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Assassin 360 http://www.rcbroughton.co.uk/sudoku/forum/viewtopic.php?f=3&t=1458 |
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Author: | Ed [ Mon Oct 01, 2018 7:58 am ] |
Post subject: | Assassin 360 |
Attachment: a360.JPG [ 66.25 KiB | Viewed 9590 times ] Made a Human Solvable for this milestone Assassin. Used one advanced step which I found while doing an earlier version. Post if you want me to put that version here to practice with (SSscore 1.50). The Assassin posted here gives both SS (3.05) and JSudoku (14 chains) a terrible time. Hope there is more than one decent way to crack this one. code: 3x3::k:4352:3073:3073:2050:4099:3332:8965:1542:1542:4352:4352:1287:2050:4099:3332:8965:8965:8965:2824:2824:1287:2569:4099:2314:2314:6155:8965:2572:2572:2572:2569:3610:4877:6155:6155:8965:2575:2575:3856:3856:3610:4877:4877:6155:3858:2579:2579:5908:5908:3610:4877:4877:3858:3858:4118:5908:5908:3099:3099:3607:3096:3096:3096:4118:4118:5913:5913:5913:3607:3096:5653:2833:4118:3342:3342:3342:5913:3607:5653:5653:2833: solution: Code: +-------+-------+-------+ | 2 9 3 | 6 4 8 | 7 1 5 | | 7 8 1 | 2 3 5 | 4 6 9 | | 5 6 4 | 1 9 7 | 2 3 8 | +-------+-------+-------+ | 3 5 2 | 9 7 6 | 8 4 1 | | 6 4 7 | 8 5 1 | 3 9 2 | | 9 1 8 | 3 2 4 | 5 7 6 | +-------+-------+-------+ | 1 7 5 | 4 8 9 | 6 2 3 | | 8 3 9 | 7 6 2 | 1 5 4 | | 4 2 6 | 5 1 3 | 9 8 7 | +-------+-------+-------+ Ed |
Author: | azpaull [ Tue Oct 02, 2018 9:39 pm ] |
Post subject: | Re: Assassin 360 |
Thanks, Ed! I'd love the "practice" version! |
Author: | Ed [ Wed Oct 03, 2018 7:56 am ] |
Post subject: | Re: Assassin 360 |
Attachment: a360Practice.JPG [ 68.4 KiB | Viewed 9581 times ] Its a very nice puzzle this one. Enjoy! Same solution as the V1 above. SSscore 1.50. I don't have a WT for it however. code: 3x3::k:4352:3073:3073:2050:4099:3332:8965:1542:1542:4352:4352:1287:2050:4099:3332:8965:8965:8965:2824:2824:1287:2569:4099:2314:2314:6155:8965:2572:2572:2572:2569:3085:4891:6155:6155:8965:2575:2575:3856:3856:3085:4891:4891:6155:3858:2579:2579:5908:5908:3605:4891:4891:3858:3858:4118:5908:5908:3605:3605:3607:3096:3096:3096:4118:4118:5913:5913:5913:3607:3096:5658:2833:4118:3342:3342:3342:5913:3607:5658:5658:2833: Ed |
Author: | wellbeback [ Fri Oct 05, 2018 12:57 am ] |
Post subject: | Re: Assassin 360 |
Thanks Ed! I'm pretty sure I didn't spot the "Human Solvable" move. But it wasn't as hard as SS and JSudoku suggest. Just a couple of small chains for me . Some corrections & clarifications thanks to Ed Assassin 360 WT: 1. "45"s Innies c5 -> r789c5 = +15(3) -> r789c4 = +16(3) -> Remaining Innies c4 -> r56c4 = +11(2) Innies n4 -> r56c3 = +15(2) -> 5 in n4 in r4c123 Innies n78 -> r7c23 = +12(2) -> r6c34 = +11(2) Innies n2 -> r3c46 = +8(2) Innies n36 -> r356c7 = +10(3) Also Innies - Outies n8 -> r8c3 = r9c4 + 4 -> Max r9c4 = 5 and Min r8c3 = 5. 2. In n1, 1 is either in 5(2) -> 5(2) = {14} or in 17(3) -> 17(3) = {179} -> 11(2)n1 cannot be {47} 3. Only possible configuration in n4 are: A) 10(3) = {145}, 10(2)s = {28},{37}, r56c3 = {69} (->r5c34 = {69}) B) 10(3) = {235}, 10(2)s = {19},{46}, r56c3 = {78} (->r5c34 = {78}) 4! Innies n236 = r3c4 + r5c7 + r6c7 = +9(3) -> Max r3c4 = 6 r3c4 cannot be 5 (in a 10(2)) r3c4 cannot be 4 (since r3c4 + r3c6 = +8(2)) Also 10(2)r3c4 cannot be [37] since that puts 8(2)c4 = {26} which leaves no solution for H+11(2)r56c4. Also r3c4 cannot be 2 since that puts 9(2)r3c6 = [63] which leaves no solution for 11(2)n1. (See Step 2). -> 10(2)r3c4 = [19] or [64] 5! 10(2)r3c4 = [19] or [64] Both of those prevent H+11(2)r56c4 from being [92] since if r56c4 was [92] that would put 10(3)n4 = {145} (See Step 3). -> 1 and 2 in n5 in c56 Since they cannot both go in 14(3)n5 -> at least one of (12) in r456c6 -> Min r56c7 = +4(2) (Innies n236) -> Max r3c4 = 5 -> 10(2)r3c4 = [19]! 6. Continuing... 10(2)r3c4 = [19] -> 9(2)r3c6 = [72] -> 6(2)n3 = {15} -> 12(2)n1 from {84} or {39} -> 11(2)n1 = {56} 7. 8(2)n2 from {26} or [35] -> H+11(2)r56c4 from [83] or [74] -> 15(2)r5c3 = {78} -> H+15(2)r56c3 = {78} -> 10(2) + 10(2) n4 = {19} and {46} -> 10(3)n4 = {235} 8. IOD n3 -> value in r4c9 can only go in n3 in r1c8 or r3c7. I.e., be from (125} -> But (25) already in r4 -> r4c9 = 1 -> 6(2)n3 = [15] Also -> IOD -> r3c8 = 3 Also (Innies n36) -> r56c7 = {35} 9. (123) already in r3 -> 5(2)n1 = [14] -> 11(2)n1 = {39} -> 17(3)n1 = {278} 10. 1 in 19(5) in r56c6 -> 1 in n8 in r89c6 Also 3 in c6 only in r789c6 11. 12(4)n9 has 2 in r7c89 and 1 in r78c7 Since r56c7 = {35} -> one of (35) must be in r7c89. H+11(2)r6c34 from [83] or [74] -> H+12(2)r7c23 from {57} or {39} -> (35) in r7 locked in r7c2389 -> 12(2)n7 = {48} -> r9c4 cannot be 4 -> (IOD) r8c3 cannot be 8. -> 23(4)r8c3 = {1679} 12. Innies c5 -> r789c5 = +15(3). Since 1 in r89c5 and r7c5 from (48) -> r789c5 = [8{16}] -> r8c34 = [97] -> r9c4 = 5 -> 14(3)n8 = {239} etc. |
Author: | Ed [ Sun Oct 07, 2018 7:04 am ] |
Post subject: | Re: Assassin 360 |
Darn, this one was too easy for wellbeback! Well done. Wait till you see what I resorted to (step 6)! Very powerful though and loved finding it. Thanks to wellbeback for some clarifications. a360 WT: Preliminaries courtesy of SudokuSolver Cage 5(2) n1 - cells only uses 1234 Cage 6(2) n3 - cells only uses 1245 Cage 15(2) n45 - cells only uses 6789 Cage 8(2) n2 - cells do not use 489 Cage 12(2) n1 - cells do not use 126 Cage 12(2) n8 - cells do not use 126 Cage 13(2) n2 - cells do not use 123 Cage 9(2) n23 - cells do not use 9 Cage 10(2) n25 - cells do not use 5 Cage 10(2) n4 - cells do not use 5 Cage 10(2) n4 - cells do not use 5 Cage 11(2) n1 - cells do not use 1 Cage 11(2) n9 - cells do not use 1 Cage 22(3) n9 - cells do not use 1234 Cage 10(3) n4 - cells do not use 89 Cage 12(4) n9 - cells do not use 789 No routine clean-up unless stated. 1.{47} blocked from 11(2)n1 by 12(2)n1 + 5(2)n1 (combined cage) 1a. 11(2) = {29/38/56}(no 4,7) = 2/3/6 2. "45" on n36: 3 innies r356c7 = 10 (no 8,9) 2a. no 1 in r3c6 3. "45" on n2, 2 innies r3c46 = 8 (no 4,8,9) = [17]/{26}/[35] 3a. no 7 in r3c4, no 3 in r3c6, no 1,5,6 in r3c7 3b. no 1,2,3,6 in r4c4 4. r3c467 as [263] (combined half-cage) blocked by 11(2)n1 = 2/3/6 4a. no 2 in r3c4, no 6 in r3c6, no 3 in r3c7 4c. no 8 in r4c4 5. "45" on n2: 2 outies r3c7 + r4c4 = 11 = [29/47/74] (no eliminations yet) 5a. "45" on n3: 1 outie r4c9 + 4 = 2 innies r3c78 (no eliminations yet) The big step. Learned this from wellbeback from a354. Hope its correct!! (Note: r3c7 = (247) at the end of step 4) 6. r4c9 sees all of n3 apart from r1c8 + r3c78 -> must repeat there 6a. -> an implied 35(6) cage wholly in n3 6b. -> from "45" on n3, there must also be a 10(3) implied cage in n3 in at least one cell of 6(2) and at least one of r3c78 6c. if the 10(3) covers both cells of the 6(2) -> 4 must be in one of r3c78 -> 6(2) = {15} 6d. if only one of 6(2) is in the 10(3) -> both r3c78 are in i. Can't be 1 from 6(2) cage since r3c78 = 9 blocked by 9(2)r3c6 (Combo Crossover Clash CCC) ii. if 2 from {24} in 6(2) -> r3c78 = 8 = [71] only permutation, but can't be [71] since from innie outie difference (iod) of +4 for n3 (step 5a) and from outies n2 = 11(step 5.), 4 is forced into both r4c49 iii. if 4 in {24} in 6(2) -> r3c78 = 6 = blocked, no permutations possible iv. if 5 from {15} in -> r3c78 = 5 = [23] only 6e. so, all positions for the implied 10(3) have 6(2) = {15} 6f. 6(2)n3 = {15} only: both locked for r1 and n3! 6g. no 7 in 12(2)n1, no 3 in r2c4, no 8 in r2c6 7. 5 & 6 in n1 are both in 11(2) = {56} or both in 17(3), but a 17(3) can't be {566} 7a. -> 11(2) = {56} only: both locked for r3 and n1 7b. h8(2)r3c46 = [17] only, r3c7 = 2, r4c4 = 9 Cracked now, but still quite a bit of work to get to simple. 8. 6 & 7 in n3 only in 35(6) -> no 6,7 in r4c9 9. "45" on n3: 1 remaining innie r3c8 - 2 = 1 remaining outie r4c9 9a. = [31/42] 10. naked pair {34} in r3c38: both locked for r3 11. "45" on n36: 2 remaining innies r56c7 = 8 = {17/35}(no 4,6) 12. "45" on n478: 2 outies r56c4 = 11 12a. but {56} blocked by 8(2)n2 = 5/6 12b. h11(2) = [74/83] 13. 15(2)r5c3 = {78} only: both locked for r5 14. "45" on n4: 2 innies r56c3 = 15 = {78} only: both locked for c3 and n4 14a. no 2,3 in both 10(2) cages in n4 15. 10(3)n4 = {235} only (hidden triple n4) : all locked for r4 15a. r4c9 = 1 -> r3c8 = 3 (iodn3=+2), r1c89 = [15] (so the implied 10(3) cage was the 5 from the 6(2) + r3c78), r23c3 = [14] 16. h8(2)r56c7 = {35} only: both locked for n6, c7 and not in r56c6 16a. 19(5)r4c6 must have 1 which is only in r56c6: 1 locked for n5 and c6 17. 5 in n5 only in c5: 5 locked for c5 18. 12(2)n1 = {39} only: both locked for r1 and n1 19. 8(2)n2 = {26} only: both locked for n2 and c4 20. hidden single 5 in n2 -> r12c6 = [85], r123c5 = [439], r3c9 = 8 21. hidden single 3 in n5 -> r6c4 = 3, r5c4 = 8 (h11(2)), r56c3 = [78] 22. r6c34 = [83] = 11 -> r7c23 = 12 = [75] only permutation, 23. 14(3)r4c5 = [7]{25} only, r56c7 = [35] 24. 7 in n6 only in 15(3) = {267} only: 2,6 locked for n6 25. r567c5 = [528], r7c4 = 4 26. r89c5 = {16} = 7 -> r8c34 = 16 = [97] only 27. hidden single 9 in r7 -> r7c6 = 9 easier now. Ed |
Author: | wellbeback [ Sun Oct 14, 2018 6:26 pm ] |
Post subject: | Re: Assassin 360 |
Excellent Ed! great Step 6 In an earlier version of my WT I used part of that - but had only got as far as: Hidden Text: If 6(2)n3 = {24} then r4c9 must be from 2 or 4. BTW - A361 gave me fits! I got nearly all the way through before I found an impossibility! Twice!! |
Author: | Andrew [ Wed Feb 13, 2019 11:53 pm ] |
Post subject: | Re: Assassin 360 |
I can see that Assassin 360 Practice is a lot easier than A360 because changing 12(2) cage at R4C5 to 14(3) cage at R4C5 takes away several important steps. Don't think that's giving anything away. Here is my walkthrough for Assassin 360 Practice: Prelims a) R1C23 = {39/48/57}, no 1,2,6 b) R12C4 = {17/26/35}, no 4,8,9 c) R12C6 = {49/58/67}, no 1,2,3 d) R1C89 = {15/24} e) R23C3 = {14/23} f) R3C12 = {29/38/47/56}, no 1 g) R34C4 = {19/28/37/46}, no 5 h) R3C67 = {18/27/36/45}, no 9 i) R45C5 = {39/48/57}, no 1,2,6 j) R5C12 = {19/28/37/46}, no 5 k) R5C34 = {69/78} l) R6C12 = {19/28/37/46}, no 5 m) R89C9 = {29/38/47/56}, no 1 n) 10(3) cage at R4C1 = {127/136/145/235}, no 8,9 o) 22(3) cage at R8C8 = {589/679} p) 12(4) cage at R7C7 = {1236/1245}, no 7,8,9 1a. 22(3) cage at R8C8 = {589/679}, 9 locked for N9 1b. 12(4) cage at R7C7 = {1236/1245}, 2 locked for N9 1c. Killer pair 5,6 in 22(3) cage and 12(4) cage, locked for N9 2a. 45 rule on N4 2 innies R56C3 = 15 = {69/78} 2b. 5 in N4 only in 10(3) cage at R4C1, locked for R4, clean-up: no 7 in R5C5 2c. 10(3) cage = {145/235}, no 6,7 2d. 45 rule on N78 3 outies R6C345 = 13 = {139/148/157/238/247/256/346} 2e. R6C3 = {6789} -> no 6,7,8,9 in R6C45 3a. 45 rule on N2 2 innies R3C46 = 8 = {17/26}/[35], no 4,8,9, no 3 in R3C6, clean-up: no 1,5,6 in R3C7, no 1,2,6 in R4C4 3b. 45 rule on N36 3 innies R356C7 = 10 = {127/136/145/235}, no 8,9, clean-up: no 1 in R3C6, no 7 in R3C4, no 3 in R4C4 3c. 4 of {145} must be in R3C7 -> no 4 in R56C7 4. Hidden killer pair 8,9 in 16(3) cage at R1C5 and R12C6 for N2, each can only contain one of 8,9 -> R12C6 = {49/58}, no 6,7 4a. Hidden killer pair 4,8 in 16(3) cage at R1C5 and R12C6 for N2, R12C6 contains one of 4,8 -> 16(3) cage must contain one of 4,8 = {178/268/349/358/457} (cannot be {169/259/367} which don’t contain 4 or 8) 4b. 16(3) cage = {178/268/349} (cannot be {358} which clashes with R45C5, cannot be {457} which clashes with R12C6), no 5 4c. R45C5 = {39}/[75] (cannot be {48} which clashes with 16(3) cage), no 4,8 5. 45 rule on C1234 3(1+2) innies R7C4 + R8C34 = 20 5a. Max R8C34 = 17 -> min R7C4 = 3 5b. Max R78C4 = 17 -> min R8C3 = 3 5c. Max R7C4 + R8C3 = 18 -> min R8C4 = 2 6. 45 rule on N2 2 innies R3C46 (step 3a) = [17/26/35/62] 6a. R3C3467 cannot be {14}[263] which clashes with R3C12 -> no 2 in R3C4, no 6 in R3C6, no 3 in R3C7, clean-up: no 8 in R4C4 6b. R3C12 = {29/38/56} (cannot be {47} which clashes with R3C67), no 4,7 6c. R356C7 (step 3b) = {127/145/235} (cannot be {136} because no 1,3,6 in R3C7), no 6 7. 45 rule on C6 4 innies R3456C6 = 18 = {1269/1278/1467/2349/2358/2367} (cannot be {1359/1458/2457/3456} which clash with R12C6, cannot be {1368} because R3C6 only contains 2,5,7) 7a. 45 rule on N2 1 outie R4C4 = 1 innie R3C6 + 2 7b. R3456C6 = {1269/1278/1467/2349/2367} (cannot be {2358} because 2{358} clashes with R45C5, and cannot be 5{238} because R4C4 + R456C6 = 7{238} clashes with R45C5), no 5 in R356C6, clean-up: no 4 in R3C7, no 7 in R4C4, no 3 in R3C4 7c. Naked pair {27} in R3C67, locked for R3, clean-up: no 3 in R2C3, no 9 in R3C12 7d. R356C7 (step 6b) = {127/235}, 2 locked for C7 7e. R3456C6 = {1269/1278/1467/2367} (cannot be {2349} which clashes with R4C4) 7f. R3456C6 = {1278/1467/2367} (cannot be {1269} = 2{169} which clashes with R356C7 = 7{12}), no 9, 7 locked for C6 7g. 45 rule on N478 3 outies R5C4 + R6C45 = 13 = {139/148/157/238/247/256/346} 7h. 7 of R3456C6 must be in R3C6 (cannot be 2{178} which clashes with R356C7 = 7{12}, cannot be 2{367} because R5C4 + R6C45 cannot contain both of 1,2 for N5 and, for completeness, 7 of {1467} must be in R3C6) -> R3C6 = 7, R3C7 = 2, R3C4 = 1 (step 3a), R4C4 = 9, clean-up: no 4 in R1C89, no 4 in R2C3, no 3 in R45C5, no 6 in R5C3, no 9 in R6C3 (step 2a) [That was the last hard step; almost there.] 7i. R45C5 = [75], clean-up: no 8 in R5C3, no 7 in R6C3 (step 2a), no 3 in R6C7 (step 7d) 7j. Naked pair {15} in R1C89, locked for R1 and N3, clean-up: no 7 in R1C23, no 3 in R2C4, no 8 in R2C6 7k. Killer pair 3,4 in R1C23 and R2C3, locked for N1, clean-up: no 8 in R3C12 7l. Naked pair {56} in R3C12, locked for R3 and N1 7m. 2 in N9 only R7C89, locked for R7 7n. 12(4) cage at R7C7 = {1236/1245} 7o. 6 of {1236} must be in R78C7 (R78C7 cannot be {13} which clashes with R356C7), no 6 in R7C89 7p. 45 rule on N3 1 remaining innie R3C8 = 1 outie R4C9 + 2, no 9 in R3C8, no 3,4,8 in R4C9 7q. 7,9 in N3 only in 35(6) cage at R1C7 = {146789/236789} 7r. 1,2 only in R4C9 -> R4C9 = {12}, R3C8 = {34} 7s. Naked pair {34} in R3C38, locked for R3 7t. Killer pair 1,2 in 10(3) cage at R4C1 and R4C9, locked for R4 7u. R7C4 + R8C34 = 20 (step 5) 7v. Max R78C4 = 15 -> min R8C3 = 5 7w. Max R7C4 + R8C3 = 17 -> min R8C4 = 3 7x. Killer pair 8,9 in R12C6 and R3C5, locked for N2 8. 24(4) cage at R3C8 = {3489/3678} (cannot be {1689/2679} because R3C8 only contains 3,4) -> R5C8 = {79}, 8 locked for R4 and N6 8a. Naked pair {79} in R5C38, locked for R5, clean-up: no 1,3 in R5C12, no 1 in R6C7 (step 7d) 8b. Killer pair 6,8 in R5C12 and R5C4, locked for R5 8c. Killer pair 6,8 in R5C12 and R6C3, locked for N4, clean-up: no 2,4 in R6C12 8d. R5C4 + R6C45 (step 7g) = {148/238/346} 8e. Killer pair 1,3 in R6C12 and R6C45, locked for R6 8f. R356C7 (step 7d) = {127/235} -> R56C7 = [17/35] 8g. 15(3) cage at R5C9 = {249/267/456} (cannot be {159} which clashes with R56C7, cannot be {357} which clashes with R6C7), no 1,3 [Cracked. The rest is fairly straightforward.] 8h. Killer pair 2,4 in R5C12 and R5C9, locked for R5 8i. Naked pair {13} in R5C67, locked for 19(5) cage at R4C6 8j. 19(5) cage at R4C6 contains 1,3 = {12367/13456} (cannot be {12358} because R4C6 only contains 4,6), no 8 8k. R5C4 = 8 (hidden single in N5) -> R5C3 = 7, R6C3 = 8 (hidden single in N4), clean-up: no 4 in R1C2, no 2 in R5C12, no 3 in R6C12 8l. Naked pair {46} in R5C12, locked for R5 and N4 -> R5C9 = 2 8m. Naked pair {19} in R6C12, locked for R6 and N4 8n. R5C9 = 2 -> R6C89 = 13 = {67} (only remaining combination), locked for R6 and N6, R4C9 = 1, R5C8 = 9, R56C7 = [35], R5C6 = 1, R1C89 = [15] 8o. Naked pair {48} in R4C78, locked for R4 and 24(4) cage at R3C8 -> R3C8 = 3, R4C6 = 6, R6C6 = 4 (cage sum), clean-up: no 9 in R12C6, no 2 in R2C3 8p. R12C6 = [85] -> R3C5 = 9, clean-up: no 4 in R1C3, no 3 in R1C4 8q. Naked pair {26} in R12C4, locked for C4 and N2 -> R6C45 = [32] 8r. R23C3 = [14] 8s. Naked pair {39} in R1C23, locked for R1 and N1 -> R12C5 = [43] 8t. R6C5 = 2 -> R7C45 = 12 = [48] 8u. R6C34 = [83] = 11 -> R7C23 = 12 = [75] 8v. R7C89 = [23] = 5 -> R89C7 = 7 = {16}, locked for C7 and N9, clean-up: no 8 in R89C9 8w. Naked pair {47} in R89C9, locked for C9 and N9 8x. Naked pair {58} in R89C8, 8 locked for C8 and N9 8y. R7C4 + R8C34 = 20 (step 5), R7C4 = 4 -> R8C34 = 16 = [97] 8z. R9C4 = 5 -> R9C23 = 8 = {26}, locked for R9 and N7 and the rest is naked singles. Rating Comment: I'll rate my walkthrough for A360 Practice at Hard 1.25; I used a few tricky combination/permutation interactions but no forcing chains this time. |
Author: | Andrew [ Mon Feb 18, 2019 10:31 pm ] |
Post subject: | Re: Assassin 360 |
When I came back to this puzzle, I was pleasantly surprised to find that the practice version had been more helpful than I'd expected, even though the 12(2) cage at R4C5 was no longer available. Step 6a of my practice version, step 4 in the walkthrough below, was one of my key steps. I wonder whether it is a Human Solvable step; none of my other steps could be described as HS. Here is my walkthrough for Assassin 360: Prelims a) R1C23 = {39/48/57}, no 1,2,6 b) R12C4 = {17/26/35}, no 4,8,9 c) R12C6 = {49/58/67}, no 1,2,3 d) R1C89 = {15/24} e) R23C3 = {14/23} f) R3C12 = {29/38/47/56}, no 1 g) R34C4 = {19/28/37/46}, no 5 h) R3C67 = {18/27/36/45}, no 9 i) R5C12 = {19/28/37/46}, no 5 j) R5C34 = {69/78} k) R6C12 = {19/28/37/46}, no 5 l) R7C45 = {39/48/57}, no 1,2,6 m) R89C9 = {29/38/47/56}, no 1 n) 10(3) cage at R4C1 = {127/136/145/235}, no 8,9 o) 22(3) cage at R8C8 = {589/679} p) 12(4) cage at R7C7 = {1236/1245}, no 7,8,9 1a. 22(3) cage at R8C8 = {589/679}, 9 locked for N9 1b. 12(4) cage at R7C7 = {1236/1245}, 2 locked for N9 1c. Killer pair 5,6 in 22(3) cage and 12(4) cage, locked for N9 2a. 45 rule on N4 2 innies R56C3 = 15 = {69/78} 2b. 5 in N4 only in 10(3) cage at R4C1, locked for R4 2c. 10(3) cage = {145/235}, no 6,7 2d. 45 rule on N78 2 outies R6C34 = 11 = [65/74/83/92] 2e. 45 rule on N78 2 innies R7C23 = 12 = {39/48/57}, no 1,2,6 2f. 45 rule on N8 1 outie R8C3 = 1 innie R9C4 + 4 -> R8C3 = {56789}, R9C4 = {12345} 2g. 45 rule on C1234 3(2+1) innies R78C4 + R8C3 = 20, max R7C4 + R8C3 = 18 -> min R8C4 = 2 2h. 45 rule on N2 2 innies R3C46 = 8 = {17/26/}/[35], no 4,8,9, no 3 in R3C6, clean-up: no 1,5,6 in R3C7, no 1,2,6 in R4C4 2i. 45 rule on C789 3 innies R356C7 = 10 = {127/136/145/235}, no 8,9, clean-up: no 1 in R3C6, no 7 in R3C4, no 3 in R4C4 2j. 4 of {145} must be in R3C7 -> no 4 in R56C7 3. Hidden killer pair 8,9 in 16(3) cage at R1C5 and R12C6 for N2, each can only contain one of 8,9 -> R12C6 = {49/58}, no 6,7 3a. Hidden killer pair 4,8 in 16(3) cage at R1C5 and R12C6 for N2, R12C6 contains one of 4,8 -> 16(3) cage must contain one of 4,8 = {178/268/349/358/457} (cannot be {169/259/367} which don’t contain 4 or 8) 3b. 16(3) cage contains of 8,9 = {178/268/349/358} (cannot be {457} which clashes with R12C6 4. R3C3467 cannot be {14}[263] which clashes with R3C12 -> no 2 in R3C4, no 6 in R3C6, no 3 in R3C7, clean-up: no 8 in R4C4 [One of my most important steps, which I found while doing the Practice version.] 4a. R356C7 (step 2i) = {127/145/235} (cannot be {136} because R3C7 only contains 2,4,7), no 6 in R56C7 4b. R3C12 = {29/38/56}, (cannot be {47} which clashes with R3C67), no 4,7 5. 45 rule on C6 4 innies R3456C6 = 18 = {1278/1467/2349/2358/2367} (cannot be {1359/1458/2457/3456} which clash with R12C6, cannot be {1368} because R3C6 only contains 2,5,7, cannot be {1269} = 2{169} because 19(5) cage at R4C6 cannot contain both of 6,9) 5a. 45 rule on N2 1 outie R4C4 = 1 innie R3C6 + 2 5b. R3456C6 = {1278/1467/2358/2367} (cannot be {2349} = 2{349} which clashes with R3C6 + R4C4 = [24]), no 9 6a. 45 rule on C5 3 innies R789C5 = 15 6b. 45 rule on N8 using R789C5 = 15, 3 innies R789C4 = 16 = {178/259/358/457} (cannot be {169} which clashes with R12C4 + R3C4 (killer ALS block), cannot be {349} which clashes with R34C4, cannot be {367} which clashes with R12C4, cannot be {268} = [862] which clashes with R8C3 + R9C4 = [62], step 2f), no 6 6c. Consider combinations for R789C4 R789C4 = {178}, locked for C4 => R34C4 = [64], R12C4 = {35}, locked for C4 or R789C4 = {259/358/457}, 5 locked for C4 -> no 5 in R6C4, clean-up: no 6 in R6C3 (step 2d), no 9 in R5C3 (step 2a), no 6 in R5C4 6d. 6 in C4 only in R123C4, locked for N2 6e. 16(3) cage at R1C5 (step 3b) = {178/349/358}, no 2 7. 45 rule on N478 2 outies R56C4 = 11 = [74/83/92] 7a. Consider placements for 6 in C4 R12C4 = {26}, locked for C4 => R56C4 = [74/83] or R34C4 = [64] => 10(3) cage at R4C1 = {235} (only remaining combination), locked for N4, no 7,8 in R56C12 => R56C3 = {78} (hidden pair in N4) => R5C34 = {78}=> R56C4 = [83] -> R56C4 = [74/83], no 9 in R5C4, no 2 in R6C4, clean-up: no 6 in R5C3, no 9 in R6C3 (step 2a) 7b. Naked pair {78} in R56C3, locked for C3 and N4, clean-up: no 4,5 in R1C2, no 2,3 in R56C12, no 4,5 in R7C2 (step 2e), no 3,4 in R9C4 (step 2f) 7c. 10(3) cage at R4C1 = {235} (hidden triple in N4), locked for R4 7d. R789C4 (step 6b) = {259/358/457} (cannot be {178} which clashes with R5C4), no 1, 5 locked for C4, clean-up: no 3 in R12C4, no 5 in R8C3 (step 2f) [5 locked for N8 is used in step 8.] 7e. 1 in C4 only in R123C4, locked for N2 7f. 16(3) cage at R1C5 (step 6e) = {349/358}, no 7, 3 locked for C5 and N2, clean-up: no 5 in R3C6 (step 2h), no 4 in R3C7, no 7 in R4C4, no 9 in R7C4 7g. Naked pair {27} in R3C67, locked for R3, clean-up: no 3 in R2C3, no 9 in R3C12 7h. R356C7 (step 4a) = {127/235}, 2 locked for C7 7i. 12(4) cage at R7C7 = {1236/1245}, 2 locked for R7 7j. 6 of {1236} must be in R78C7 (R78C7 cannot be {13} which clashes with R356C7), no 6 in R7C89 8. 5 in C4 only in R789C4, locked for N8, clean-up: no 7 in R7C4 8a. R6C34 = 11 (step 2d), R7C23 = 12 (step 2e), R789C4 (step 7d) = {259/358/457} 8b. Consider placements for R6C4 = {34} R6C4 = 3 => R6C3 = 8, R7C23 = [75], no 5 in R7C4 => R789C4 = {358/457} or R6C4 = 4, R4C4 = 9 => R789C4 = {358} -> R789C4 = {358/457}, no 2,9 [Cracked. I spent quite a lot of time earlier trying to eliminate {259} before the puzzle was ready for me to make this important elimination. The rest is straightforward.] 8c. R9C4 = 5, R8C3 = 9 (step 2f), clean-up: no 3 in R1C2, no 3 in R7C23 (step 2e), no 7 in R7C5 8d. 2 in C4 only in R12C6 = {26}, locked for C4 and N2 -> R3C46 = [17], R3C7 = 2, R4C4 = 9, clean-up: no 4 in R1C89, no 4 in R2C3 8e. Naked pair {15} in R1C89, locked for R1 and N3, clean-up: no 7 in R1C2, no 8 in R2C6 8f. Naked pair {34} in R13C3, locked for C3 and N1, R7C3 = 5, R7C2 = 7 (step 2e), R4C3 = 2, R2C3 = 1 -> R3C3 = 4, R1C3 = 3 -> R1C2 = 9, R6C3 = 8, R6C4 = 3 (cage sum), R5C34 = [78], R7C4 = 4 -> R7C5 = 8, R9C3 = 6, R9C2 = 2 (cage sum), clean-up: no 4 in R2C6, no 8 in R3C12, no 1 in R56C1 8g. Naked pair {56} in R3C12, locked for R3 and N1 -> R2C2 = 8 8h. R8C34 = [97], R9C5 = 1 -> R8C5 = 6 (cage sum) 8i. Naked pair {39} in R79C6, locked for C6 -> R2C6 = 5, R1C6 = 8, R8C6 = 2 8j. Naked triple {146} in R456C6, locked for N5 and 19(5) cage at R4C6 -> R4C5 = 7 8k. R456C6 = {146} = 11 -> R56C7 = 8 = [35] 8l. 12(4) cage at R7C7 = {1236} (only remaining combination) -> R78C7 = [61], R7C89 = {23}, locked for R7 and N9, clean-up: no 8 in R89C9 8m. R89C9 = [47] 8n. Naked pair {89} in R9C89, locked for R9 and N9 -> R8C8 = 5, R1C8 = 1 9. 45 rule on N3 1 remaining innie R3C8 = 1 outie R4C9 + 2 -> R3C8 = {38}, R4C9 = {16} 9a. R3C9 = 8 (hidden single in C9), R3C8 = 3, R4C9 = 1 9b. R3C8 = 3 -> R4C78 + R5C8 = 21 = {489} (only remaining combination) -> R4C78 = {48}, R5C8 = 9, clean-up: no 1 in R5C2 and the rest is naked singles. Rating Comment: I'll rate my walkthrough for A360 at 1.5. One of my three forcing chains is long enough for the full 1.5, rather than Easy 1.5. At last I've caught up and finished my backlog of Assassins which started last October. |
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