While this one doesn't require exotic techniques, the endgame requires a fair bit of finesse. I didn't see any spots where chains were needed, though, which Ruud's comment seems to imply--what spot do you have in mind for this?
1. 15(5) in N8 = {12345}, and the remaining cells of N8 = {6789}. 24(3) in N3 = {789}. 45 rule on R1 => R2C3467 = 10 = {1234}. 45 rule on N147 => R37C4 = 13 => R3C4 = {4567}.
2. 45 rule on N3 => R3C79 = 8 = {26|35}. The 1 in N3 is locked in the 13(4) cage (it's required in all possible combos). 45 rule on N1 => R3C13 = 11 = {29|38|47} ({56} is blocked by the 8(2) cage we just found). 1 in N1 is locked in the 15(4) cage (because it cannot go in the 19(3) cage, obviously). Between the two of them, the 15(4) cage in N1 and 13(4) cage in N3 produce an x-wing on 1 in R12 => 1 is blocked from R12C456.
3. Min. value of each cell in R1C456 = 5, because if any cell in R1C456 were 4 or less the max sum of that cell + R2C46 = 9 and so the remaining two cells would add to 18 or greater, which is impossible.
4. 45 rule on C5 => R159C5 = 9 = {126|135|234} => R1C5 = {56}, R59C5 = {1(2|3)} (locking 1 in those cells in C5).
5. The only place for the 1 in N2 to go is now R3C6! 45 rule on N369 => R7C6 = 9.
6. R6C5 = {345} (difference between 18 and possible sums of remaining two cells = {678}). 45 rule on N5 => R4C5 = {678}. 9 is locked in C5/N2 in R23C5 => R23C5 = {(2|3)9}, R4C5 = {67}.
7. 4 is locked in C5 in R6C5 => R78C5 = {68}, R37C4 = [67], R4C5 = 7, R1C5 = 5, R23C5 = {29}, R2C46 = {34}, R2C37 = {12}, R23C5 = [92], R3C8 = 9, R59C5 = {13}, R1C46 = [87], R2C12 = {56}, R3C2 = 8, R3C79 = R4C7 = {35}, R34C3 = [74], R3C1 = 4.
8. 45 rule on R5 => R5C456 = 10 = {136} or {235}, with 3 locked in those cells in N5/R5. 45 rule on R6789 => R6C46 = 11 = [92], R5C45 = {13}, R5C6 = 6, R4C46 = [58], R34C7 = [53], R3C9 = 3, R4C89 = {26}, R4C12 = {19}. 4 is locked in 21(3) cage in R5C789 => it is {489}, R5C123 = {257}.
9. R6C7 = {17}, R7C7 = {28}. 45 rule on N9 => R7C79 = 10 = {28} => R78C5 = [68]. 45 rule on N7 => R7C13 = {13}, R6C3 = {68}, R7C28 = {45}.
10. 3 is locked in N4/R6 in R6C12 => R7C1 = 1, R6C12 = [83], R67C3 = [63], R1C1 = 3, R9C3 = 8.
11. 45 rule on R9 => R8C3467 = 13 => they can only contain the numbers 1..7 => in C3 the only spot for the 9 is R1C3, R8C3 = {25}, R2C3 = 1, R1C2 = 2, R2C7 = 2, R67C7 = [18], R7C9 = 2, R4C89 = [26], 7 is locked in N9/C7 in R89C7 => the remaining cells of the 18(4) cage = 11 => the 9 cannot go in it => R8C9 = 9, R5C7 = 9, R78C8 = [53], R7C2 = 4, R6C89 = [75], R2C89 = [87], R5C89 = [48]. Only possible combo in the hidden 13(4) cage in R8C3467 = {1246} => R9C7 = 7, R8C6 = 4, and you carry on.....
Assassin 29
Assassin 29
Last edited by nd on Mon Dec 18, 2006 8:41 pm, edited 2 times in total.
My solution followed a fairly similar path. However in places my moves were in a different order and in some cases my logic was different. It was possibly due to doing some things in a different order, essentially the order in which I saw the next moves, that I didn't need any "finesse in the endgame".
Here is my walkthrough. You will see that I have started making more use of remaining valid combinations, which I had started doing on some of the more difficult puzzles, although they are not as necessary here. The "Killer Configuration Tables" link on the Weekly Assassin page is very helpful and easy to use. Thanks for that, Ruud!
1. 15(5) cage in N8 = {12345}, remaining cells in N8 = {6789}
2. 45 rule on R1 4 outies R2C3467 = 10 = {1234}, naked quad for R2
3. 24(3) cage in N3 = {789}, naked triple for N3
4. 13(4) cage in N3 = {1246/1345} = 14{26/35}, 1,4 locked for N3, 5/6 in R1
5. R3C79 = {26/35}
6. 45 rule on N7 2 innies R7C13 = 4 = {13}
7. 45 rule on N9 2 innies R7C79 = 10 = {28/46}, hidden quad {6789} locked in R7C45679, 7,9 in R7 locked in R7C456, R8C5 = {68}, R7C28 = {245}
8. 45 rule on C123 2 outies R37C4 = 13, R7C4 = {6789} -> R3C4 = {4567}
9. 45 rule on C789 2 outies R37C6 = 10, R7C6 = {6789} -> R3C6 = {1234}
10. R7C5 = {6789}, R8C5 = {68} -> R6C5 = {1345}
11. 45 rule on N5 2 innies R46C5 = 11 -> R6C5 = {345}, R4C5 = {678}
12. 45 rule on R1234 2 innies R4C46 = 13 = {49/58/67}
13. 45 rule on R6789 2 innies R6C46 = 11 = {29/38/47/56} -> 1 in N5 locked in R5
14. 45 rule on R5 3 innies R5C456 = 10 = 1{27/36/45}
15. 45 rule on C5 3 innies R159C5 = 9 = {126/135/234} -> max. 6 in R1C5 or R5C5
16. Only valid combinations for 27(5) cage in N2 with R1C5 = max. 6 and R2C46 = {1234} are {13689/14589/14679/23589/23679/24579/24678/34569/34578} -> R1C5 = {56}, R1C46 = {6789}
17. Killer pair 5/6 in R1C5789, no other 5,6 in R1
18. R1C5 = {56} -> R159C5 = 1{26/35} (step 15) -> R59C5 = 1{2/3}, 1 in C5 locked in R59C5
19. 15(4) cage in N1 = {1239/1248/1347} = 1{239/248/347}, 1 locked for N1 -> 1 in R3 locked in N2 -> R3C6 = 1, R34C7 = {26/35}, R7C6 = 9 (step 9), R7C45 = {678}, R3C4 = {567} (step 8)
20. Naked triple {678} in R478C5 -> R1C5 = 5, R3C4 = {67}, R7C4 = {67}(step 8), killer pair 6,7 in C4
21. R6C5 = {34}, R4C5 = {78} (step 11), 6 in C5 locked in R78C5 -> R7C4 = 7, R78C5 = {68}, R6C5 = 4, R4C5 = 7, R3C4 = 6 (step 8), 6 in C6 locked in N5
22. R3C79 = {35}, 13(4) cage in N3 = {1246}, R4C7 = {35}
23. 9 in C5 locked in R23C5 -> R23C5 = {29}, R2C46 = {34}, R2C37 = {12}, R23C5 = [92], R2C89 = {78}, R3C8 = 9
24. 27(5) cage = {34578} -> R1C4 = 8, R1C6 = 7
25. R2C12 = {56}, R3C2 = 8
26. Only remaining combination for 15(4) cage in N1 (step 19) = {1239}, R3C13 = {47}, R4C3 = {47} -> R4C3 = 4, R3C3 = 7, R1C3 = 4
27. R4C46 = 13 (step 12) = [58], 5 in C6 locked in R89C6, R34C7 = [53], R3C9 = 3, R4C89 = {26}, R4C12 = {19}
28. R6C4 = 9 (single in C4) -> R6C6 = 2 (step 13), R289C6 = naked triple {345}, R5C6 = 6, R5C45 = {13}
29. 4,9 in N6 locked in C5 -> 21(3) cage = {489}, 14(3) cage in R5 = {257}
30. R7C4 = 7 (step 21), R7C3 = {13} -> R6C3 = {68} -> 3 in N4 locked in R6C12 -> R7C1 = 1, R6C12 = [83], R67C3 = [63], R4C12 = [91]
31. 8 in C3 locked in R89C3, only valid combination for 25(4) in N7 = {2689} ({4678} blocked by 4,6,7 in C3) -> R9C1 = {26}, R9C2 = {269}, R89C3 = {289}, 16(3) cage in N7 = {457}
32. 45 rule on R9 4 outies R8C3467 = 13 = 1{237/246/345}, 1 locked for R8, no 8,9 -> R8C3 = 2, R9C1 = 6, R9C2 = 9, R9C3 = 8, R9C4 = 2 (single in N8)
33. R1C2 = 2, R1C1 = 3, R2C3 = 1, R1C3 = 9, R2C7 = 2, R1C789 = {146}
34. 7 in R9 locked in N9, only valid combination for 18(4) cage = {1467} -> R8C7 = 6, R9C789 = {147}
35. R7C79 = 10 {step 7) = [82], R7C8 = 5, R8C89 = [39], R6C7 = 1, R6C89 = [75]
and the rest is simple elimination
Here is my walkthrough. You will see that I have started making more use of remaining valid combinations, which I had started doing on some of the more difficult puzzles, although they are not as necessary here. The "Killer Configuration Tables" link on the Weekly Assassin page is very helpful and easy to use. Thanks for that, Ruud!
1. 15(5) cage in N8 = {12345}, remaining cells in N8 = {6789}
2. 45 rule on R1 4 outies R2C3467 = 10 = {1234}, naked quad for R2
3. 24(3) cage in N3 = {789}, naked triple for N3
4. 13(4) cage in N3 = {1246/1345} = 14{26/35}, 1,4 locked for N3, 5/6 in R1
5. R3C79 = {26/35}
6. 45 rule on N7 2 innies R7C13 = 4 = {13}
7. 45 rule on N9 2 innies R7C79 = 10 = {28/46}, hidden quad {6789} locked in R7C45679, 7,9 in R7 locked in R7C456, R8C5 = {68}, R7C28 = {245}
8. 45 rule on C123 2 outies R37C4 = 13, R7C4 = {6789} -> R3C4 = {4567}
9. 45 rule on C789 2 outies R37C6 = 10, R7C6 = {6789} -> R3C6 = {1234}
10. R7C5 = {6789}, R8C5 = {68} -> R6C5 = {1345}
11. 45 rule on N5 2 innies R46C5 = 11 -> R6C5 = {345}, R4C5 = {678}
12. 45 rule on R1234 2 innies R4C46 = 13 = {49/58/67}
13. 45 rule on R6789 2 innies R6C46 = 11 = {29/38/47/56} -> 1 in N5 locked in R5
14. 45 rule on R5 3 innies R5C456 = 10 = 1{27/36/45}
15. 45 rule on C5 3 innies R159C5 = 9 = {126/135/234} -> max. 6 in R1C5 or R5C5
16. Only valid combinations for 27(5) cage in N2 with R1C5 = max. 6 and R2C46 = {1234} are {13689/14589/14679/23589/23679/24579/24678/34569/34578} -> R1C5 = {56}, R1C46 = {6789}
17. Killer pair 5/6 in R1C5789, no other 5,6 in R1
18. R1C5 = {56} -> R159C5 = 1{26/35} (step 15) -> R59C5 = 1{2/3}, 1 in C5 locked in R59C5
19. 15(4) cage in N1 = {1239/1248/1347} = 1{239/248/347}, 1 locked for N1 -> 1 in R3 locked in N2 -> R3C6 = 1, R34C7 = {26/35}, R7C6 = 9 (step 9), R7C45 = {678}, R3C4 = {567} (step 8)
20. Naked triple {678} in R478C5 -> R1C5 = 5, R3C4 = {67}, R7C4 = {67}(step 8), killer pair 6,7 in C4
21. R6C5 = {34}, R4C5 = {78} (step 11), 6 in C5 locked in R78C5 -> R7C4 = 7, R78C5 = {68}, R6C5 = 4, R4C5 = 7, R3C4 = 6 (step 8), 6 in C6 locked in N5
22. R3C79 = {35}, 13(4) cage in N3 = {1246}, R4C7 = {35}
23. 9 in C5 locked in R23C5 -> R23C5 = {29}, R2C46 = {34}, R2C37 = {12}, R23C5 = [92], R2C89 = {78}, R3C8 = 9
24. 27(5) cage = {34578} -> R1C4 = 8, R1C6 = 7
25. R2C12 = {56}, R3C2 = 8
26. Only remaining combination for 15(4) cage in N1 (step 19) = {1239}, R3C13 = {47}, R4C3 = {47} -> R4C3 = 4, R3C3 = 7, R1C3 = 4
27. R4C46 = 13 (step 12) = [58], 5 in C6 locked in R89C6, R34C7 = [53], R3C9 = 3, R4C89 = {26}, R4C12 = {19}
28. R6C4 = 9 (single in C4) -> R6C6 = 2 (step 13), R289C6 = naked triple {345}, R5C6 = 6, R5C45 = {13}
29. 4,9 in N6 locked in C5 -> 21(3) cage = {489}, 14(3) cage in R5 = {257}
30. R7C4 = 7 (step 21), R7C3 = {13} -> R6C3 = {68} -> 3 in N4 locked in R6C12 -> R7C1 = 1, R6C12 = [83], R67C3 = [63], R4C12 = [91]
31. 8 in C3 locked in R89C3, only valid combination for 25(4) in N7 = {2689} ({4678} blocked by 4,6,7 in C3) -> R9C1 = {26}, R9C2 = {269}, R89C3 = {289}, 16(3) cage in N7 = {457}
32. 45 rule on R9 4 outies R8C3467 = 13 = 1{237/246/345}, 1 locked for R8, no 8,9 -> R8C3 = 2, R9C1 = 6, R9C2 = 9, R9C3 = 8, R9C4 = 2 (single in N8)
33. R1C2 = 2, R1C1 = 3, R2C3 = 1, R1C3 = 9, R2C7 = 2, R1C789 = {146}
34. 7 in R9 locked in N9, only valid combination for 18(4) cage = {1467} -> R8C7 = 6, R9C789 = {147}
35. R7C79 = 10 {step 7) = [82], R7C8 = 5, R8C89 = [39], R6C7 = 1, R6C89 = [75]
and the rest is simple elimination