | 1 7 6 | | 7 9 6 | 5 4 1 | 8 2 3 | +-------+-------+-------+ Cheers Ed |
Author: | Ed [ Fri Dec 07, 2018 10:44 pm ] |
Post subject: | Re: Assassin 364 |
Here's how I solved it. Steps 8, 19 & 26 are my keys with one of those steps getting no (useful) eliminations! WT 364: Prelims courtesy of SudokuSolver Preliminaries Cage 4(2) n7 - cells ={13} Cage 6(2) n1 - cells only uses 1245 Cage 14(2) n2 - cells only uses 5689 Cage 13(2) n9 - cells do not use 123 Cage 13(2) n6 - cells do not use 123 Cage 9(2) n56 - cells do not use 9 Cage 9(2) n8 - cells do not use 9 Cage 9(2) n3 - cells do not use 9 Cage 11(2) n45 - cells do not use 1 Cage 21(3) n2 - cells do not use 123 Cage 20(3) n8 - cells do not use 12 Cage 13(4) n9 - cells do not use 89 Cage 14(4) n12 - cells do not use 9 Cage 26(4) n7 - cells do not use 1 No routine clean-up done unless stated 1. "45" on n7: 1 outie r6c1 = 1 1a. "45" on n3: 1 outie r4c9 = 1 2. 4(2)n7 = {13} only: both locked for n7 and r7 3. "45" on n8: 1 innie r7c6 + 6 = 1 outie r9c7 = [28] only permutation 3a. r7c6 = 2 -> r6c56 = 11 (no 9) 3b. no 7 in 9(2)n8, no 6,8 in r8c5 3c. no 5 in 13(2)n9 4. 21(3)n2: {489} blocked by 14(2)n2 needing an 8 or 9 4a. = {579/678}(no 4) 4b. must have 7: 7 locked for n2 and c6 4c. no 4 in r6c5 (sp11(2)) 5. 14(2)r23c5 = {59/68}; 9(2)r78c5 = [81]/[63]/{45} 5a. if 14(2) = {68} -> 9(2) = {45}; or 14(2) = {59} 5b. -> 5 locked in one of those two cages: locked for c5 (combined cages) 5c. no 6 in r6c6 (sp11(2)) 6. "45" on n2: 1 innie r3c4 + 4 = 1 outie r1c3 6a. r1c3 = (5678), r3c4 = (1234) 6b. hidden quad 1,2,3,4 in n2 -> r123c4+r1c5 = {1234} 6c. 17(3)r3c4 can only have one of 1,2,3,4 -> no 2,3,4 in r4c45 7. 20(3)r7c4 = {389/479/569/578} = two of 6..9 7a. -> r456c4 must have two of 6..9 for c4 7b. r4c5 = (6789) 7c. sp11(2)r6c56 must have one of 6,7,8 7d. -> killer quad 6,7,8,9 in those four areas: all locked for n5 7e. r4c7 = (456) Ready for the first advanced step - which totally cracked one of the previous versions of this puzzle 8. 21(3)n2 = {579}/678} 8a.if {579} -> 14(2)n2 = {68} (combined cage) 8b. r9c7 = 8 -> r89c6 + r9c5 = 14 = {149/167/347/356} 8c. if {149} -> 9(2)n8 = [63] only (combined cage) 8d. 9 in c6 in one of 21(3)n2 or r89c6 -> 14(2)n2 = {68} or 9(2)n8 = [63] 8e. must have 6: 6 locked for c5 8f. no 5 in r6c6 (sp11(2)) 9. 6 in c5 in 14(2)n2 = {68} or 6 in 9(2)n8 -> no {18} in 9(2)n8 since it would block all 6 in c5 (locking-out cages) 9a. 9(2) = [63]/{45} 10. 8 in n8 only in 20(3) = {389/578}(no 4,6) = 3 or 5 10a. 8 locked for c4 11. 9(2)n8 = [63]/{45} = 3 or 5 11a. killer pair 3,5 with 20(3) (step 10): both locked for n8 12. 3 in c6 only in n5: 3 locked for n5 12a. no 8 in r6c6 (sp11(2)) 13. 8 in c6 only in 21(3)n2 = {678} only: 6,8 locked for n2, 6 for c6 14. 14(2)n2 = {59}: both locked for c5 14a. r78c5 = [63] 14b. 13(2)n9 = {49} only: both locked for n9 and r7 15. "45" on n9: 2 remaining innies r78c9 = 11 = [56] only permutation 16. 16(4)r6c1: must have 7 or 8 for r7c1 = [1]{258} only 16a. R7C1 = 8 16b. r8c12 = {25} both locked for r8 16c. r7c4 = 7 17. r8c4 = 8 (hidden single n8) 17a. r9c4 = 5 (cage sum) 18. 17(3)r3c4 must have 6 or 9 for r4c4, and 7 or 8 for r4c5 = {179/368/467}(no 2) 18a. no 6 in r1c3 (IODn2=-4) Next key step 19. "45" on n2: 3 outies r1c3 + r4c45 = 21 = [5][97]/[7][68]/[8][67]: 19a. note: must have 5 in r1c3 or 6 in r4c4 19b. note2: must have 7 in r1c3 or r4c5 19c. note: no eliminations yet (can take 7 from r4c3 but not important to this optimised solution) 20. 11(2)r6c3: [56] blocked by step 19a 20a. = {29}/[74] = 4 or 9 21. 13(2)n6: {49} blocked by 11(2)n4 21a. = [58]/{67}(no 4,9; no 5 in r6c8) 22. hidden pair 5,6 in r6. 13(2)n6 can only have one of 5,6 -> r6c2 = (56) 23. "45" on r6: 2 remaining innies r6c29 = 9 = [54/63] 24. hidden pair 2,9 in r6 -> 11(2)r6c3 = {29} only 25. "45" on n1: 3 innies r1c3 + r23c1 = 17 25a. but {458} blocked by 6(2)n1 needing 4 or 5 25b. must have 5,7,8 for r1c3 = {278/359/368/467} 25c. note: if has 7 in r1c3 must have {46} in r23c1 25d. note: no eliminations yet The final crack by removing 6 from r6c2 26. from step 19b. must have 7 in r1c3 or r4c5 26a. if in r1c3 -> r23c1 = {46} (step 25c) -> no 6 in r6c2 (same cage) 26b. if in r4c5 -> 7 in r6 only in 13(2)r6c78 = {67} 26c. -> both places have 6 -> no 6 in r6c2 27. r6c2 = 5 27a. r6c9 = 4 (h9(2)r6c29), r6c56 = [83], r4c5 = 7 -> r34c4 = 10 = [19/46] (no 3) 27b. no 7 in r1c3 (IODn2=-4) 27c. r8c12 = [52] 28. 31(6)r2c1 = {23489}[5]/{23678}[5] 28a. must have 8 -> r5c2 = 8 28b. must have 2 & 3 which are only in c1: locked for c1 29. naked pair {14} in r3c24: both locked for r3 30. naked pair {67} in r6c78: locked for n6 30a. r4c67 = [45], naked pair {19} in r89c6: 1 locked for n8 and c6, r9c5 = 4, r5c6 = 5 31. 22(5)r5c3 must have 1 for n5 = {13459/13567}(no 2) 31a. must have 3: 3 locked for r5 31b. r5c5 = 1 32. naked pair {29} in r5c89: both locked for r5 and n6 Straightforward now. Ed |
Author: | wellbeback [ Sat Dec 08, 2018 9:22 pm ] |
Post subject: | Re: Assassin 364 |
Thanks Ed! This was the puzzle that kept on giving. As you wrote - several key steps needed. As usual I wrote my WT before reading yours. Some similarities and some differences. Where there were similarities we often approached each step from opposite directions. Assassin 364 WT: 1. Outies n3 -> r4c9 = 1 Outies n7 -> r6c1 = 1 -> 1 in n5/r5 in r5c456 2. 4(3)n7 = {13} Outies - Innies n8 -> r9c7 = r7c6 + 6 -> [r7c6,r9c7] = [28] 3. Innies n2 -> r1c45 + r23c4 = +10(4) = {1234} -> 21(3)n2 = {7(68|59)} Also Since Max r3c4 = 4 -> both r4c45 are Min 5. 4! 1 in c6 only in r589c6 9 in c6 in one of: a) r123c6 -> 14(2)n2 = {68} b) r5c6 -> 1 in r89c6 c) r89c6 -> 22(4)n8 = [{149}8] In none of those cases can 9(2)n8 be {18} -> 8 in n8 in 20(3)n8 -> 20(3)n8 = {8(57|39)} 5! 6 in c4 only in n5 in r456c4 Also -> 1 in n8 in 22(4)n8 -> 3 in n8 in 20(3) or 9(2) -> 3 in c6 in n5 in r456c6 -> 13(3) r6c5 from [832] or [742] If the former -> 14(2)n2 = {59} -> 9(2)n8 = [63] -> 20(3)n8 = {578} If the latter -> 7 in 20(3)n8 = {578} -> 9(2)n8 = [63] -> 14(2)n2 = {59} Either way 20(3)n8 = {578}, 9(2)n8 = [63], 14(2)n2 = {59}, 21(3)n2 = {678}, 22(4)n8 = [{149}8] -> 9 in c4 in n5 in r456c4 Also 5 in c6 in n5 in r45c6 Also -> r46c5 = {78} (Having read Ed's WT the next step is more complicated than it need be since 13(2)n9 can already only be {49})! 6! Remaining Innies n9 -> r78c9 = +11(2) 3 in r9 only in r9c89 -> 13(4)n9 cannot contain a 6 -> 6 in n9 in 13(2) or H11(2) -> 6 in r9 in n7 in r9c123 -> 2 in n7 in r8c12 -> 2 in r9 in r9c89 -> 13(4)n9 = [{17}{23}] -> 13(2)n9 = {49} -> r78c9 = [56] -> 16(4)r6c1 can only be [18{25}] -> 20(3)n8 = [785] Also 26(4)n7 = {4679} with r8c3 from (49) Also 22(4)n8 = [{149}8] with r8c6 from (49) 7. (27) already in c6 and 1 already in r4c9 -> 9(2)r4 from {36} or {45} r4c4 from (69) and r4c5 from (78) -> 17(3)r3c4 from [197], [368], [467] The first of these -> r6c56 = [83] -> In all cases 9(2)r4 can only be {45} 8. 8 in n5 in r46c5 and 3 in n5 in r56c6 -> 11(2)r6 cannot be {38} Remaining Innies r6 -> r6c29 = +9(2) (No 9) -> 9 either in 11(2)r6c3 = {29} or 13(2)r6 = {49} -> 11(2)r6 cannot be {47} -> 11(2)r6c3 from {29} or [56] 9. 5 in r7c9 prevents H9(2)r6c29 = [45] -> 4 in n4 in r5c123 -> 4 in n5 only in r46c6 -> 22(4)n8 = [9418] -> 26(4)n7 = [4{679}] -> 4 in n4 in r5c12 -> 31(6) = {2349(58|67)} 10. Innies n1 = r1c3 + r23c1 = +17(3) Innies - Outies n2 -> r1c3 = r3c4 + 4 Since r3c4 from (134) -> r1c3 from (578) But r1c3 = 7 -> r23c1 = +10(2) for which there is no solution -> r1c3 from (58) -> r3c4 from (14) -> 17(3)r3c4 from [197] or [467] -> r4c5 = 7 -> 13(3)r6c5 = [832] (This next step is essentially Ed's Step 19a). 11! 5 in r6 only in r6c23 r1c3 from (58) If r1c3 = 5 puts 5 in r6c2 If r1c3 = 8 puts 17(3)r3c4 = [467] -> 5 not in r6c3 Either way r6c2 = 5 12. -> r6c9 = 4 -> 9(2)r4 = [45] Also 13(2)n6 = {67} -> 11(2)r6 = {29} Also r8c12 = [52] Also -> 31(6) = {234589} -> r5c2 = 8 -> r5c1 = 4 -> r234c1 = {239} -> Innies n1 can only be r1c3 = 5, r23c1 = {39} -> r4c1 = 2 and r3c4 = 1 -> r4c4 = 9 -> 11(2)r6 = [92] -> r5c456 = [615] Also 6(2)n1 = [42] etc. |
Author: | Andrew [ Mon Feb 04, 2019 5:59 am ] |
Post subject: | Re: Assassin 364 |
Another Assassin which I'd skipped over at the time and had just started when I saw that A369 had been posted, so I continued with it. As wellbeback said, it kept giving, well at least for a while. Thanks Ed for pointing out a flawed step and hinting at an alternative way to get the same result. Here's my walkthrough for Assassin 364: Prelims a) R23C5 = {59/68} b) R3C23 = {15/24} c) R3C78 = {18/27/36/45}, no 9 d) R4C67 = {18/27/36/45}, no 9 e) R6C34 = {29/38/47/56}, no 1 f) R6C78 = {49/58/67}, no 1,2,3 g) R7C23 = {13} h) R78C5 = {18/27/36/45}, no 9 i) R7C78 = {49/58/67}, no 1,2,3 j) 21(3) cage at R1C6 = {489/579/678}, no 1,2,3 k) 20(3) cage at R7C4 = {389/479/569/578}, no 1,2 l) 14(4) cage at R1C3 = {1238/1247/1256/1346/2345}, no 9 m) 13(4) cage at R8C7 = {1237/1246/1345}, no 8,9 n) 26(4) cage at R8C3 = {2789/3689/4589/4679/5678}, no 1 Steps Resulting From Prelims and Immediate Placements 1a. Naked pair {13} in R7C23, locked for R7 and N7, clean-up: no 6,8 in R8C5 1b. R3C78 = {18/27/36} (cannot be {45} which clashes with R3C23), no 4,5 1c. 13(4) cage at R8C7 = {1237/1246/1345}, 1 locked for N9 1d. 45 rule on N3 1 outie R4C9 = 1 -> R2C89 + R3C9 = 20 = {389/479/569/578}, no 2, clean-up: no 8 in R4C67 1e. 45 rule on N7 1 outie R6C1 = 1 2. 45 rule on N8 1 outie R9C7 = 1 innie R7C6 + 6 -> R7C6 = 2, R9C7 = 8, clean-up: no 1 in R3C8, no 7 in R4C7, no 5 in R6C8, no 7 in R78C5, no 5 in R7C78 2a. R7C6 = 2 -> R6C56 = 11 = {38/47/56}, no 9 2b. 45 rule on N9 2 remaining innies R78C9 = 11 = [56/65/92] (cannot be {47} which clashes with R7C78), no 4,7, no 3,9 in R8C9 2c. 13(4) cage at R8C7 = {1237/1345} (cannot be {1246} which clashes with R78C9), no 6 2d. 9 in N9 only in R7C789, locked for R7 2e. 45 rule on R6 2 remaining innies R6C29 = 9 = {27/36/45}, no 8,9 2f. 9 in R6 only in R6C34 = {29} or R6C78 = {49} -> R6C34 = {29/38/56} (cannot be {47} locking-out cages), no 4,7 [2 in R6 only in R6C29 and R6C34 would give the same elimination.] 3a. 45 rule on N2 4 innies R1C45 + R23C4 = 10 = {1234}, 4 locked for N2 3b. 45 rule on N2 1 outie R1C3 = 1 innie R3C4 + 4 -> R1C3 = {5678} 3c. 7 in N2 only in 21(3) cage at R1C6, locked for C6, clean-up: no 2 in R4C7, no 4 in R6C5 (step 2a) 3d. 17(3) cage at R3C4 can only contain one of 1,2,3,4 -> no 2,3,4 in R4C45 4. 45 rule on R1 3 innies R1C126 = 2 outies R2C47 + 15 4a. Max R1C126 = 24 -> max R2C47 = 9, no 9 in R2C7 5. 16(4) cage at R1C7 = {1249/1258/1348/1456/2347/2356} (cannot be {1267/1357} which clash with R3C78) 5a. 7 on {2347} must be in R1C789 (R1C789 cannot be {234} which clash with R1C45, ALS block), no 7 in R2C7 6. 26(4) cage at R8C3 = {2789/4589/4679/5678} 6a. 8 of {2789/4589/5678} must be in R8C3 -> no 2,5 in R8C3 7. R23C5 = {59/68}, R78C5 = {45}/[63/81] -> combined cage = {59}[63]/{59}[81]/{68}{45}, 5 locked for C5, clean-up: no 6 in R6C6 (step 2a) 7a. 22(4) cage at R8C6 = {1489/1678/3478/3568} 7b. 7 of {3478} must be in R9C5, 6 of {3568} must be in R9C5 (R89C6 cannot be {56} which clashes with 21(3) cage at R1C6), no 3 in R9C5 7c. 22(4) cage = {1489/1678/3478} (cannot be {3568} because R89C6 = {35} clashes with 21(3) cage at R1C6 + R46C6, killer ALS block), no 5 in R89C6 7d. Consider combinations for R23C5 = {59/68} R23C5 = {59} => 21(3) cage at R1C6 = {678}, 6,8 locked for C6, R4C6 = {345}, R6C6 = {345} => R89C6 cannot be {34}, ALS block or R23C5 = {68}, locked for C5 => R78C5 = {45}, 4 locked for N8 -> 22(4) cage = {1489/1678} (cannot be {3478}), no 3 in R89C6, 1 locked for N8, clean-up: no 8 in R7C5 [My original step 7d was flawed. Thanks Ed for suggesting an alternative way, which I’ve rewritten in my solving style.] 7e. 3 in C6 only in R456C6, locked for N5, clean-up: no 8 in R6C3, no 8 in R6C6 (step 2a) 7f. Killer pair 5,6 in R23C5 and R78C5, locked for C5, clean-up: no 5 in R6C6 (step 2a) 7g. 8 in N8 only in 20(3) cage at R7C4, locked for C4, clean-up: no 3 in R6C3 7h. 20(3) cage = {389/578}, no 4,6 7i. Killer triple 7,8,9 in R23C5, R4C5 and R6C5, locked for C5 7j. 22(4) cage = {1489} (only remaining combination), 4,9 locked for N8, clean-up: no 5 in R78C5 7k. R78C6 = [63], clean-up: no 8 in R23C5, no 7 in R7C78, no 5 in R8C9 (step 2b) 7l. Naked pair {59} in R23C5, locked for C5 and N2 7m. Naked triple {678} in 21(3) cage at R1C6, 6,8 locked for C6, clean-up: no 3 in R4C7 7n. Naked triple {578} in 20(3) cage at R7C4, 5,7 locked for C4, clean-up: no 6 in R6C3 7o. 9 in C4 only in R456C4, locked for N5 7p. Naked pair {49} in R7C78, locked for R7 and N9, clean-up: no 2 in R8C9 (step 2b) 7q. R78C9 = [56], clean-up: no 3,4 in R6C2 (step 2e) 7r. 16(4) cage at R6C1 = {1258} (only possible combination, cannot be {1249} because R7C1 doesn’t contain 4,9) -> R7C1 = 8, R8C12 = {25}, locked for R8 and N7 7s. Naked pair {17} in R8C78, locked for R8 and N9 7t. R2C89 + R3C9 (step 1d) = {389/479/578} (cannot be {569} because 5,6 only in R2C8), no 6 [Note. There is now the Unique Rectangle elimination R6C78 cannot be {49} because R7C78 = {49} but I don’t use that type of step since it doesn’t fully solve a puzzle.] 8. 17(3) cage at R3C4 = [197/368/467] (cannot be {269} because no 7,8 in R4C5, cannot be {278} because no 7,8 in R4C4), no 2 in R3C4, clean-up: no 6 in R1C3 (step 3b) 8a. Consider permutations for 17(3) cage 17(3) cage = [179] => R6C5 = 8, R6C6 = 3 (cage sum) => R4C67 = {45} (only remaining combination) or 17(3) cage = [368/467] => R4C67 = {45} (only remaining combination) -> R4C67 = {45}, locked for R4 [This proved to be a key step.] 8b. 4 in N4 only in R5C123, locked for R5 8c. 4 in N5 only in R46C6, locked for C6 -> R89C6 = [91], R9C5 = 4, R8C3 = 4, clean-up: no 2 in R3C2 8d. 4 in N4 only in R5C12, locked for 31(6) cage at R2C1, no 4 in R23C1 9. 45 rule on N1 3 innies R1C3 + R23C1 = 17 = {278/359/368} (cannot be {269} because R1C3 only contains 5,7,8) 9a. 5 of {359} must be in R1C3 -> no 5 in R23C1 9b. 8 of {278} must be in R1C3 -> no 7 in R1C3, clean-up: no 3 in R3C4 (step 3b) 9c. 17(3) cage at R3C4 (step 8) = [197/467] -> R4C5 = 7, R6C5 = 8, R6C6 = 3 (cage sum), R5C6 = 5, R4C67 = [45], clean-up: no 6 in R6C2 (step 2e) 9d. Killer pair 1,4 in R3C23 and R3C4, locked for R3, clean-up: no 8 in R3C8 9e. Killer pair 3,7 in R2C89 + R3C9 (step 7t) and R3C78, locked for N3 9f. 1 in N3 only in 16(4) cage at R1C7 (step 5) = {1249/1456} (cannot be {1258} which clashes with R1C3), no 8, 4 locked for N3 9g. 5 of {1456} must be in R1C8 -> no 6 in R1C8 9h. R2C89 + R3C9 (step 7t) = {389/578} 9i. 5 of {578} must be in R2C8 -> no 7 in R2C8 10. 1,5 in R5 only in 22(5) cage at R5C3 = {12568/13567}, no 9, 6 locked for R5 10a. 8 of {12568} only in R5C3 -> no 2 in R5C3 11. R1C3 + R23C1 (step 9) = {278/359/368} 11a. 4 in N4 only in 31(6) cage at R2C1 = {234589/234679} 11b. {234589} only has one of 2,7, {234679} must have one of 2,7 in R6C2 so cannot have both in R23C1 -> R1C3 + R23C1 = {359/368} (cannot be {278} because cannot have both of 2,7 in R23C1), no 2,7, 3 locked for N1 and 31(6) cage, no 3 in R45C1 + R5C2 [Cracked.] 11c. 31(6) cage = {234589/234679}, 2 locked for N4, clean-up: no 9 in R6C4 11d. R4C4 = 9 (hidden single in N5) -> R3C4 = 1 (cage sum), R1C5 = 2, R1C3 = 5 (step 3b), R3C23 = [42], R6C3 = 9 -> R6C4 = 2, clean-up: no 7 in R3C78, no 4 in R6C78 [Removing any need for the Unique Rectangle.] 11e. Naked pair {67} in R6C78, locked for R6 and N6 -> R16C9 = [94] 11f. Naked pair {36} in R3C78, locked for R3 and N3 11g. Naked pair {78} in R23C9, 8 locked for C9 and N3 -> R2C8 = 5 11h. Naked pair {14} in R1C78, locked for R1 and N3 -> R2C7 = 2 11i. R5C4567 = [6153] -> R5C3 = 7 (cage sum) and the rest is naked singles. Rating Comment: I'll rate my WT for A364 at Easy 1.5 because I used a locking-out cages step and a couple of forcing chains. I wasn't sure how to rate my final breakthrough in step 11b, but not any higher. |
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