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Assassin 384 http://www.rcbroughton.co.uk/sudoku/forum/viewtopic.php?f=3&t=1511 |
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Author: | Ed [ Sun Sep 15, 2019 8:03 am ] |
Post subject: | Assassin 384 |
Attachment: a384.JPG [ 64.65 KiB | Viewed 6885 times ] triple click code: 3x3::k:4864:4864:3073:3073:2562:2562:2307:6148:6148:2053:4864:4864:5126:5126:5126:2307:6148:6148:2053:2823:0000:2825:5126:5126:8458:8458:8458:2053:2823:0000:2825:4619:4619:4619:8458:2316:4365:0000:0000:7694:7694:2831:8458:8458:2316:4365:3344:7694:7694:7694:2831:2831:4625:4625:4365:3344:0000:7694:5395:5395:2324:4625:4625:2581:2581:0000:5395:3350:3350:2324:2583:2583:2840:2840:2840:5395:5395:3858:3858:2056:2056: solution: Code: +-------+-------+-------+ | 7 3 4 | 8 9 1 | 2 6 5 | | 5 8 1 | 6 2 3 | 7 9 4 | | 2 9 6 | 7 4 5 | 3 8 1 | +-------+-------+-------+ | 1 2 9 | 4 3 7 | 8 5 6 | | 8 4 5 | 1 6 2 | 9 7 3 | | 3 6 7 | 9 5 8 | 1 4 2 | +-------+-------+-------+ | 6 7 8 | 2 1 4 | 5 3 9 | | 9 1 3 | 5 7 6 | 4 2 8 | | 4 5 2 | 3 8 9 | 6 1 7 | +-------+-------+-------+ Cheers Ed |
Author: | wellbeback [ Sun Sep 22, 2019 1:06 am ] |
Post subject: | Re: Assassin 384 |
Thanks Ed! Happy to find a couple of moves early on which cracked it for me. Not too difficult this one and quite a short solution path. Assassin 384 WT: 1. Outies n9 -> r6c8 + r6c9 + r9c6 = +15(3) Since r9c6 from (6789) -> r6c89 between +6 and +9 -> 9 not in r6c89 Innies n36 = r46c7 + r6c89 = +15(4) Since r6c89 between +6 and +9 -> r46c7 between +6 and +9 -> 9 not in r46c7 -> 9 in 33(6) in n6 -> Outies n3 = r4c8 + r5c78 = +21(3) = {489} or {579} 2! Outies c89 = r35c7 = +12(2) (Regardless of whether outies n3 = {489} or {579}) -> r35c7 = [39] -> Remaining cells in 33(6) (r3c89 and r45c8) are [{18}{57}] or [{27}{48}] 3. Innies n2 = r13c4 = +15(2) -> 12(2)r1 and 11(2)c4 from [57][83] or [48][74] or [39][65] 4! Outies r12 = r3c156 + r4c1 = +12(4) Since 3 and one of (12) already in r3 and since r3c1 is max 5 -> Only solutions are: For r3c789 = [3{18}] (A) r3c156,r4c1 = [{245}1] For r3c789 = [3{27}] (B) r3c156,r4c1 = [{145}2] (C) r3c156,r4c1 = [4{16}1] But (C) is impossible since that puts r13c4 = [78] which leaves no solution for 10(2)n2. 5. (Edited to make clearer hopefully) Step 4(A) has 8 already in r3 so puts r3c4 from (67) -> r1c4 from (98) -> r1c3 from (34) -> 8(3)c1 = [{25}1] Step 4(B) -> 8(3)c1 = [{15}2] -> In both cases 8(3)c1 = {125} 6! Cracked Innies c1 = r189c1 = +20(3) doesn't have a 5 -> Must have a 9 9 in r3 only in r3c23 -> HS 9 in c1 -> r8c1 = 9 7. Basically all singles from here -> 10(2)n7 = [91] Since Innies r9 = r9c45 = +11(2) -> (HS 1 in r9) 8(2)r9 = {17} -> 15(2)r9 = [96] -> r9c45 = {38} -> 11(3)n7 = [4{25}] Also 10(2)n9 = {28} -> 9(2)n9 = {45} -> r7c89 = {39} Also 13(2)n8 = {67} Also Innies n8 -> r7c4 = 2 -> 21(5)n8 = [{145}{38}] with 1 in r7c56 Also NS r8c3 = 3 Also Innies c1 -> r1c1 = 7 -> 12(2)r1 can only be [48] -> 11(2)c4 = [74] -> r3c789 = [3{18}] -> r45c8 = {57} etc. |
Author: | Andrew [ Wed Sep 25, 2019 5:02 am ] |
Post subject: | Re: Assassin 384 |
Thanks Ed for your latest Assassin. I found it a very challenging puzzle and it took me a long time to solve it. It took me a long time to reach the 'early' placements, partly because I missed the key part of wellbeback's step 2 and Ed's step 4. Here is my walkthrough for Assassin 384: Prelims a) R1C34 = {39/48/57}, no 1,2,6 b) R1C56 = {19/28/37/46}, no 5 c) R12C7 = {18/27/36/45}, no 9 d) R34C2 = {29/38/47/56}, no 1 e) R45C9 = {18/27/36/45}, no 9 f) R67C2 = {49/58/67}, no 1,2,3 g) R78C7 = {18/27/36/45}, no 9 h) R8C12 = {19/28/37/46}, no 5 i) R8C56 = {49/58/67}, no 1,2,3 j) R8C89 = {19/28/37/46}, no 5 k) R9C67 = {69/78} l) R9C89 = {17/26/35}, no 4,8,9 m) 8(3) cage at R2C1 = {125/134} n) 11(3) cage at R5C6 = {128/137/146/236/245}, no 9 o) 11(3) cage at R9C1 = {128/137/146/236/245}, no 9 1a. 8(3) cage at R2C1 = {125/134}, 1 locked for C1, clean-up: no 9 in R8C2 1b. 45 rule on C1 3 innies R189C1 = 20 = {389/479/569/578}, no 2, clean-up: no 8 in R8C2 2. 45 rule on N2 2 innies R13C4 = 15 = [78/87/96] -> R1C3 = {345}, R4C4 = {345} 3a. 45 rule on N3 3 outies R4C8 + R5C78 = 21 = {489/579/678}, no 1,2,3 3b. 45 rule on C89 2 outies R35C7 = 12 = [39]/{48/57}, no 1,2,6, no 9 in R3C7 4. 45 rule on N8 2 innies R7C4 + R9C6 = 11 = [29/38/47/56] 5. 45 rule on C456789 2 outies R16C3 = 11 = [38/47/56] 6a. 45 rule on R9 2 innies R9C45 = 11 = {29/38/47/56}, no 1 6b. 45 rule on R9 3 outies R7C56 + R8C4 must contain 1 for N8 = 10 = {127/136/145}, no 8,9 6c. 9 in R9 only in R9C45 = {29} or R9C67 = {69} -> R9C45 = {29/38/47} (cannot be {56}, locking-out cages), no 5,6 6d. Hidden killer pair 1,5 in 11(3) cage at R9C1 and R9C89 for R9, neither can contain both of 1,5 -> 11(3) cage at R9C1 = {128/137/146/245}, R9C89 = {17/35}, no 2,6 [Alternatively R9C89 = {26} clashes with R9C45 = {29} or R9C67 = {69}.] 6e. R8C89 = {19/28/46} (cannot be {37} which clashes with R9C89), no 3,7 6f. 11(3) cage at R9C1 = {128/146/245} (cannot be {137} which clashes with R9C89), no 3,7 6g. 8 of {128} must be in R9C1 -> no 8 in R9C23 7a. 45 rule on C789 3 innies R469C7 = 15 7b. Min R69C7 = 7 -> max R4C7 = 8 7c. 45 rule on N9 2 outies R6C89 = 1 innie R9C7 7d. Max R6C89 = 9, no 9 in R6C89 7e. 9 in N6 only in R4C8 + R5C78, locked for 33(6) cage at R3C7 7f. R4C8 + R5C78 (step 3a) contains 9 = {489/579}, no 6 [Oops! At this stage I missed R35C7 cannot be {48/57} which clash with R4C8 + R5C78 = {489/579}. To express this another way, the 12+9 in R4C8 + R5C78 cannot be the same 12 that are in R35C7 because of the overlap at R5C7. If I’d eliminated the other 9s from N6 earlier, as wellbeback and Ed did, I might have then spotted it when I found step 3b. It would have simplified things, including the time I spent trying to find a nice way to do step 11.] 7g. R45C9 = {18/27/36} (cannot be {45} which clash with R4C8 + R5C78), no 4,5 7h. 45 rule on N3 3 innies R3C789 = 12 = {138/156/237/246} (cannot be {147/345} which clash with R4C8 + R5C78) 7i. R12C7 = {18/27/45} (cannot be {36} which clashes with R3C789), no 3,6 8. 45 rule on R12 2 outies R3C56 = 1 innie R2C1 + 4 8a. Max R2C1 = 5 -> max R3C56 = 9, no 9 in R3C56 8b. 9 in R3 only in R3C23, locked for N1 8c. R189C1 (step 1b) = {389/479/569/578} 8d. 9 of {389/479/569} must be in R8C1 -> no 3,4,6 in R8C1, clean-up: no 4,6,7 in R8C2 8e. 4 of {479} must be in R9C1 -> no 4 in R1C1 9. 11(3) cage at R9C1 (step 6f) = {128/146/245} 9a. Consider combinations for R189C1 (step 1b) = {389/479/569/578} R189C1 = {389/479/569} => R8C1 = 9, R8C2 = 1 => 11(3) cage = {245} or R189C1 = {578} => R9C1 = {58} => 11(3) cage = {128/245} -> 11(3) cage = {128/245}, no 6, 2 locked for R9 and N7, clean-up: no 8 in R8C1 9b. 6 in R9 only in R9C67 = {69}, 9 locked for R9, clean-up: no 3,4 in R7C4 (step 4) 10. R469C7 = 15 (step 7a) = {159/168/249/267/456} (cannot be {258/348/357} because R9C7 only contains 6,9), no 3 10a. 6 of {168/267/456} must be in R9C7 -> no 6 in R46C7 10b. 6 in C7 only in R789C7, locked for N9, clean-up: no 4 in R8C89 10c. Killer triple 7,8,9 in R8C1, R8C56 and R8C89, locked for R8, clean-up: no 1,2 in R7C7 [The best way I could find for this step, even though it’s not a pure forcing chain.] 11. R7C4 + R9C6 (step 4) = [29/56] 11a. Consider combinations for R8C56 = {49/58/67} R8C56 = {49}, 9 locked for N8 => R9C56 = [69], 6 in C7 only in R78C7 = {36}, 3 locked for N9, R9C89 = {17} => R7C89 = {45} (hidden pair in N9), 5 locked for R7 => R7C4 = 2 or R8C56 = {58/67} => R7C4 + R9C6 = [29] (cannot be [56] which clashes with R8C56) -> R7C4 + R9C6 = [29] -> R9C7 = 6, clean-up: no 1 in R1C5, no 4 in R8C56, no 3 in R78C7 11b. R35C7 = [39] (hidden pair in C7), clean-up: no 8 in R4C2 11c. R3C7 = 3 -> R3C789 (step 7h) = {138/237}, no 4,5,6 11d. 33(6) cage at R3C7 = {138}{579}/{237}{489}, CPE no 7,8 in R12C8 11e. 45 rule on N9 2 remaining innies R7C89 = 12 = {39/48} (cannot be {57} which clashes with R9C89), no 1,5,7 11f. 45 rule on N9 2 remaining outies R6C89 = 6 = {15/24} 11g. Killer pair 4,5 in R45C8 and R6C89, locked for N6 11h. 4 in N6 only in R45C8 + R6C89, CPE no 4 in R7C8, clean-up: no 8 in R7C9 [With hindsight, step 14 would follow from here.] 11i. R45C9 = {36} (hidden pair in N6), locked for C9, clean-up: no 9 in R7C8, no 5 in R9C8 11j. R7C56 + R8C4 (step 6b) = {136/145}, no 7 11k. 9 in R8 only in R8C12 = [91] or R8C89 = {19}, 1 locked for R8 (locking cages), clean-up: no 8 in R7C7 11l. 1 in N8 only in R7C56, locked for R7 12. R189C1 (step 1b) = {389/479/569/578} 12a. Consider combinations for 11(3) cage at R9C1 (step 9a) = {128/245} 11(3) cage = {128} = 8{12}, 1 locked for N7 => R8C12 = [73] => R189C1 = [578] or 11(3) cage = {245}, R9C1 = {45} => R189C1 = {479/569/578} -> R189C1 = {479/569/578}, no 3 12b. Killer pair 4,5 in R189C1 and 8(3) cage at R2C1, locked for C1 13. R469C7 = 15 (step 7a), R9C7 = 6 -> R46C7 = 9 = {18/27} 13a. Consider combinations for R3C89 (step 11c) = {18/27} R3C89 = {18} or R3C89 = {27}, 7 locked for 33(6) cage at R3C7 => 7 in N6 only in R46C7 = {27} => R12C7 = {18} (hidden pair in C7) -> 1,8 in R12C7 + R3C89, locked for N3 14. R4C8 + R5C78 (step 3a) = {489/579} -> R45C8 = {48/57}, R6C89 (step 11f) = {15/24}, R7C89 (step 11e) = [39/84] 14a. 18(4) cage at R6C8 = {15}[39]/{24}[39] (cannot be {15}[84] which clashes with R45C8) -> R7C89 = [39], clean-up: no 4 in R6C2, no 1 in R8C89, no 5 in R9C9 [Cracked, at last. The rest is straightforward.] 14b. Naked pair {28} in R8C89, locked for R8, clean-up: no 5 in R8C56 14c. Naked pair {17} in R9C89, locked for R9, 7 locked for N9 14d. 11(3) cage at R9C1 = {245} (only remaining combination), 4,5 locked for N7, 4 locked for R9, clean-up: no 8,9 in R6C2 14e. Naked pair {67} in R8C56, locked for R8, 6 locked for N8 -> R8C123 = [913], clean-up: no 9 in R1C4 14f. R13C4 (step 2) = 15 = {78}, locked for C4 and N2 -> R9C45 = [38], clean-up: no 2,3 in R1C56 14g. R34C4 = 11 = [74], R1C4 = 8 -> R1C3 = 4, R8C4 = 5, R78C7 = [54], clean-up: no 6 in R1C56, no 2 in R3C89 (step 11f), no 7 in R4C2 14h. R1C56 = [91], R7C56 = [14], R256C4 = [619] 14i. Naked pair {18} in R3C89, locked for R3 and N3, 8 locked for 33(6) cage at R3C7, clean-up: no 3 in R4C2 14j. Naked pair {27} in R12C7, locked for C7 and N3 14k. Naked pair {25} in R3C16, locked for R3 -> R3C5 = 4, clean-up: no 6,9 in R4C2 14l. R45C8 = 12 = {57}, locked for C8, 5 locked for N6 14m. 8(3) cage at R2C1 = {125} (only remaining combination), 2,5 locked for C1 14n. 17(3) cage at R5C1 = {368} (only remaining combination), 6 locked for C1, 3 locked for N4 14o. R1C1 = 7, R1C2 = 3 (hidden single in R1) -> R2C23 = 9 = [81], clean-up: no 5 in R6C2 14p. R4C1 = 1 (hidden single in C1) -> R46C7 = [81] 14q. R4C7 = 8 -> R4C56 = 10 = {37}, locked for R4 and N5 14r. Naked pair {56} in R56C5, locked for C5 and N5 14s. R1C3 = 4 -> R6C3 = 7 (step 5), R6C2 = 6, R3C2 = 9 -> R4C2 = 2 and the rest is naked singles. Rating Comment: I'll rate my walkthrough for A384 at Hard 1.5. |
Author: | Ed [ Sat Sep 28, 2019 2:12 am ] |
Post subject: | Re: Assassin 384 |
3 very different experiences with this puzzle! Huge shortcut by wellbeback. I would only look for that sort of step when really stuck. Didn't need it for this one. My steps 4 (same as wellbeback's step 2) & 6 got me hooked on this puzzle. Step 18 is my final cracker. a384 WT: Preliminaries Cage 15(2) n89 - cells only uses 6789 Cage 8(2) n9 - cells do not use 489 Cage 12(2) n12 - cells do not use 126 Cage 13(2) n47 - cells do not use 123 Cage 13(2) n8 - cells do not use 123 Cage 9(2) n9 - cells do not use 9 Cage 9(2) n3 - cells do not use 9 Cage 9(2) n6 - cells do not use 9 Cage 10(2) n9 - cells do not use 5 Cage 10(2) n7 - cells do not use 5 Cage 10(2) n2 - cells do not use 5 Cage 11(2) n14 - cells do not use 1 Cage 11(2) n25 - cells do not use 1 Cage 8(3) n14 - cells do not use 6789 Cage 11(3) n7 - cells do not use 9 Cage 11(3) n56 - cells do not use 9 1. "45" on n9: 2 outies r6c89 = 1 innie r9c7 1a. -> no 9 in r6c89 2. "45" on c789: 3 innies r469c7 = 15 2a. min. r69c7 = 7 -> max r4c7 = 8 3. "45" on n3: 3 outies r45c8 + r5c7 = 21 and must have 9 for n6 3a. = {489/579}(no 1,2,3,6) 3b. 9 locked for 33(6) cage 4. "45" on c89: 2 outies r35c7 = 12 4a. but {48/57} both blocked by clash with {48/57} in h21(3)n6 (step 3a)(combo crossover clash CCC) 4b. = [39] only permutation 4c. no 6 in the two 9(2) cages in c7 5. r3c7 = 3 -> from "45" on n3: r3c89 = 9 5a. but cannot be {45} because r45c8 = 4 or 5 (same cage) 5b. = {18/27}(no 4,5,6) 6. 9(2)n6 sees one cell of the h9(2)r3c89 -> they must have different combinations 6a. -> {18/27} blocked from 9(2)n6 since r45c8 needs one of 7 or 8 (same cage as h9(2)) 6b. {45} also blocked by r45c8 = 4 or 5 6c. 9(3)n6 = {36} only: both locked for n6 and c9 7. r9c7 = 6 (hsingle c7), r9c6 = 9 7a. one remaining innie n8 -> r7c4 = 2 8. "45" on n2: 2 innies r13c4 = 15 = [96/87/78] 8a. r1c3 = (345) 9. "45" on r12: 1 innie r2c1 + 4 = 2 outies r3c56 9a. max. r2c1 = 5 -> max. r3c56 = 9 (no 9) 10. 9 in r3 only in n1: locked for n1 11. hidden killer triple 678 in n1: r3c23 can have at most one of 6,7,8 (since 9 must be there) -> 19(4)n1 must have at least 2 of 6,7,8 11a. = {1378/1468/1567/2368/2467} 11b. can't have more than two of 6,7,8 -> r3c23 must have one off -> r3c23 from {6789} 11c. -> killer triple 6,7,8 in r3 with r3c489: locked for r3 12. hidden killer triple 3,4,5 in n1: 19(4) must have exactly one of 3,4,5 (step 11a), r1c3 has one -> r23c1 must have exactly one of 3,4,5 12a. 8(3)n1 = {125/134} ->r23c1 = {15/25/14}/[31] = 1 or 5 (other permutations don't have one of 3,4,5) 12b. 1 must be in 8(3): locked for c1 13. 19(4)n1: {1567} blocked by r23c1 = 1 or 5 13a. = {1378/1468/2368/2467}(no 5) 14. 8(2)n9 = {17}[35](no 2) = 1 or 3 14a. 11(3)n7: must have 2 for r9 14b. = {128/245}(no 3,7) 14c. 2 locked for n7 15. "45" on r9: 2 innies r9c45 = 11 = {38/47}(no 1,5) 15a. r9c45 = 11 -> r7c56 + r8c4 = 10 = {136/145}(no 7,8) 16. 10(2)n7 = [91]{37/46}(no 8, no 9 in r8c2) 17. "45" on c1: 3 innies r189c1 = 20 = {389/479/569/578}(no 2) Final cracker step 18. 7 in n8 in r89 -> 10(2)n7 and 8(2)n9 cannot be {37}+{17} 18a. -> r89c1 <> [75] 18b. -> h20(3)c1: {578} as [875] only permutation is blocked 18c. h20(3)c1 = {389/479/569} 18d. must have 9 -> r8c1 = 9, r8c2 = 1 19. 11(3)n7 = {245} only: 4 & 5 locked for n7 and r9 19a. -> h20(3)c1 must have 4 or 5 = {479/569}(no 3) 19b. r1c1 = (67) 20. killer pair 4,5 in c1 between 8(3) and r9c1: both locked for c1 21. 8(2)n9 = {17} only: both locked for n9, 7 for r9 22. 10(2)n9 = {28} only: 8 locked for n9 and r8 23. 9(2)n9 = {45}: both locked for c7 and n9 23a. r7c89 = [39] 23b. r7c89 = 12 -> r6c89 = 6 = {15/24}(no 7,8) 24. naked triple {678} in r7c123: 6,7 locked for n7, 6 for r7 24a. r8c3 = 3 24b. no 9 in r1c4 25. 13(2)n8 = {67}: 6 locked for n8 26. "45" on n2: 2 innies r13c4 = 15 = {78} only: both locked for c4 and n2 26a. r9c45 = [38] 27. r34c4 = [74] only permutation 27a. r1c34 = [48] 27b. r8c4 = 5, r78c7 = [54] 28. 10(2)n2 = [91] only permutation 28a. r256c4 = [619] 28b. r7c56 = [14] 29. r12c8 = [69] (both hsingles n3) 29a. r19c1 = [74](h20(3)c1) 29b. r12c7 = [27], r12c9 = [54] (cage sum) 30. naked pair {18} in r3c89: both locked for r3 and 8 for 33(6) cage 30a. -> r45c8 = {57} only: both locked for c8 30b. r6c89 = [42] only permutation h6(2) 31. 18(3)r4c5 must have 1 or 8 for r4c7 = {378} only = {37}[8]: 3 and 7 locked for r4 and n5 31a. r4c8 = 5 32. hidden single 2 in n5 -> r5c6 = 2 33. 11(2)r3c2 = [92] only permutation 34. "45" on c456789: 1 remaining outie r6c3 = 7 easy now Ed |
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