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 Assassin 55 Goto page Previous  1, 2
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CathyW
Master

Joined: 31 Jan 2007
Posts: 161
Location: Hertfordshire, UK

 Posted: Wed Jun 20, 2007 7:51 pm    Post subject: Assassin 55 V2 continuation 40. Ruling out 11(2) in N8/c5 = {38} a) If 11(2) in N8/c5 = {38}, 6(2) = {24} -> 3,8 not elsewhere in N8, 2,4 not elsewhere in N2 -> r6c5 = 1 -> r4c46 <> 5 -> 8 locked to r4c46 not elsewhere N5/r4 -> r5c7 of 13(3) <> 5. -> r4c4 <> 5 (additional elimination) b) 11(3) r1c34+r2c3 = {128/137/146/236/245}. If {245}, 5 must go in r1c4 -> r12c3 <> 5. c) Hidden pair {23} in N5 -> r5c4, r6c6 <> 4,5 -> r4c6 <> 6,7 d) O-I of N9 = 0: r7c7 <> 3 (no 1 or 2 in r6c9); r9c6 <> 7 (min 3 in r6c9) e) 27(5) in r34 can’t have both 8 and 9 as would conflict with r4c6 -> remaining options: {14679/15678/23679/24579/24678/34569/34578} f) All 3 of r2 locked in split cage 17(4) r2c2468 Options: {1358/1367/2357} -> r2c6 <> 9 -> 9 locked to r3c46 -> r3c3 <> 9 -> 20(3) in N1 must have 9. g) If r5c9 = 8, r1c8 = 8 -> r1c1 <> 8 If r5c9 = 9, r5c5 = 6, r5c1 = 8 -> r1c1 <> 8 Either option r1c1 <> 8 h) 17(4) r6c456 + r7c5 = 1 + {259/349/367} If {259} r5c5 = 6; if {349} r5c5 = 6; if {367} r5c5 = 9 -> Killer pair of 6 and 9 -> r4c5 <> 6,9 i) If r5c9 = 8, one of r46c7 = 9 -> r7c7 <> 9 If r5c9 = 9, r5c5 = 6, r7c5 = 9 -> r7c7 <> 9 Either option r7c7 <> 9 -> r9c6 <> 6 j) Options for O-I N9 (r6c9 + r9c6 = r7c7) If r7c7 = 4, r6c9 + r9c6 = [31] If r7c7 = 5, r6c9 + r9c6 = [41] ([32] blocked by r6c6) If r7c7 = 6, r6c9 + r9c6 = [42] If r7c7 = 7, r6c9 + r9c6 = [34] If r7c7 = 8, r6c9 + r9c6 = [35/71] Edit - got a bit further and have now reached conflict which would rule out 11(2) c5 = {38} k) UR move - 6(2) N2 = {24} -> r12c7 can't both be 2,4 -> r1c6 <> 7 -> options for 13(3) = {157/625} must have 5, not elsewhere in N3/c7 -> rules out r6c9 = 4, r9c6 = 1 from j above -> r12c7 <> 4 -> 4 locked to r3c79, not elsewhere in r4. l) UR move - 6(2) N2 = {24} -> r12c3 can't both be 2,4 -> r1c4 <> 5 m) 17(3) c9 = [278/458/719] -> r4c9 <> 3,4 n) 15(3) c1 = {159/168/249/258/267/348/456} If {348}, r4c1 = 4 -> r4c1 <> 3 o) Resorted to JSudoku which found a Grouped Turbot Fish (would never have found this on my own! ) Hopefully I have the notation correct for the loop: [r6c6]=3=[r23c6]-3-[r4c7]=3=[r6c79]-3-[r6c6] -> r6c123 <> 3 Thanks to a tip from Glyn I think we've now reached conflict situation to prove the 11(2) in N8/c5 <> {38} p) If r5c1 = 6 -> r5c5 = 9, r5c9 = 8, r4c6 = 8, r6c6 = 3, r4c5 = 5, r5c4 = 2, r5c6 = 4 CONFLICT no options for 9(3) in r5. -> r5c1 <> 6 -> r5c5 = 6 -> r7c5 = 9 - NP {89} in r4c46 -> r4c23 <> 9 -> r3c1 <> 8, r34c1 <> 7 q) 31(5) in N478 must have 9 which is locked to r6c23, not elsewhere in N4/r6 -> r5c1 = 8 leads to several singles but then CONFLICT as no place for 3 in c6. Thus, if 11(2) in N8/c5 = {38} leads to conflict -> 11(2) = {29} ... Phew! With just a few hours to spare before Assassin 56 is released. Reaching solution with 11(2) in N8/c5 = {29} 41. If 11(2) = {29}, 6(2) = {15}, r345c5 = {678}, r67c5 = {34} -> 2, 9 not elsewhere in N8, 1,5 not elsewhere in N2 -> r4c46 = {59} not elsewhere in N5/r4 -> r6c6 = 2, r6c4 = 8 -> r4c6 = 9, r4c4 = 5, r5c5 = 6, r4c5 = 7, r3c5 = 8 -> 1 locked to r5 in N5, r5c237 <> 1 42. 27(5) in r34 must have 8 -> r4c7 = 8 -> r5c9 = 9, r5c1 = 8, r1c8 = 9 43. 7 locked to r5c78 -> r6c9 <> 7 44. HS r3c4 = 9 45. 17(3) in c9 = [53/71]9 -> 2 locked to r789c9, not elsewhere in N9 -> 4 locked to r123c7, not elsewhere in c7 46. 13(3) r1c67 + r2c7 = {247/256} -> 2 locked to r12c7 -> r3c7 <> 2 -> 2 locked to r3c23, not elsewhere in N1 -> r3c2 <> 6 -> r4c2 <> 2 (cell ‘sees’ both r3c23) 47. HS r2c1 = 9 -> 9 locked to r6c23 -> r7c3 <> 9 -> cage 31(5) must have 9. 48. Split 17(4) in r2c2468 = {1367/1457/2357} must have 7 -> r2c37 <> 7 49. 4 locked to r46c8 + r6c9 in N6. r78c8 ‘sees’ all these -> r78c8 <> 4 50. Options for 12(3) r8c7 + r9c67 = {138/147/156/345} – no 9 -> r7c7 = 9 -> r6c9 = (134), r9c6 = (568) -> 12(3) = {138/156}no 7 and must have 1 within r89c7, not elsewhere in N9/c7 51. 12(3) r8c9 + r9c89 = {237/246/345}. Combo analysis: r89c9 <> 7. 52. 16(3) r89c1 + r9c2, Max from r89c1 = 13 -> r9c2 <> 1,2 53. Naked Quad {2457} in r1235c7 -> r689c7 <> 5, r9c6 <> 6, r6c9 <> 3 54. xy wing with r6c9 as pivot -> r6c7 <> 3 -> r6c7 = 6 -> r4c9 = 3, r6c9 = 1, r3c9 = 5, r9c6 = 8 … Fairly straightforward from here to solution. Last edited by CathyW on Thu Jun 21, 2007 8:34 pm; edited 4 times in total
sudokuEd
Grandmaster

Joined: 19 Jun 2006
Posts: 257
Location: Sydney Australia

 Posted: Wed Jun 20, 2007 9:24 pm    Post subject: Wow Cathy - you have been busy. Haven't looked at your steps, but I think you have solved it. Looks like you found the only way to solve this one! Good old tri-furcation . I spent hours trying different innies - and even ventured into the left side . But... just don't quite feel ready to congratulate us yet - need to be absolutely convinced there is no other way. Will try to find some "nice loops" from where we were yesterday. Hope you don't mind if I stay back-tracked for a bit longer. BTW: I really liked your summary (step 38) of my hypothetical. It showed that 8 in r345c5 -> {15} in r12c5 -> 5 in r4c46. But couldn't find a way to use it. Seems I have a couple more sessions with this puzzle to feel satisfied. Cheers Ed
CathyW
Master

Joined: 31 Jan 2007
Posts: 161
Location: Hertfordshire, UK

Posted: Thu Jun 21, 2007 8:28 am    Post subject:

 sudokuEd wrote: But... just don't quite feel ready to congratulate us yet - need to be absolutely convinced there is no other way. Will try to find some "nice loops" from where we were yesterday. Hope you don't mind if I stay back-tracked for a bit longer.

I don't mind at all I will be very interested if you (or anyone else) can find a way without trifurcation - albeit not yet complete on proving conflict with 11(2) = {38}

Edit: Conflict now reached - see above.

Last edited by CathyW on Thu Jun 21, 2007 8:36 pm; edited 1 time in total
sudokuEd
Grandmaster

Joined: 19 Jun 2006
Posts: 257
Location: Sydney Australia

Posted: Thu Jun 21, 2007 12:26 pm    Post subject:

Getting a bit excited. Found a really nice lead to follow-up but no time now. Will post the start - can someone check it? Keep going if you want .

Starts at step 55 but follows on from step 38.
55.No 5 in r6c7 because of 7's in r5. Here's how.
55a. 7 in r5c6 -> h13(3)n6 = {256} -> 5 locked for n6
55b. 7 in r5c7 -> h13(3)n6 = {256} -> 5 locked for n6
55c. 7 in r5c8 -> r46c8 in h13(3)n6 = {247}-> r5c7 = [1/5],r6c9 = [1/3] and r4c9 = [1/3/5/]: naked triple 1/3/5/ for n6
55d. -> no 5 in r6c7

56. no 4 r456c7. Here's how.
56a. 4 in r456c7 -> 4 in n3 in r3c9 -> r4c9 = 5 (only combination)
56b. 4 in r456c7 -> h13(3)n6 = {256}
56c. But this means 2 5's in n6
56d. -> no 4 r456c7

57. no 7 r7c7. Here's how.(Actually quite proud of this one!)
57a. r789c8 must have 1 of 8/9 for c7 because of r1c8 -> r789c7 must have 1 of 8/9 for c7.
57b. if 8/9 in r89c7 then 12(3) cage = {129/138} only
57c. -> r9c6 = {123} and r7c7 = 3..7
57d. if r7c7 = 7 -> 2 outies n9 = 7 = [43]
57e. -> r89c7 = {18}
57f. 7 in r7c7 -> naked quad 1/2/4/5/ in r1235c7
57g. but this forces 2 1's into c7
57h. of course, if 8/9 is in r7c7 for c7 then r7c7 !=7
57i. -> r7c7 !=7 !!

Why stop there? Have to be careful though - mistakes happen so easily.
58. When 4 in r7c7.
58a..c. same as step 57
58d. if r7c7 = 4 -> 2 outies n9 = 4 = [13/31]
58e. but [13] is blocked the same way as step 57.(r89c7 = {18} and 4 in r7c7 -> naked quad 1/2/5/7 in r123c7 :Clash with r89c7)
58f. but [31] can have r89 = {38} (though {29} is blocked as above)

59. same trick with 5 in r7c7. This time the outies n9 = 5 = [32/41]
59a. [32] is blocked by {19} in c7: clash with 1 is naked quad
59b. [41] can have r89 = {38}

Don't have time to work out what happens for 3 and 6 yet: or what the outies will be with r7c7 = 8/9.
Should be at this marks pic: copy-paste into SudoCue
 Code: .-----------------------.-----------------------.-----------.-----------------------.-----------------------. | 3456789     3456789   | 12345678    12345678  | 1245      | 1246        2457      | 89          689       | |           .-----------:           .-----------:           :-----------.           :-----------.           | | 456789    | 123567    | 1245678   | 12345678  | 1245      | 123456789 | 2457      | 13        | 689       | :-----------:           :-----------'           :-----------:           '-----------:           :-----------: | 12345678  | 123567    | 123456789   123456789 | 5678      | 123456789   2457      | 13        | 2457      | |           :-----------'           .-----------'           '-----------.           '-----------:           | | 12345678  | 123456789   123456789 | 56789       56789       56789     | 13689       2456      | 13457     | |           :-----------------------'-----------.           .-----------'-----------------------:           | | 689       | 12345       12345       12345     | 689       | 1457        157         257       | 89        | :-----------+-----------------------.-----------'-----------'-----------.-----------------------+-----------: | 123456789 | 123456789   123456789 | 45678       1234        23456     | 13689       2456      | 1347      | |           '-----------.           '-----------.           .-----------'           .-----------'           | | 123456789   123456789 | 123456789   123456789 | 234679    | 123456789   345689    | 456789      123457    | :-----------.           :-----------.           :-----------:           .-----------:           .-----------: | 123456789 | 123456789 | 123456789 | 123456789 | 234789    | 123456789 | 123456789 | 456789    | 123457    | |           '-----------:           '-----------:           :-----------'           :-----------'           | | 123456789   123456789 | 123456789   123456789 | 234789    | 123456789   123456789 | 45679       123457    | '-----------------------'-----------------------'-----------'-----------------------'-----------------------'
Andrew
Grandmaster

Joined: 11 Aug 2006
Posts: 300
Location: Lethbridge, Alberta

 Posted: Sat Jun 23, 2007 4:39 am    Post subject: Just managed to finish V1 before we move from Calgary to Lethbridge, about 2 hours drive south of Calgary. Will be packing up my computer as soon as I've posted this message and won't be on-line again for about a week so I don't know when I'll get to try Assassin 56. When I first saw the comments in this thread, I was expecting this puzzle to be harder than it turned out to be. It was still a very long solution so, while it was a V1, it was definitely one of the harder ones. I hope that Ruud keeps up his excellent mixture of hard puzzles like this one and slightly easier ones. I've worked through Para's and Mike's walkthroughs this evening but haven't had time for more than a glance at Cathy's walkthrough. Sorry Cathy! I'll look through it when my computer is in the new home. [Edit. As promised I've now worked through Cathy's walkthrough, after our move, apart from the multi-colouring and nice loops which are techniques that I haven't yet learned. Ed commented that Cathy and Mike were the only ones that found the narrow solution path. Not sure if I did.] Here is my walkthrough. There is one heavy combination analysis step with a summary at the end for those who don't want to work through the details. Initially this step was even heavier but then I spotted the locked 5 in C5 which simplified the step and provided further eliminations. 1. R12C5 = {49/58/67}, no 1,2,3 2. R23C2 = {16/25/34}, no 7,8,9 3. R23C8 = {49/58/67}, no 1,2,3 4. R89C5 = {19/28/37/46}, no 5 5. 10(3) cage in N1 = {127/136/235} (cannot be {145} which clashes with R23C2), no 4,8,9 6. 19(3) cage at R1C3 = {289/379/469/478/568}, no 1 7. R345C1 = {489/579/678}, no 1,2,3 8. R5C678 = {128/137/146/236/245}, no 9 9. 22(3) cage at R8C7 = 9{58/67} -> no 9 in R9C89 10. 18(3) cage in N9 = {189/279/369/378/459/468/567} 10a. 9 only in R8C9 -> no 1,2 in R8C9 11. 19(5) cage at R6C2 = 1{2349/2358/2367/2457/3456} 12. 45 rule on R5 3 innies R5C159 = 22 = 9{58/67}, 9 locked for R5 13. 45 rule on N9 2 outies R6C9 + R9C6 – 14 = 1 innie R7C7 13a. Min R6C9 + R9C6 = 15 -> no 1,2,3,4,5 in R6C9 and R9C6 13b. Max R6C9 + R9C6 = 18 -> max R7C7 = 4 14. 45 rule on R89 4 innies R8C2468 = 13 = 1{237/246/345}, no 8,9, 1 locked for R8, clean-up: no 9 in R9C5 15. 45 rule on C12 3 innies R456C2 = 19 = {289/379/469/478/568}, no 1 16. 45 rule on C89 3 innies R456C8 = 7 = {124}, locked for C8 and N6, clean-up: no 9 in R23C8 17. 45 rule on C1234 2 innies R46C4 = 17 = {89}, locked for C4 and N5 17a. 19(3) cage at R1C3 (step 6) = {289/379/469/478/568}, 8,9 only in R12C3 -> no 2 in R12C3 18. 45 rule on C6789 2 innies R46C6 = 3 = {12}, locked for C6 and N5 19. 19(4) cage at R6C4 has R6C4 = {89}, R6C6 = {12}, valid combinations {1279/1369/1378/1459/1468/2359/2368/2458} -> no 8,9 in R7C5 20. R5C159 (step 12) = 9{58/67} 20a. 8,9 only in R5C19 -> no 5 in R5C19 21. R5C678 (step 8) = {137/146/236/245} (cannot be {128} because 1,2 only in R5C8), no 8 21a. 1,2 only in R5C8 -> no 4 in R5C8 21b. 4 only in R5C6 -> no 5 in R5C6 22. R5C234 = {138/147/237/246} (cannot be {156/345} which clash with all combinations in R5C678), no 5 22a. 1 only in R5C3 -> no 8 in R5C3 23. 5 in N5 locked in R456C5, locked for C5, clean-up: no 8 in R12C5 24. 45 rule on N1 2 innies R3C13 – 9 = 1 outie R1C4 24a. Min R1C4 = 2 -> min R3C13 = 11, no 1 in R3C3 25. 45 rule on C9 2 outies R19C8 – 6 = 2 innies R67C9 25a. Min R67C9 = 7 -> min R19C8 = 13 -> no 3 in R19C8 26. 3 in C8 locked in R78C8, locked for N9 27. 19(4) cage at R6C9 = 3{169/178/259/268/457} 27a. 1,2,4 only in R7C9 and each combination requires 1/2/4 -> R7C9 = {124} 28. 18(3) cage in N9 = {189/279/459/468/567} 28a. If 18(3) cage = {468/567} there must be a 9 in R89C7 (if R9C6 = 9 R89C7 = {58/67} which would clash with 18(3) cage) -> no 9 in R7C8 29. If R8C9 = 9, R6C9 <> 9 If R8C9 <>9, 9 in R89C7 (step 27a) -> R9C6 <>9 -> R6C9 + R9C6 <> 18 -> no 4 in R7C7 (step 13) 30. 4 in N9 locked in R789C9, locked for C9 31. 23(5) cage at R3C5 has R4C4 = {89}, R4C6 = {12}, consider the options 31a. R4C46 = [81] -> R345C5 = 14 = {257/347/356} (cannot be {149/158/167/248} which clash with R4C46, cannot be {239} because 2, 9 only in R3C5), also R6C46 = [92] -> R67C5 = 8 = [53/62/71] 31aa. R345C5 = {257} clashes with R67C5 31ab. R345C5 = {347} clashes with R12C5 31ac. R345C5 = {356} -> R67C5 = [71] -> R12C5 = {49} -> R89C5 = {28} 31b. R4C46 = [82] -> R345C5 = 13 = {157/346} (cannot be {148/238/247/256} which clash with R6C46, cannot be {139} because 1,9 only in R3C5), also R6C46 = [91] -> R67C5 = 9 = {36}/[54/72] 31ba. R345C5 = {157} -> R67C5 = {36} -> R12C5 = {49} -> R89C5 = {28} 31bb. R345C5 = {346} clashes with R12C5 31c. R4C46 = [91] -> R345C5 = 13 = {247/256/346} (cannot be {139/148/157} which clash with R6C46, cannot be {238} because 2,8 only in R3C5), also R6C46 = [82] -> R67C5 = 9 = {36}/[54] 31ca. R345C5 = {247} clashes with R12C5 31cb. R345C5 = {256} clashes with R67C5 31cc. R345C5 = {346} clashes with R67C5 31d. R4C46 = [92] -> R345C5 = 12 = {147/156/345}(cannot be {129/237/246} which clash with R6C46, cannot be {138} because 1,8 only in R3C5), also R6C46 = [81] -> R67C5 = 10 = {37/46} 31da. R345C5 = {147} clashes with R67C5 31db. R345C5 = {156} -> R67C5 = {37} -> R12C5 = {49} -> R89C5 = {28} 31dc. R345C5 = {345} clashes with R67C5 Summary R4C46 = [81/82/92] (no valid combinations for R345C5 with [91]) -> R6C46 = [81/91/92] R345C5 = {156/157/356} -> no 2,4,8,9 in R3C5, no 4 in R4C5 For {157}, 1 only in R3C5 -> no 7 in R3C5 R67C5 = {36/37}/[71], no 2,4,5 R12C5 = {49}, no 6,7, naked pair {49} locked for C5 and N2 R89C5 = {28}, no 1,3,4,6,7,9, naked pair {28} locked for N8 32. 4 in N5 locked in R5C46, locked for R5 33. R5C234 (step 22) = {138/147/237/246} 33a. 4 only in R5C4 -> no 6 in R5C4 34. 12(3) cage at R1C6, min R1C6 = 3 -> max R12C7 = 9, no 9 35. 26(5) cage at R6C7, max R6C8 + R7C7 = 6 -> min R6C7 + R78C6 = 20 = {389/…} 35a. 8 only in R6C7 and only other 9 in R7C6 -> no 3 in R6C7 and R7C6 35b. Valid combinations for 26(5) cage with R6C8 = {124} and R7C7 = {12} {12689/14579/14678/23489/24569/24578} 35c. All combinations with 4 must have 4 in R6C8 -> no 4 in R78C6 36. R5C6 = 4 (hidden single in C6) -> R5C78 = 7 = [52/61] (step 21), no 3,7 in R5C7 37. Killer pair 5/6 in R5C159 and R5C7, locked for R5 38. R5C234 (step 22) = {138/237} = 3{18/27} 39. 3 in N6 locked in R4C79, locked for R4 40. R345C5 (step 31 summary) = {156/157/356} 40a. 1,3 only in R3C5 -> no 6 in R3C5 41. 16(3) cage in N3 = {169/259/358/367} (cannot be {178/268} which clash with R23C8) 42. R345C9 = {179/269/278/359/368} 42a. 1,2 only in R3C9 -> no 7 in R3C9 42b. 1,2 only in R3C9 and {359} requires 9 in R5C9 -> no 9 in R3C9 43. 23(5) at R2C6 has {124} = R4C8, valid combinations {12389/12569/12578/13469/13478/13568/14567/23459/23468/23567} (cannot be {12479} because 1,2,4 only in R3C7 and R4C8) 43a. All combinations with 9 require {12/14/24} which must be in R3C7 and R4C8 -> no 9 in R3C7 44. 9 in N3 locked in 16(3) cage = 9{16/25}, no 3,7,8 45. Killer pair 5/6 in 16(3) cage and R23C8, locked for N3 46. 3 in C9 locked in R34C9 -> R345C9 (step 42) = 3{59/68}, no 1,2 7 46a. 5 only in R4C9 -> no 9 in R4C9 47. R1C8 = 9 (hidden single in C8, not sure how long that has been there) -> R12C5 = [49], R12C9 = {16/25} 48. Killer pair 5/6 in R12C9 and R345C9, locked for C9 49. R7C7 = {12}, R7C9 = {124} -> 1/2/4 in 18(3) cage (step 28) = {189/279/459/468} (cannot be {567}) 49a. 2 only in R9C9 and 9 only in R8C9 -> no 7 in R89C9 50. R6C9 = 7 (hidden single in C9) 51. R67C5 (step 31 summary) = {36/37} (cannot now be [71]) -> no 1 in R7C5 52. R3C5 = 1 (hidden single in C5) -> R46C6 = [21], clean-up: no 6 in R2C2 53. 19(4) cage at R6C9 (step 27) = 37{18/45}, no 2,6 54. 22(3) cage at R8C7 = {679} (cannot be {589} which must have 5,8 in R78C7 and would then clash with the part of the 19(4)cage that is in N9), no 5,8 -> no 6,7 in R9C8 54a. 6,7 in N9 locked in R89C7 = {67}, locked for C7 -> R9C6 = 9 -> R8C9 = 9 (hidden single in N9), R5C7 = 5, R5C8 = 2, R6C8 = 4, R4C8 = 1 55. Naked triple {358} in R789C8, locked for C8 and N9 -> R23C8 = {67}, locked for N3, clean-up: no 1 in R12C9 (step 47) = {25}, locked for C9 and N3 56. R7C7 = 2 (hidden single in C7) 57. 1 in C7 locked in R12C7 -> 12(3) cage at R1C6 = 1{38/47} (cannot be {156} because 5,6 only in R1C6), no 5,6 58. 26(5) cage at R7C7 = {24569/24578} (cannot be {23489} because 8,9 only in R7C7) = 245{69/78}, no 3 58a. 5 locked in R78C6, locked for C6 and N8 59. 3 in C6 locked in R123C6, locked for N2 60. R5C3 = 1 (hidden single in R5, saw that a long time ago but forgot about it) -> R5C2 = 8, R5C4 = 3, R5C159 = [976], R67C5 = [63], R4C5 = 5, R46C4 = [89] (cage sums), R34C9 = [83], R4C7 = 9, R6C7 = 8, R78C6 = {57} (step 58), locked for C6 and N8 61. R8C8 = 3 (hidden single in C8) 62. 23(5) cage at R2C6 = {13469} (only remaining combination), no 8 -> R3C7 = 4, R23C6 = {36}, locked for C6 and N2 -> R1C6 = 8, clean-up: no 3 in R2C2 63. 6 in R1 locked in R1C123, locked for N1, clean-up: no 1 in R2C2 [Alternatively X-wing in 6 on R23C68] 64. 1 in N1 locked in 10(3) cage = 1{27/36}, no 5 65. R5C1 = 9 -> R34C1 = [57/84] 66. 6 in R4 locked in R4C23 in 28(5) cage 67. R3C13 – 9 = R1C4 (step 24), R1C4 = {257} -> R3C13 = 11, 14 or 16 67a. If R3C13 = 11 -> [83] 67b. If R3C13 = 14 -> [59] 67c. R3C13 cannot total 16 -> R3C3 = {39}, R1C4 = {25} 68. 7 in C4 locked in R23C4 -> no 7 in R4C23 -> R4C1 = 7 (hidden single in R4), R3C1 = 5, R3C3 = 9 (hidden single in R3), R1C4 = 5 (step 67b), R12C9 = [25], clean-up: no 2 in R23C2 = [43], R4C23 = [64] 69. 10(3) cage in N1 = {127} (only remaining combination) -> R1C2 = 7, R12C1 = [12], R12C3 = [68], R12C7 = [31], R23C4 = [72], R23C8 = [67], R23C6 = [36], R6C1 = 3 70. R7C2 = 9 (hidden single in C2) 71. R6C1 + R7C2 = [39] -> R7C1 + R8C2 = 8 = [62], R6C23 = [52], R9C2 = 1, R9C9 = 4, R9C8 = 5 (cage sum), R7C89 = [81], R7C4 = 4, R89C5 = [82], R89C1 = [48], R89C4 = [16], R89C7 = [67], R9C3 = 3, R8C3 = 5 (cage sum), R7C3 = 7, R78C6 = [57] and the rest is naked singles, naked pairs and cage sums in N2 I haven't had enough time to check it properly. If you find any typos or other errors, please tell me by PM and I'll make the necessary corrections. I'm sure there will be a number of things that I ought to have seen earlier so no need to point those out to me. [Edit. A few minor corrections have been made. I didn't think they were significant enough to colour code them.]Last edited by Andrew on Wed Jul 25, 2007 4:31 am; edited 2 times in total
sudokuEd
Grandmaster

Joined: 19 Jun 2006
Posts: 257
Location: Sydney Australia

Posted: Sun Jun 24, 2007 12:22 pm    Post subject:

Making more progress on Candy A55V2. Feels more like a mine-field. Can someone please check these next batch of steps? Can't bear the thought of having made a mistake and 'wasting' any more time ..

A big thankyou to Glyn for helping do some groundwork for n9 moves. But any mistakes are not his.

Feel free to add some more too.

59c. Glyn pointed out that 5 in r7c7 -> 5 in n3 in r3c9 and 4 in r6c9 (from step 59.)-> r45c9 = [39]: but this forces 9 in c8 into both r1 & r789
59d. no 5 r7c7

Going to be a little more systematic now.
60. 3 in r7c7 -> 2 outies n9 = [12] -> r789c7 = [3]{19}
..............................................= [3]{46} blocked since have no 8/9 (step 57a)

61. 4 in r7c7 -> 2 outies n9 = [31]
i. [13] blocked: 1 in r6c9 -> 1 in n9 in r789c7 = [4]{18}: clashes with r1235c7
ii. [31]: 3 in r6c9 -> 3 in n9 in r789c7 = [4]{38}

62. 6 in r7c7 -> 2 outies n9 = [42] (remembering can't have repeats on these 2 outies & only have {1..3} available in r9c6)
62a. -> r789c7 = [6]{19}
...............= [6]{37/46} blocked since have no 8/9 (step 57a)

63. 8 in r7c7 -> 2 outies n9 = [71/35]: others blocked.
i. [17] Blocked: 1 in r6c9 -> 1 in n9 in r789c7 = {14}: but this clashes with r1235c7
ii. [71]-> r789c7 = [8]{56} ({[8]{29} leaves no 8/9 for r789c8: [8]{47} clashes with r123c7)
iii. [35]: 3 in r6c9 -> 3 for n9 in r789c7 = [8]{34}
iv. [43] Blocked: r789c7 = [8]{27/45} both clash with r1235c7

64. 9 in r7c7 -> 2 outies n9 = [18/45]. Here's how.
i. [18] -> 1 for n9 in r89c7 -> r789c7 = [9]{13}
ii. [36] Blocked: 3 in r6c9 -> 3 in n9 in r789c7: not possible with r9c6 = 6 in a 12(3) cage: forces 2 3's in cage.
iii. [45]: 4 in r6c9 -> h13(3)n6 = {256} -> 6 for n9 in r789c7 = [9]{16}
iv. [72] Blocked: 7 in r6c9 -> h13(3) = {256} -> 6 in n9 in r789c7 = [9]{46} and 4 in c8 forced into n9: but this means 2 4's n9.

65. In summary: 2 outies n9 = [12/31/42/71/35/18/45]
65a. r9c6 = {1,2,5,8}

66. In summary: r789c7 = [3]{19}/[4]{38}/[6]{19}/[8]{34/56}/[9]{13/16} (no 2,7)
66a. 12(3)n8 = {129/138/156/345}(no 7)

67. 2 in c7 only in n3: 2 locked for n3
67a. 17(3)n3 = [458/539/548/719]
67b. no 7 r4c9

68. r789c7 = [1/2/4/5/7](step 66): -> hidden quint with r1235c7
68a. no 1 r46c7

Time to move elsewhere.
69. 17(4)n5: no {2357/2456} combo's. Here's how.
69a. Combo's with-out 1 must have {23/34} in r67c5 (step 38)
69b. -> {2456} blocked
69c. {2357} combo. must have r67c5 = {23}(step 38) -> r6c6 = 5 -> r4c6 = 6: but this leaves no 6 for c5

70. no 6 in r6c6. Here's how.
70a. combo's with 6 in 17(4)n5 = {1268/1367}
i. {1268} = [8126] ([8162]: r56c5 = [12] clashes with 6(2)n2)
ii {1367}: r6c4 = {67} -> r4c4 = {67}(h13(2)n5) -> r7c5 = {67} -> r6c6 = 3.
70b. -> no 6 in r6c6
70c. -> no 5 r4c6 (h11(2)n5)

71. "45" c5: r46c46 = 24 = h24(4)n5, and taking into account h13(2) & h11(2)
71a. from step 37d. r4c46 = {89}/{78}/{68}/[57]/[59]
71a. -> h24(4) = [8952/9843/7863/8754/6873/5784/5982]
71b. 8 locked for n5 (no 8 r45c5)
71c. no 6 in r4c6, no 5 in r6c6

72. no 8 in r789c4 because of 8's in c5. Here's how.
72a. 8 in r3c5 -> 8 in n5 in r6c4 -> no 8 r789c4
72b. 8 in r89c5 -> no 8 in r789c4

73. weak links on 8 in r5 and n3 -> no 8 r1c1

74."45" n5: -> r456c5 + r5c46 = 45 - (13+11) = 21 = h21(5)n5
74a. must have 1 for n5 and no 8
74b. h21(5) n5 = {12369/12459/12567/13467}

75.But {12459} is blocked. Here's how.
75a. h21(5)n5 = {12459} must have r45c5 = [59] -> r6c5 = 1 (step 37ii,37iii) -> r5c46 = [24]: but this forces 2 4's into r5 in 9(3)n4 and r5c6.

76. h21(5)n5 = {12369/12567/13467} = 6{..}
76a. 6 locked in r45c5 for n5 and c5
76b. no 7 r46c4 (h13(2))

77. 17(4)n5 = {1259/1349/1457/2348} ({1358} blocked since 5 & 8 only in r6c4)

78. from step 71a. h24(4) = [8952/9843/8754/5784/5982]
78a. -> when r6c6 = 3, r6c4 = 4
78b. -> [42] blocked from i/o n9 since it means r6c6 = 3: but this will require 2 4's in r6

79. from step 65. 2 outies n9 = [12/31/71/35/18/45]
79a. no 6 r7c7

80. r6c46 = [52/43/54/84/82] (step 78)
80a. -> 17(4) cage = {1259/1349/1457/2348} =
i.[5129]
ii. [4139]
iii. [5147]
iv. [8243/8342]
v. [8324/8423]

81. [12] blocked from 2 outies n9 by 17(4) cage. Here's how.
81a. r6c9 + r9c6 = [12] & [3] in r7c7 i.17(4)n6 = [5129/4139/5147]: 2 1's in r4
ii. 17(4)n6 = [8243]: 2 3's r7
iii. 17(4)n6 = [8342]: 2 2's n8
iv. 17(4)n6 = [8423]:2 2's c7
81b. 2 outies n9 = [31/71/35/18/45]
81e. no 3 r7c7, no 2 r9c6

82. from step 66: r789c7 = [4]{38}/[8]{34/56}/[9]{13/16}
82a. no 9 r89c7

83. 27(5)n6 must have 9 because of 9's in c7. Here's how.
83a. 9 in r4c7 -> 9 in c6 in r78c7 in 27(5)n6.
83b. 9 elsewhere in c7 in r67 must be in 27(5)n6

84. 27(5) = {12789/13689/14589/14679/23589/23679/24579/34569}

85. 4 in r7c7 -> r89c7 = {38}, r6c9 = 3, r9c6 = 1
i. {14589/14679} blocked by 1 in r9c6
ii. {24579} -> r6c7 = 9 (only candidate)
iii. {34569} -> r6c7 = 9 (cannot be 6 as that forces h13(3)n6 = {247}, but no 2,4,7 available for r6c8

86. 8 in r7c7 -> r6c9 + r9c6 + r89c7 = [71{56}]/[35{34}]
i. {12789} -> r6c7 = 9 (only candidate)
ii. {13689} -> r6c8 = 6 (only candidate) and 1 in r78c6 -> 2 outies n9 = [35] -> 3 in r78c6 -> r6c7 = 9
iii. {14589} -> r6c7 = 9 (only candidate)
iv. {23589} -> r6c7 = {3/9}

NOw, obviously if I can just get rid of that 3 from r6c7 then 9 will be locked in the 27(5) in r67c7. Am planning to look at I/O on n69 to see what happens.

Can anyone see an easier way?
 Code: .-----------------------.-----------------------.-----------.-----------------------.-----------------------. | 345679      3456789   | 12345678    12345678  | 1245      | 12467       2457      | 89          689       | |           .-----------:           .-----------:           :-----------.           :-----------.           | | 456789    | 123567    | 1245678   | 12345678  | 1245      | 123456789 | 2457      | 13        | 689       | :-----------:           :-----------'           :-----------:           '-----------:           :-----------: | 12345678  | 123567    | 123456789   123456789 | 578       | 123456789   2457      | 13        | 457       | |           :-----------'           .-----------'           '-----------.           '-----------:           | | 12345678  | 123456789   123456789 | 589         5679        789       | 3689        2456      | 1345      | |           :-----------------------'-----------.           .-----------'-----------------------:           | | 689       | 12345       12345       12345     | 69        | 1457        157         257       | 89        | :-----------+-----------------------.-----------'-----------'-----------.-----------------------+-----------: | 123456789 | 123456789   123456789 | 458         1234        234       | 3689        2456      | 1347      | |           '-----------.           '-----------.           .-----------'           .-----------'           | | 123456789   123456789 | 123456789   12345679  | 23479     | 123456789   489       | 456789      123457    | :-----------.           :-----------.           :-----------:           .-----------:           .-----------: | 123456789 | 123456789 | 123456789 | 12345679  | 234789    | 123456789 | 134568    | 456789    | 123457    | |           '-----------:           '-----------:           :-----------'           :-----------'           | | 123456789   123456789 | 123456789   12345679  | 234789    | 158         134568    | 45679       123457    | '-----------------------'-----------------------'-----------'-----------------------'-----------------------'
mhparker
Grandmaster

Joined: 20 Jan 2007
Posts: 345
Location: Germany

Posted: Mon Jul 02, 2007 6:46 am    Post subject:

 sudokuEd wrote: Can anyone see an easier way?

Yes, I could (although it wasn't easy). Key moves were 87, 103a and an ALS-XZ move at step 112!

Here goes:

Assassin 55V2 Walkthrough, continued...

87. Nishio: if r7c5 = 9, then...
87a. 9 in n5 locked in r4, and
87b. 9 in n9 locked in c8
87c. -> 9 in n3 locked in c9
87d. Steps 87a and 87c -> 9 in n6 in r6c7
87e. but this would leave nowhere to place the 9 in 31/5 at r6c2
87f. Conclusion: no 9 in r7c5

88. 9 no longer available in 17(4)n5
88a. -> 17(4)n5 = {1457/2348} (see step 77) = {(5/8)..}
88b. {58} in 17(4)n5 only in r6c4
88c. -> r6c4 = {58}
88d. -> r46c4 (innies c1234, step 5) = {58}, locked for c4 and n5
88e. cleanup: no 3 in r6c6 (step 6)

89. 5 in c5 locked in n2 -> not elsewhere in n2

90. Hidden pair on {58} in 35(5)n2 at r3c5+r4c4
90a. -> r3c5 = {58}

91. 7 in 35(5)n2 locked in r4c56 -> not elsewhere in r4 and n5

92. {1457} combo for 17(4)n5 blocked by {14} in r5c6
92a. -> 17(4)n5 = {2348} (no 1,5,7) (see step 88a)
92b. -> r6c4 = 8 (at last, a placement!)
92c. -> r4c4 = 5 (step 5)
92d. -> r3c5 = 8
92e. cleanup: no 3 in 11(2)n8
92f. 8 not available in r6c23+r78c4 for 31(5)n4
92g. -> max. r6c23+r78c4 = {5679} = 27
92h. -> no 1,2,3 in r7c3

93. 1,5 in c5 locked in 6(2)n2 = {15}
93a. -> no 1 elsewhere in n2 (5 already gone)

94. 7 in r5 locked in n6 -> not elsewhere in n6 (r6c9)

95. 9(3)r5 and r5c6 form killer pair on {14} in r5 -> no 1 in r5c7

96. Naked quad on {2457} in c7 at r1235c7 -> no 4,5 elsewhere in c7 (2,7 already gone)

97. 1 in c7 locked in r89c7 -> not elsewhere in n9, and no 1 in r9c6
97a. Cleanup: no 9 in r9c8 ({129} combo now unavailable)
97b. 12(3)r8c7 = {1(38|56)} = {(3/6)..}
97c. {13} in 12(3)r8c7 only in r89c7 -> no 8 in r89c7

98. 12(3)r8c9 = {237/246/345} = {(3/6)..}
98a. {23} only in r89c9 -> no 7 in r89c9
98b. 12(3)r8c7 and 12(3)r8c9 form killer pair on {36} in n9 -> no 3,6 elsewhere in n9

99. 4 in c7 locked in n3 -> not elsewhere in n3 (r3c9)

100. 1 in n5 locked in r5 -> not elsewhere in r5

101. innies r12: r2c2468 = h17(4)r2
101a. 3 locked, 8 unavailable
101b. -> h17(4)r2 = {1349/1367/2357} = {(1/5)..}
101c. -> h17(4)r2 and r2c5 form killer pair on {15} in r2 -> no 1,5 elsewhere in r2
101d. h17(4)r2: 5 only in r2c2 -> no 2 in r2c2 -> no 6 in r3c2
101e. 9 only in r2c6 -> no 4 in r2c6

102. 11(3)n1 = {128/137/146/236/245}
102a. {13} only in r1c34 -> no 7 in r1c34
102b. {15} only in r1c3 -> no 4,8 in r1c3

103. 21(4)n69 = {1479/1578/2379/2478/3459}
103a. {2379} and {3459} both blocked by 12(3)r8c9
103b. -> 21(4)n69 = {(149/158/248)7}
103c. -> no 3 in r6c9
103d. 7 in 21(4)n69 locked in n9 -> not elsewhere in n9 (r9c8)

104. 12(3)r8c9 = {(26/35)4}
104a. 4 locked for n9

105. {14} in 21(4)n69 only available in r6c9
105a. -> {1479} combo blocked
105b. -> 21(4)n69 = {1578/2478}
105c. -> no 9 in r78c8

106. Hidden Single (HS) in c8 at r1c8 = 9

107. HS in c9 at r5c9 = 9
107a. Cleanup: no 4 in r4c9

108. Naked Single (NS) at r5c5 = 6
108a. -> r5c1 = 8
108b. Cleanup: no 2,7 in r3c1

109. HS in c7 at r7c7 = 9

110. HS in r4/c7 at r4c7 = 8

111. 9 in r6 locked in n4 -> not elsewhere in r4

Here's a neat one - the last tricky move. Haven't used ALS in a Killer before:

112. ALS-XZ: r46c9 ({134}) and r6c56 ({234}) have 4 as restricted common
112a. r6c7 can see common candidate digit 3 in both ALS's
112b. -> no 3 in r6c7
112c. -> r6c7 = 6

The rest is pretty easy now.
_________________
Cheers,
Mike
mhparker
Grandmaster

Joined: 20 Jan 2007
Posts: 345
Location: Germany

 Posted: Mon Jul 02, 2007 2:26 pm    Post subject: A few more moves, just to deliver the final blow... Assassin 55V2 (final episode) 113. r89c7 = {13} 113a. -> r9c6 = 8 113b. -> r6c9 = 1 (outies n9, r6c9+r9c6 = 9(2)) 113c. -> r4c9 = 3 113d. -> r3c9 = 5 (last digit in cage) 113e. Cleanup: no 3 in r2c2 114. HS in c7 at r5c7 = 5 114a. -> r5c68 = [17] (only remaining permutation) 115. HS in c8/n9 at r9c8 = 6 115a. -> r89c9 = {24}, 2 locked for c9/n9 116. NS at r7c9 = 7 117. Naked Pair (NP) on {24} in r6 at r6c68 -> no 2,4 elsewhere in r6 118. NS at r6c5 = 3 119. 11(2)n8 and r7c5 form killer pair on {24} in n8 -> no 2,4 elsewhere in n8 120. Split 19(4) at r23c6+r3c7+r4c8 = {2467} (only possible combo, due to {158} unavailable) 120a. -> no 3,9 in r23c6 120b. 6 only available in r23c6 -> no 6 elsewhere in n2 121. HS in c6 at r4c6 = 9 121a. -> r4c5 = 7, r6c6 = 2 (step 6) 121b. -> r7c5 = 4, r5c4 = 4 121c. -> r6c8 = 4 121d. -> r4c8 = 2 122. HS in r2 at r2c1 = 9 122a. Cleanup: no 3 in r1c2 123. HS in r3/n2 at r3c4 = 9 124. 2 in c1 locked in n7 -> not elsewhere in n7 125. HS in r7 at r7c1 = 2 126. Split 8(3) at r78c6 = {35}, 3 locked for n8 127. 5 in r9 locked in n7 -> not elsewhere in n7 128. 6 in c4 locked in 31(5)n4 = {6..} 128a. -> no 6 in r7c3 129. NS at r7c3 = 8 129a. -> r78c8 = [58] 129b. -> r78c6 = [35] 130. HS in c2 at r1c2 = 8 130a. -> r1c1 = 3 (last digit in cage) 130b. Cleanup: no 5 in r2c2 131. NS at r1c4 = 2 131a. -> r12c9 = [68] 132. HS in n1 at r1c3 = 5 132a. -> r2c3 = 4 (last digit in cage) 133. r12c5 = [15] 134. HS in c4 at r2c4 = 3 134a. -> r23c8 = [13] 134b. Cleanup: no 7 in r3c2 135. HS in c7 at r2c7 = 2 (could have also derived this by cage-splitting on 13(3)n2) 136. Split 23(4) at r6c23+r78c4 = {1679} (only combo without any of {2348}, which are unavailable) 136a. -> no 5 in r6c2 136b. {79} locked in r6c23 -> r78c4 = {16}, locked for n8 137. NS at r9c4 = 7 137a. -> r89c3 = [63] (only possible permutation) And the rest is just naked singles._________________Cheers, Mike
CathyW
Master

Joined: 31 Jan 2007
Posts: 161
Location: Hertfordshire, UK

 Posted: Mon Jul 02, 2007 4:40 pm    Post subject: Well done guys! Perhaps you can help me out with the 57 V1.5 now!
Andrew
Grandmaster

Joined: 11 Aug 2006
Posts: 300
Location: Lethbridge, Alberta

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