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Ix Killer 8 http://www.rcbroughton.co.uk/sudoku/forum/viewtopic.php?f=3&t=1422 |
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Author: | ixsetf [ Sat Dec 23, 2017 11:18 pm ] |
Post subject: | Ix Killer 8 |
Another puzzle using the near symmetry theme, this time along a different axis. SS Score: 1.40 I have a V2 for this one as well, which I intend to post at a later point. Code: paste into solver: 3x3::k:1793:0000:0000:0000:0000:0000:4355:4355:0000:1793:1793:4880:4880:0000:1807:4355:0000:3330:0000:0000:3083:4880:0000:1807:3328:3330:3330:0000:2835:3083:3084:3084:3328:3342:3342:0000:4114:2835:3083:0000:0000:2061:0000:0000:0000:0000:4114:0000:1286:0000:2061:2833:2833:0000:2565:2565:1286:0000:4618:4618:4618:2833:0000:2565:0000:5124:1032:2311:2311:0000:5897:0000:0000:5124:5124:0000:1032:0000:0000:5897:5897: Solution: 436752918 125894736 978613452 251489673 763521894 894367521 612978345 389145267 547236189 As always, any feedback or suggestions are appreciated. |
Author: | Andrew [ Thu Dec 28, 2017 5:20 am ] |
Post subject: | Re: Ix Killer 8 |
Thanks ixsetf for another challenging killer! It felt quite a lot harder than the SS score to find a way in but, after I'd managed that, I'll agree with the score. Here's my walkthrough: Prelims a) R23C6 = {16/25/34}, no 7,8,9 b) 13(2) cage at R3C7 = {49/58/67}, no 1,2,3 c) R45C2 = {29/38/47/56}, no 1 d) R4C45 = {39/48/57}, no 1,2,6 e) R4C78 = {49/58/67}, no 1,2,3 f) 16(2) cage at R5C1 = {79} g) R56C6 = {17/26/35}, no 4,8,9 h) 5(2) cage at R6C4 = {14/23} i) 4(2) cage at R8C4 = {13} j) R8C56 = {18/27/36/45}, no 9 k) 7(3) cage at R1C1 = {124} l) 19(3) cage at R2C3 = {289/379/469/478/568}, no 1 m) 11(3) cage at R6C7 = {128/137/146/236/245}, no 9 n) 10(3) cage at R7C1 = {127/136/145/235}, no 8,9 o) 20(3) cage at R8C3 = {389/479/569/578}, no 1,2 p) 23(3) cage at R8C8 = {689} Steps resulting from Prelims 1a. 7(3) cage at R1C1 = {124}, locked for N1 1b. 16(2) cage at R5C1 = {79}, locked for N4, clean-up: no 2,4 in R45C2 1c. 4(2) cage at R8C4 = {13}, locked for N8, clean-up: no 6,8 in R8C56 1d. 23(3) cage at R8C8 = {689}, locked for N9 1e. 8,9 in R7 only in R7C456, locked for N8 [The order of step 2 has been changed to simplify it.] 2. 20(3) cage at R8C3 + 23(3) cage at R8C8 total 43 2a. Max R8C2389 = 30 -> min R8C38 = 13, no 3 in R8C3 2b. Max R8C38 = 17 -> min R8C2389 = 26 = {3689/4689/4789/5689/5789/6789} (cannot be {3789/4589} because R9C23 must total at least 11, cannot be {4679/5678/5679} because R9C46 = {24/25} clash with R8C56), 8,9 locked for R9 2c. 45 rule on N7 3 innies R7C3 + R8C2 + R9C1 = 15 = {168/249/258/267/348/456} (cannot be {159/357} which clash with 10(3) cage at R7C1) 2d. 8,9 of {168/249/258/348} must be in R8C2 -> no 1,2,3 in R8C2 2e. 8,9 of {249/348} must be in R8C2, 4 of {456} must be in R7C3 -> no 4 in R8C2 3. R27C2 = {12} (hidden pair in C2) 3a. 7(3) cage at R1C1 = {124}, 4 locked for C1 3b. R9C2 = 4 (hidden single in C2) -> R89C3 = 16 = {79}, locked for C3 and N7, clean-up: no 1 in R6C4 3c. R8C2 = 8 (hidden single in N7), clean-up: no 3 in R45C2 3d. Naked pair {56} in R45C2, locked for C2 and N4 3e. 10(3) cage at R7C1 = {136/235}, 3 locked for C1 and N7, clean-up: no 2 in R6C4 3f. Naked pair {12} in R7C23, locked for R7 and N7 3g. R35C1 = {79} (hidden pair in C1) 3h. R9C57 = {13} (hidden pair in R9) 3i. 3 in C2 only in R13C2, locked for N1 3j. Naked triple {568} in R123C3, locked for C3 3k. 2 in N9 only 2 in N9 only in R8C79, locked for R8, clean-up: no 7 in R8C56 3l. Naked pair {45} in R8C56, locked for R8 and N8 3m. R9C1 = 5 (hidden single in R9) 3n. R78C1 = {36} -> R7C2 = 1 (cage sum), R7C3 = 2 -> R6C4 = 3, R2C2 = 2, R8C4 = 1, R9C5 = 3, R9C7 = 1, clean-up: no 5 in R3C6, no 9 in R4C45, no 5 in R56C6 4. R23C6 = [34/43/52] (cannot be {16} which clashes with R56C6), no 1,6 4a. Killer pair 4,5 in R23C6 and R8C6, locked for C6, clean-up: no 8,9 in R3C7 4b. R4C78 = {49/67} (cannot be {58} which clashes with R4C45), no 5,8 4c. Killer pair 4,7 in R4C45 and R4C78, locked for R4, clean-up: no 6 in R3C7 4d. R4C139 = {123} (hidden triple in R4) -> R46C1 = [28] (hidden pair in C1) 4e. Killer triple 4,5,6 in R4C2, R4C45 and R4C78, locked for R4, clean-up: no 7 in R3C7 4f. 18(3) cage at R7C5 = {378/468/567} (cannot be {369} which clashes with R7C1, cannot be {459} because 4,5 only in R7C7), no 9 4g. R7C4 = 9 (hidden single in R7) 4h. 8 in R7 only in 18(3) cage = {378/468} -> R7C7 = {34} 4i. Killer pair 3,6 in R7C1 and 18(3) cage, locked for R7 4j. 19(3) cage at R2C3 = {478/568}, no 2 4k. 19(3) cage at R2C3 = {478/568}, CPE no 8 in R2C5 4l. 3 in C3 only in 12(3) cage at R3C3 = {138/345}, no 6 4m. 8 in R4 only in R4C456, locked for N5 4n. 11(3) cage at R6C7 = {146/245}, no 7 4o. 11(3) cage at R6C7 = {146/245}, CPE no 4 in R45C8, clean-up: no 9 in R4C7 4p. 1 of {146} must be in R6C8 -> no 6 in R6C8 5. Consider combinations for R4C45 = {48/57} 5a. R4C45 = {48} => R4C6 = 9, R3C7 = 4 or R4C45 = {57} => R4C7 = 4 (hidden single in R4) -> 4 in R34C7, locked for C7 5b. R7C7 = 3, R78C1 = [61] 5c. Naked pair {27} in R8C79, locked for R8 and N9 -> R89C3 = [97], R8C8 = 6, clean-up: no 7 in R4C7 5d. R56C6 = {17} (cannot be {26} which clashes with R9C6, locked for C6 and N5 -> R7C56 = [78], R4C6 = 9 -> R3C7 = 4, R4C78 = [67], R45C2 = [56], clean-up: no 3 in R2C6 5e. R6C5 = 6 (hidden single in N5) 5f. R5C45 = {25} (hidden pair in N5), locked for R5 5g. 11(3) cage at R6C7 = {245} (only remaining combination), 2, locked for N6 5h. 5 in R67 only in 11(3) cage and R67C9 -> 5 in R67C9, locked for C9 6. All cells of 19(3) cage at R2C3 (step 4k) = {478/568} ‘see’ R2C6 = {45} -> 4 in R2C46, locked for R2 and N2, also no 5 in R2C5 6a. R12C1 = [41], R2C5 = 9 6b. 3 in R2 only in R2C89, locked for N3 6c. 45 rule on N3 2 remaining innies R1C9 + R2C8 = 11 = [65/83] 6d. 17(3) cage at R1C7 = {179/278}, no 5, 7 locked for C7 and N3 -> R8C79 = [27], R6C7 = 5, R67C8 = [24] 6e. 17(3) cage = {179} -> R12C7 = [97], R1C8 = 1 6f. R3C9 = 2 (hidden single in N3), R3C6 = 3 -> R2C6 = 4, R8C45 = [45], R4C45 = [48] 6g. R3C4 = 6 (hidden single in R3), R9C46 = [26], R5C45 = [52], R2C23 = [58] 6h. R3C3 = 8 -> R45C3 = 4 = {13} and the rest is naked singles. Rating Comment: I'll rate my walkthrough at Easy 1.5. I used a short forcing chain for my second breakthrough and then what I'll describe as an extended CPE, or it might be called a CPE killer pair, for the final wrapping up step. I'll look forward to trying the V2 but no hurry; I've got lots of other things to catch up on. |
Author: | ixsetf [ Sun Jan 07, 2018 4:57 pm ] |
Post subject: | Re: Ix Killer 8 |
A V2 of this puzzle as promised. SS Score: 2.10 Code: paste into solver: 3x3::k:1793:0000:0000:5907:5907:5907:4355:4355:0000:1793:1793:4880:4880:5907:1807:4355:3350:3330:0000:0000:3083:4880:5140:1807:3350:3330:3330:0000:2822:3083:3084:3084:5140:3342:3342:4373:4114:2822:3083:0000:5140:2061:5140:4373:4373:0000:4114:0000:0000:0000:2061:2833:2833:4373:2565:2565:2560:0000:4618:4618:4618:2833:0000:2565:2560:5124:1032:2311:2311:0000:5897:0000:0000:5124:5124:0000:1032:0000:0000:5897:5897: Solution: 135967842 246813579 987524631 452391768 763482915 891756423 318679254 629145387 574238196 As always, any feedback or suggestions are appreciated. |
Author: | Andrew [ Mon Apr 02, 2018 10:14 pm ] |
Post subject: | Re: Ix Killer 8 |
Thanks ixsetf for this V2. Quite a hard one, definitely harder than Ix Killer 7 V2. It took me a while to find some steps, but I didn't need to use any technically difficult steps. Here is my walkthrough for Ix Killer 8 V2: Prelims a) R23C6 = {16/25/34}, no 7,8,9 b) 13(2) cage at R2C8 = {49/58/67}, no 1,2,3 c) R45C2 = {29/38/47/56}, no 1 d) R4C45 = {39/48/57}, no 1,2,6 e) R4C78 = {49/58/67}, no 1,2,3 f) 16(2) cage at R5C1 = {79} g) R56C6 = {17/26/35}, no 4,8,9 h) 10(2) cage at R7C3 = {19/28/37/46}, no 5 i) 4(2) cage at R8C4 = {13} j) R8C56 = {18/27/36/45}, no 9 k) 7(3) cage at R1C1 = {124} l) 19(3) cage at R2C3 = {289/379/469/478/568}, no 1 m) 11(3) cage at R6C7 = {128/137/146/236/245}, no 9 n) 10(3) cage at R7C1 = {127/136/145/235}, no 8,9 o) 20(3) cage at R8C3 = {389/479/569/578}, no 1,2 p) 23(3) cage at R8C8 = {689} Steps resulting from Prelims 1a. 7(3) cage at R1C1 = {124}, locked for N1 1b. 16(2) cage at R5C1 = {79}, locked for N4, clean-up: no 2,4 in R45C2 1c. 4(2) cage at R8C4 = {13}, locked for N8, clean-up: no 6,8 in R8C56 1d. 23(3) cage at R8C8 = {689}, locked for N9 [Two easy placements which the original version didn’t have.] 2a. 45 rule on N3 1 innie R1C9 = 2 2b. 45 rule on N7 1 innie R9C1 = 5 2c. 7(3) cage at R1C1 = {124}, 2 locked for R2, clean-up: 5 in R3C6 2d. 10(3) cage at R7C1 = {127/136}, no 4, 1 locked for N7, clean-up: no 9 in 10(2) cage at R7C3 2e. 7 of {127} must be in R78C1 (R78C1 cannot be {12} which clashes with R12C1, ALS block), no 7 in R7C2 2f. 20(3) cage at R8C3 = {389/479}, no 6 2g. 10(2) cage at R7C3 = {28/46} (cannot be {37} which clashes with 20(3) cage), no 3,7 2h. 9 in R7 only in R7C456, locked for N8 2i. 2 in N9 only in R789C7 + R7C8, CPE no 2 in R6C7 3. 20(3) cage at R8C3 + 23(3) cage at R8C8 total 43 3a. Max R9C2389 = 30 -> min R8C38 = 13, no 3 in R8C3 3b. Max R8C38 = 17 -> min R9C2389 = 26 -> R9C2389 = {3689/4679/4689/4789/6789} (cannot be {3789} because R9C23 must total at least 11) 3c. R9C46 = {26/27/28} (other combinations clash with R8C2389 and/or with R8C56), no 4, 2 locked for R9 and N8, clean-up: no 7 in R8C56 3d. Naked pair {45} in R8C56, locked for R8 and N8, clean-up: no 6 in R7C3 3e. R9C2389 = {3689/4679/4689/4789} (cannot be {6789} which clashes with R9C46) 3f. Killer triple 6,7,8 in R9C2389 and R9C46, locked for R9 3g. Min R7C56 = 13 -> max R7C7 = 5 4. 45 rule on N2 1 outie R2C3 = 1 innie R3C5 + 4, no 3 in R2C3, no 6,7,8,9 in R4C2 4a. 23(4) cage at R1C4 = {1589/1679/3479/3578} (cannot be {3569/4568} which clash with R23C6) 4b. 23(4) = {1679/3479/3578} (cannot be {1589} because 19(3) cage at R2C3 cannot be 6{67}), 7 locked for N2 4c. Consider placement of 2 in N2 R3C4 = 2 => R2C34 = {89} or R3C5 = 2 => R2C3 = 6 or R3C6 => R2C6 = 5 -> no 5 in R2C3, no 1 in R3C5 5. Combined cages R23C6 + R56C6 + R8C6 = {16}{35}4/{34}{17}5/{34}{26}5/[52]{17}4, 4,5 locked for C6 6. 7(3) cage at R1C1 = {124}, 10(3) cage at R7C1 (step 2d) = {127/136}, 10(2) cage at R7C3 = [28/46/82], 20(3) cage at R8C3 (step 2f) = {389/479} 6a. Consider placement for 4 in N4 4 in R46C1 => R12C1 = {12}, locked for C1 => 10(3) cage = {136} (cannot be {127}, ALS block) or 4 in R456C3 => 10(2) cage = {28}, locked for N7 => 10(3) cage = {136} -> 10(3) cage = {136}, locked for N7, 10(2) cage = {28}, 20(3) cage at R8C3 = {479}, 4 locked for R9 6b. R35C1 = {79} (hidden pair in C1) 6c. 8 in C1 only in R46C1, locked for N4, clean-up: no 3 in R45C2 6d. Naked pair {56} in R45C2, locked for C2 and N4 6e. Max R45C3 = 7 -> min R3C3 = 5 6f. 1 in C3 only in R456C3, locked for N4 7. 45 rule on N6 1 innie R5C7 = 1 outie R7C8 + 4, no 1,2,3,4 in R5C7, no 7 in R7C8 7a. 2 in C7 only R789C7, locked for N9, clean-up: no 6 in R5C7 7b. 17(4) cage at R4C9 = {1259/1268/1349/1358/1367/2348/2357} (cannot be {1457/2456} which clash with R4C78) 8. R4C2 = {56}, R4C45 = {39/48/57}, R4C78 = {49/58/67} -> combined cage R4C24578 = 5{39}{67}/5{48}{67}/6{39}{58}/6{57}{49}, 5,6 locked for R4 9. 12(3) cage at R3C3 = {129/138/237/246/345} (cannot be {147} which clashes with 20(3) cage at R8C3, ALS block, cannot be {156} because 5,6 only in R3C3) 9a. 12(3) cage = {129/138/237/345} (cannot be {246} because R3789C3 = 68{79} clash with R2C3), no 6 in R3C3 9b. Consider combinations for 12(3) cage 12(3) cage = {129/138/237} => R12C3 = [56] (hidden pair in C3) or 12(3) cage = {345} => R67C3 = [12] (hidden pair in C3) => R12C3 = {68} (hidden pair in C3) -> R12C3 = [56/68/86], clean-up: no 3,5 in R3C5 (step 4) 9c. 19(3) cage at R2C3 = {289/469/568}, no 3 9d. R2C3 + R3C5 (step 4) = [62/84] 9e. {568} must be 6{58} (cannot be 8{56} because R23C4 + R3C5 = {56}4 clashes with R23C6) 9f. 19(3) cage = 6{49}/6{58}/[892], no 6 in R23C4 9g. 19(3) cage + R3C5 = 6{49}2/6{58}2/[892]4 -> 2 in R3C45, locked for R3, clean-up: no 5 in R2C6 9h. R23C6 = {16/34}, R56C6 = {17/26/35} -> combined cage R2356C6 = {16}{35}/{34}{17}/{34}{26}, 3 locked for C6 9i. 3 in N1 only in R13C2, locked for C2 -> R7C2 = 1, R78C1 = {36}, locked for C1, clean-up: no 5 in R5C7 (step 7) 9j. 17(4) cage at R4C9 (step 7b) = {1259/1268/1349/1358/1367/2348/2357} 9k. Killer triple 7,8,9 in R4C78, 17(4) cage and R5C7, locked for N6 9l. 11(3) cage at R6C7 = {146/236/245} = [164/425/524/614/623], no 3 in R6C7, no 3,4,5 in R6C8 9m. 3 in N6 only in 17(4) cage = {1349/1358/1367/2348/2357} 9n. 17(4) cage = {1349/1358/1367/2357} (cannot be {2348} which combined with R4C78 = {67} clashes with 11(3) cage) 9o. 17(4) cage = {1349/1358/1367} (cannot be {2357} which combined with R7C9 = {3457} clashes with 11(3) cage), no 2, 1 locked for N6 9p. R6C8 = 2 (hidden single in N6) -> 11(3) cage = [425/524/623], clean-up: no 6 in R5C6 10. 18(3) cage at R7C5 = {279/378/468/567) (cannot be {369} which clashes with R7C1) Consider combinations for 18(3) cage 18(3) cage = {279} => R7C3 = 8, R7C4 = 6 or 18(3) cage = {378/468/567} => R7C4 = 9 (hidden single in R7) -> R7C4 = {69} 10a. Killer triple 3,6,9 in R7C1, R7C4 and 18(3) cage, locked for R7, clean-up: no 7 in R5C7 (step 7) 10b. 11(3) cage at R6C7 (step 9p) = [425/524], no 6, CPE no 4,5 in R45C8 + R7C7, clean-up: no 8,9 in R4C7 10c. 18(3) cage = {279/378}, no 6, 7 locked for R7 and N8 10d. R9C23 = {47} (hidden pair in R9) -> R8C3 = 9 10e. 12(3) cage at R3C3 (step 9a) = {138/237/345}, 3 locked for C3 11. 20(4) cage at R3C5 = {1289/1478/2378/2468} (cannot be {1379/1568} because R3C5 only contains 2,4, cannot be {2567/3467} because R5C7 only contains 8,9, cannot be {2369} because 3,6 only in R5C5, cannot be {2459} which clashes with R8C5, cannot be {3458} because 3,5 only in R5C5, cannot be {1469} which clashes with R23C6), no 5, CPE no 8 in R5C4 11a. R35C5 cannot be {24} because R4C6 + R5C7 cannot total 14, R3C5 = {24} -> no 2,4 in R5C5 11b. R3C5 = 2 (hidden single in C5) -> R2C3 = 6 (step 4), clean-up: no 1 in R3C6, no 7 in R3C7 11c. R3C5 = 2 -> 20(4) cage = {1289/2378} 11d. 3 of {2378} must be in R4C6 -> no 7 in R5C5 11e. 20(4) cage = {1289} (cannot be {2378} = [2738] which clashes with combined cage R4C45 + R4C78 = {48}{67}/{57}[49]) -> R4C6 + R5C57 = {189}, 1 locked for N5, CPE no 9 in R5C4, clean-up: no 7 in R56C6 11f. Killer pair 3,6 in R23C6 and R56C6, locked for C6 11g. 2 in N5 only in R5C46, locked for R5 11h. 1 in R3 only in R3C89, locked for N3 11i. 13(3) cage at R2C9 = {139/148/157}, no 6 11j. 1 in C7 only in R89C7, locked for N9 12. Consider combinations for R23C6 = [16]/{34} R23C6 = {16} => R56C6 = {35}, locked for N5 => R4C45 = {48}, locked for N5 => R4C6 = 9 or R23C6 = {34} => R56C6 = [26] => R9C6 = 8 => R4C6 = {19} -> R4C6 = {19} 12a. R4C6 + R5C57 (step 11e) = {189}, 8 locked for R5 13. 45 rule on R1 2 outies R2C57 = 3 innies R1C123 + 3 13a. Max R2C57 = 17 -> max R123C3 = 14, min R1C13 = 6 -> max R1C2 = 8 13b. 9 in N1 only in R3C12, locked for R3, clean-up: no 4 in R2C4 (step 9g), no 4 in R2C8 13c. 13(3) cage at R2C9 (step 11h) = {139/148/157} 13d. 9 of {139} must be in R2C9 -> no 3 in R2C9 14. R5C7 + R7C8 (step 7) = [84/95] 14a. R35C7 cannot be [89] because R3C7 + R2C8 = [85] would clash with R5C7 + R7C8 = [95], R5C7 = {89} -> no 8 in R3C7, clean-up: no 5 in R2C8 14b. Hidden killer pair 8,9 in 17(3) cage at R1C7 and R5C7 for C7, R5C7 = {89} -> 17(3) cage must contain one of 8,9 in R12C7 = {359/368/458} (cannot be {467} which doesn’t contain one of 8,9), no 7 14c. One of 8,9 must be in R12C7 -> no 8,9 in R1C8 14d. 4 of {458} must be in R1C78 (R1C78 cannot be {58} which clashes with R1C3), no 4 in R2C7 14e. 13(2) cage at R2C8 = [94/76] (cannot be [85] which clashes with 17(3) cage) 14f. Naked quad {6789} in R2489C8, locked for C8 14g. 7 in C8 only in R2C8 + R3C7 = [76] or R4C78 = [67] -> 6 in R34C7, locked for C7 14h. 17(3) cage = {359/458}, 5 locked for N3 14i. 13(3) cage at R2C9 (step 11i) = {139/148}, no 7 14j. R2C8 = 7 (hidden single in N3) -> R3C7 = 6, clean-up: no 1 in R2C5 15a. Naked pair {34} in R23C6, locked for C6 and N2, R8C56 = [45], R56C6 = [26], R9C6 = 8, R9C4 = 2 (hidden single in R9), clean-up: no 9 in R2C4 (step 9g), no 8 in R4C4 15b. Naked pair {58} in R23C4, locked for C4 and N2, clean-up: no 7 in R4C5 15c. 18(3) cage at R7C5 (step 10c) = {279} (only remaining combination) -> R7C7 = 2, R7C56 = {79}, locked for R7 15d. 10(2) cage at R7C3 = [82], R2C2 = 4, R23C6 = [34] 15e. 13(3) cage at R2C9 (step 14i) = {139} (only remaining combination) -> R2C9 = 9, R3C89 = {13}, locked for R3 and N3, 23(3) cage at R8C8 = [896], R4C8 = 6 -> R4C7 = 7, clean-up: no 5 in R4C5 15f. R139C3 = [574], R3C3 = 7 -> R45C3 = 5 = [23] and the rest is naked singles. Rating Comment: I'll also rate this V2 at Hard 1.5, well maybe Very Hard 1.5. There were a lot more 1.5 level steps needed than for Ix Killer 7 V2. The start of step 14 was the hardest part for me to find. |
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