Prelims
a) R12C1 = {19/28/37/46}, no 5
b) R1C23 = {15/24}
c) R12C4 = {18/27/36/45}, no 9
d) R2C23 = {89}
e) R3C45 = {79}
f) R4C45 = {19/28/37/46}, no 5
g) R78C2 = {59/68}
h) R89C7 = {89}
i) 11(3) cage at R7C3 = {128/137/146/236/245}, no 9
j) 19(3) cage at R7C6 = {289/379/469/478/568}, no 1
k) 11(3) cage at R8C8 = {128/137/146/236/245}, no 9
l) 14(4) cage at R8C1 = {1238/1247/1256/1346/2345}, no 9
m) 28(7) cage at R2C6 = {1234567}, no 8,9
1a. 45 rule on N14 1 outie R7C1 = 8, clean-up: no 2 in R12C1, no 6 in R78C2
1b. Naked pair {59} in R78C2, locked for C2 and N7 -> R2C23 = [89], clean-up: no 1 in R12C1, no 1 in R1C3, no 1 in R1C4
1c. Naked pair {79} in R3C45, locked for R3 and N2, clean-up: no 2 in R12C4
1d. Naked pair {89} in R89C7, locked for C7 and N9
1e. 9 in N3 only in R1C89 -> 16(3) cage at R1C7 = {169/259/349}, no 7,8
1f. R1C1 = 7 (hidden single in R1) -> R2C1 = 3, clean-up: no 6 in R1C4
1g. 45 rule on N7 1 outie R7C4 = 2 -> R78C3 = 9 = {36}, locked for C3 and N7, clean-up: no 8 in R4C5
1h. 6 in N1 only in R3C12, locked for R3 and 15(4) cage at R3C1, no 6 in R4C12
1i. 15(4) cage = {1356/2346}, no 9 -> R4C2 = 3, clean-up: no 7 in R4C45
1j. 45 rule on N2 2 innies R23C6 = {12}, locked for C6, N2 and 28(7) cage at R2C6, clean-up: no 8 in R1C4
1k. Naked quint {34567} in R4C6 + R5C456 + R6C4, locked for N5
1l. 45 rule on N8 2 remaining innies R78C5 = 7 = {16/34}
1m. 45 rule on N8 2 outies R6C56 = 10 = [19/28]
1n. 45 rule on N3 2 outies R4C79 = 13 = [49/58]/{67}, no 1,2, no 4,5 in R4C9
1o. Naked quad {1247} in 14(4) cage at R8C1, 7 locked for R9
1p. 3 in R3 only in R3C789, locked for N3, clean-up: no 4 in 16(3) cage at R1C7
1q. R1C23 = {24} (cannot be [15] which clashes with 16(3) cage), locked for R1 and N1, clean-up: no 5 in 16(3) cage, no 5 in R2C4
1r. Naked triple {169} in 16(3) cage, 1,6 locked for N3, 6 locked for R1
1s. R2C45 = {46} (hidden pair in N2), 4 locked for R2
1t. Naked triple {156} in R3C123, 1,5 locked for R3 -> R23C6 = [12]
1u. 15(4) cage = {1356} (only remaining combination, cannot be {2346} because 2,4 only in R4C1), 5 locked for C1
1v. Killer pair 4,6 in R2C5 and R78C5, locked for C5
1w. Killer pair 8,9 in R6C6 and 19(3) cage at R7C6, locked for C6 -> R1C5 = 8 (hidden single in R1)
2a. 18(4) cage at R2C7 = {2367/2457} (cannot be {3456} because R2C78 must contain two of 2,5,7), 2 locked for R2
2b. R3C7 = {34} -> no 4 in R4C7, clean-up: no 9 in R4C9
2c. 8 in R3 only in R3C89, locked for 24(4) cage at R2C9, no 8 in R4C9, clean-up: no 5 in R4C7
2d. Naked pair {67} in R4C79, locked for R4 and N6
2e. 24(4) cage at R2C9 = {3678/4578}, 7 locked for C9
2f. 45 rule on N4 4 innies R45C13 = 23 must contain 8 for N4 = {1589/4568} (cannot be {2489/2678} because R4C1 only contains 1,5), no 2,7, 5 locked for N4
2g. 6,9 only in R5C1 -> R5C1 = {69}
3a. R78C5 (step 1l) = {16/34}
3b. 19(3) cage at R7C6 = {379/478/568} (cannot be {469} which clashes with R78C5)
3c. Hidden killer pair 6,7 in R5C6 and 19(3) cage for C6, 19(3) cage only contains one of 6,7 -> R5C6 = {67}
3d. 17(3) cage at R8C4 = {179/359/458} (cannot be {368/467} which clash with R78C5), no 6
3e. 7 of {179} must be in R8C4 -> no 1 in R8C4
3f. Consider permutations for R6C56 (step 1m) = [19/28]
R6C56 = [19] => R78C5 = {34}, locked for N8 => 17(3) cage = {179}
or R6C56 = [28] => R4C45 = {19}, then caged X-Wing for 9 in R3C45 and R4C45, no other 9 in C45 => 17(3) cage = {458}
-> 17(3) cage = {179/458}, no 3
3g. 5 of {458} must be in R9C5 -> no 5 in R89C4
3h. 19(3) cage = {379/568} (cannot be {478} which clashes with 17(3) cage), no 4
3i. 45 rule on N9 3 outies R6C789 = 15 = {159/258/348} (cannot be {168/249} which clash with R6C56)
3j. Consider placement for 3 in R6
R6C4 = 3 => R12C4 = [54] => 17(3) cage = {179}
or R6C789 = {348}, 8 locked for R6 => R6C56 = [19] => R78C5 = {34}, 4 locked for N8
-> 17(3) cage = {179}
[Cracked. The rest is straightforward.]
3k. 17(3) cage = {179} -> R8C4 = 7, R3C45 = [97], R9C45 = [19], R89C7 = [98], R78C2 = [95], R4C4 = 8 -> R4C5 = 2, R6C56 = [19], clean-up: no 6 in R78C5
3l. Naked pair {34} in R78C5, locked for C5, 3 locked for N8 -> R2C5 = 6, R1C6 = 3 (hidden single in C6), R5C5 = 5, R4C6 = 4, R58C6 = [78] (hidden pair in C6)
4a. R8C1 = 1 (hidden single in N7) -> R34C1 = [65], R3C2 = 1, R34C1 = [51], R5C1 = 9 -> R5C3 =8 (cage sum)
4b. R4C8 = 9 -> R5C789 = 8 = {134}, 3,4 locked for R5 and N6 -> R5C4 = 6, R5C2 = 2, R6C1 = 4, R1C23 = [42], R9C1 = 2
4c. 3 in R9 only in R9C89 -> 11(3) cage at R8C8 = {236} (only possible combination) -> R8C8 = 2, R9C89 = {36}, locked for N9, 6 locked for R9, R8C9 = 4
4d. R2C7 = 2 (hidden single in R2), R6C7 = 5, R7C78 = 8 = {17}, 1 locked for N9 -> R7C9 = 5, R6C8 = 8
4e. R24C9 = [76] = 13 -> R3C89 = 11 = [38]
and the rest is naked singles.
Login
Register
FAQ
Search
