Assassin 22

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nd
Hooked
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Posts: 45
Joined: Sun Jun 25, 2006 8:59 am
Location: Toronto

Assassin 22

Post by nd »

A very tough one, though no exotic tricks are required.

1. R23C3 = R34C5 = {79} (eliminating {79} in the rest of R3). 45 rule on C5 -> R56C5 = 13 = {58}. 45 rule on C1234 -> R56C4 = 5 = {14|23}. R56C6 = 17 + 14 - (13 + 5) = 13 = {49|67}.

2. 45 rule on R12 -> R2C3467 = 29 = {5789} -> R23C7 = [86|95], R2C46 = {5789} with 5 locked in those cells in R2/N2.

3. 45 rule on N5 -> R4C456 = 14. 45 rule on N2 -> R1C46 = 10. 45 rule on N1235 -> R3C1289 = 14. 45 rule on R1234 -> R5C19 = 4 = {13} -> R56C4 = [23|41], but placing 4 in R5C4 results in an impossible combo in the 14(3) cage so R56C4 = [23], R56C6 = [49|76], R4C46 = {1(4|6)} with 1 locked in those cells in R4/N5. 45 rule on R5 -> R6C37 = 10 = {28|46} ({19} is disallowed because a 1 can't go in a 19(3) cage).

4. 45 rule on C4 -> R1789C4 = 26 -> the 1 is locked in the 14(3) cage in C4 -> R1C46 = [46|64|73|82|91]. 45 rule on N3 -> R3C89 - R1C6 = 1 -> R1C6 <> 1 -> [91] is eliminated as a possibility from R1C46. We have now eliminated 9 from R1C456 -> X-wing on 9 on R23 in conjunction with R23C3 -> R23C7 = [86], R6C37 = [64|82].

5. 45 rule on R3 -> R3C46 = 9 = {18} (because {567} are blocked) -> R12C5 = {23}, R1C46 = {46}, R3C1289 = {2345} -> R3C1 = {45}, R3C2 = {234} -> R4C23 = {234}.

6. In N1 the 6 must go in the 12(3) cage = {(15|24)6} -> hidden {45} pair in conjunction with R3C1 -> R3C2 = {23} -> 4 is locked in N4/R4 in R4C23 -> R4C46 = {16}, R4C5 = 7, R3C5 = 9, R23C3 = [97], R56C6 = [49], R56C5 = [85], R1C46 = [46], R4C46 = [61], R3C46 = [18], R2C46 = [75], R1C23 = {28}, R3C2 = 3, R12C5 = [32], R1C78 = {19}.

7. Mop-up. 45 rule on N1 -> R3C1 = 4, R45C1 = [93], R78C1 = {28}, R5C9 = 1, R3C89 = [25], R4C9 = 8, R4C78 = {35}, 19(3) cage in N4 has a 5 locked in it -> R5C23 = {56}, R6C3 = 8, R1C23 = [82], R4C23 = [24], R5C78 = {79}, R6C7 = 2, R78C9 = {29} (because the 2 in N9/C9 cannot go in a 14(2) cage!), R9C89 = [86], R6C89 = {46}, R6C12 = {17}, R78C2 = {69}, R5C23 = [56], x-wing on 9 in R78 -> R9C4 = 9, R89C3 = {35}, R78C4 = {58}, R7C3 = 1, and you carry on....
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