Prelims
a) R1C12 = {29/38/47/56}, no 1
b) R2C56 = {14/23}
c) R3C45 = {17/26/35}, no 4,8,9
d) R45C8 = {14/23}
e) R56C2 = {29/38/47/56}, no 1
f) R8C45 = {17/26/35}, no 4,8,9
g) R89C9 = {49/58/67}, no 1,2,3
h) 11(3) cage at R1C8 = {128/137/146/236/245}, no 9
i) 22(3) cage at R3C6 = {589/679}
j) 20(3) cage at R3C9 = {389/479/569/578}, no 1,2
k) 11(3) cage at R4C3 = {128/137/146/236/245}, no 9
l) 11(3) cage at R8C1 = {128/137/146/236/245}, no 9
1a. 45 rule on R1 2 outies R2C49 = 8 = {17/26/35}, no 4,8,9
1b. Combined cage R2C49 + R2C56 = {17}{23}/{26}{14}/{35}{14}, 1 locked for R2
1c. 34(7) cage at R2C1 = {1234789/1235689/1245679/1345678}, 1 locked for C1
1d. 45 rule on R89 3 outies R7C278 = 20 = {389/479/569/578}, no 1,2
1e. 45 rule on C1 3 outies R129C2 = 11 = {128/137/146/236/245}, no 9, clean-up: no 2 in R1C1
1f. 45 rule on C9 4 innies R1267C9 = 12 = {1236/1245}, no 7,8,9, clean-up: no 1 in R2C4
1g. 45 rule on C9 2 outies R16C8 = 14 = [59/68/86]
1h. 11(3) cage at R1C8 can only contain one of 5,6,8 -> no 5,6 in R12C9, clean-up: no 2,3 in R2C4
1i. R67C9 must contain one of 5,6 -> 15(3) cage at R6C8 = 6{45}/8{16}/8{25}/9{15}, no 3 in R67C9
1j. 20(3) cage at R3C9 = {389/479/578} (cannot be {569} which clashes with R89C9), no 6
1k. 38(7) cage at R8C8 = {1256789/1346789/2345789}, CPE no 7,8,9 in R9C9, clean-up: no 4,5,6 in R8C9
1l. 45 rule on N2 5 innies R1C456 + R2C4 + R3C6 = 32 = {26789/35789/45689}, no 1
1m. 45 rule on N3 2 innies R1C7 + R3C9 = 13 = {49/58}/[67], no 1,2,3, no 7 in R1C7
1n. 45 rule on N23 2 innies R3C69 = 1 outie R1C3 + 14
1o. Max R3C69 = 17 -> max R1C3 = 3
1p. Min R3C69 = 15, no 4,5 in R3C69, clean-up: no 8,9 in R1C7
2a. 11(3) cage at R1C8 = {128/146/236/245}, R1267C9 (step 1f) = {1236/1245}, R1C7 + R3C9 (step 1m) = [49/58/67]
2b. Consider permutations for R89C9 = [76/85/94]
R89C9 = [76], no 7 in R3C9 => no 6 in R1C7 = {45} => 11(3) cage at R1C8 = {128/146/236} (cannot be {245} which clashes with R1C7)
or R89C9 = [85/94] => R1267C9 = {1236} => 11(3) cage at R1C8 = {128/236}
-> 11(3) cage at R1C8 = {128/146/236}, no 5, clean-up: no 9 in R6C8 (step 1g)
2c. Naked pair {68} in R16C8, locked for C8
2d. Consider placements for R1C8 = {68}
R1C8 = 6
or R1C8 = 8 => R67C9 = {45}, locked for C9 => R89C9 = [76]
-> R1C7 + R3C9 = [49/58], no 6,7
3a. 9 in R9 only in R9C345678, locked for 38(7) cage at R8C8, no 9 in R8C8
3b. 38(7) cage = {1256789/1346789/2345789}, 8 locked for R9
3c. 38(7) cage = {1256789/1346789/2345789} sees R9C9 = {456} -> 38(7) cage + R9C9 must contain all of 4,5,6, 6 locked for R9
3d. 45 rule on R9 3 outies R8C189 = 17
3e. Consider placement for 7 in R9
7 in R9C12 => 11(3) cage at R8C1 = [371] -> R8C89 = 14 = [59]
or 7 in R9C345678, locked for 38(7) cage
-> no 7 in R8C8
3f. 38(7) cage = {1256789/1346789/2345789}, 7 locked for R9
3g. 11(3) cage = {128/137/146/236/245}
3h. 6,7 of {137/236} must be in R8C1 -> no 3 in R8C1
3i. R8C189 = 17, max R8C89 = 14 -> no 2 in R8C1
3j. R89C9 = 13 -> R8C89 cannot total 13 (CCC) -> no 4 in R8C1
3k. 5 of {245} must be in R8C1 -> no 5 in R9C12
3l. 5 in R9 only in R9C3456789, CPE no 5 in R8C8
4a. 31(6) cage at R1C3 = {125689/134689/135679/145678/234589/234679/235678} (cannot be {124789} = 1{289}[47] which clashes with R1C12 + R1C8)
4b. R1C7 + R3C9 (step 2d) = [49/58], R3C69 = R1C3 + 14 (step 1n)
4c. 31(6) cage = {125689/135679/145678/234589/234679/235678} (cannot be {134689} = 1{389}[46] because then R3C69 = [79] = 16)
4d. 31(6) cage = {125689/145678/234589/234679/235678} (cannot be {135679} = 1{369}[57] because R3C69 cannot both be 8)
4e. 31(6) cage = {125689/234589/234679/235678} (cannot be {145678} = 1{4578}6 because R3C69 = [98] = 17), 2 locked for R2, clean-up: no 9 in R1C1
4f. 9 in R1 only in 31(6) cage = {125689/234589/234679}, locked for N2
4g. 22(3) cage at R3C6 = {589/679}, 9 locked for R4
4h. 8 of {589} must be in R3C6 -> no 8 in R4C67
[I was slow in spotting]
5a. 4 in N2 only in R1C456 or R2C56 = {14}
5b. Consider permutations for R1C7 + R3C9 (step 2d) = [49/58]
R1C7 + R3C9 = [49]
or R1C7 + R3C9 = [58] => R1C8 = 6, R12C9 = 5 = [32], R2C56 = {14}
or R1C8 = 6, R12C9 = 5 = [41]
-> no 4 in R1C456
5c. 4 in N2 only in R2C56 = {14}, locked for R2, 1 locked for N2, clean-up: no 7 in R2C4 (step 1a), no 7 in R3C45
5d. Killer pair 5,6 in R2C4 and R3C45, locked for N2
5e. 11(3) cage at R1C8 = [632/812] -> R1C9 = {13}, R2C9 = 2
5f. R1C12 = {47/56} (cannot be {38} which clashes with R1C89), no 3,8
5g. 31(6) cage at R1C3 (step 4f) = {125689/234679} (cannot be {234589} which clashes with R1C12) -> R2C4 = 6, clean-up: no 2 in R3C45, no 2 in R8C5
5h. 22(3) cage at R3C6 = {589/679}
5i. 7 of {679} must be in R3C6 -> no 7 in R4C67
6a. Naked pair {35} in R3C56, locked for R3, 3 locked for N2
6b. R1C39 = {13} (hidden pair in R1)
6c. 34(7) cage at R2C1 is missing two numbers totalling 11, R1C12 = 11 and R1C1 ‘sees’ all of the 34(7) cage -> the value in R1C2 must be in R89C1
6d. R1C2 = {4567} -> no 8 in R8C1
6e. 8 in C1 only in R234567C1, locked for 34(7) cage, no 8 in R2C2
6f. R129C2 (step 1e) = {137/236/245} (cannot be {146} because R2C2 only contains 3,5,7) = [731/632/452] -> R9C2 = {12}, no 5 in R1C2, no 7 in R2C2, clean-up: no 6 in R1C1
6g. No 5 in R1C2 -> no 5 in R8C1
6h. 11(3) cage at R8C1 = {137/146/236}, R9C2 = {12} -> no 2 in R9C1
7a. 7 in N3 only in 21(4) cage at R2C7 = {1479/1578} (cannot be {3567} which clashes with R2C2), 1 locked for R3 and N3
[Cracked, the rest is fairly straightforward.]
7b. R12C9 = [32] -> R1C8 = 6 (cage sum), R6C8 = 8 -> R67C9 = 7 = {16}, 6 locked for C9, clean-up: no 3 in R5C2, no 7 in R8C9
7c. R1C3 = 1 -> 31(6) cage at R1C3 (step 5g) = {125689} -> R1C7 = 5, R3C9 = 8, R8C9 = 9 -> R9C9 = 4, R9C1 = 3, clean-up: no 6 in R1C2
7d. Naked pair {79} in R2C78, locked for R2 and N3
7e. Naked pair {14} in R3C78, 4 locked for R3
7f. R3C6 = 7 -> R4C67 = 15 = {69}, 6 locked for R4
7g. R1C2 = R8C1 (step 6c) -> R1C2 = R8C1 = 7, R1C1 = 4, R9C2 = 1 (cage sum), clean-up: no 4 in R56C2
7h. R8C189 = 17 (step 3d), R8C19 = [79] -> R8C8 = 1, R3C78 = [14], R67C9 = [16]
[Alternatively 38(7) cage at R8C8 contains 6 so must contain 1.]
7i. Naked pair {23} in R45C8, locked for C8 and N6
7j. Naked pair {57} in R79C8, 7 locked for C8 and N9 -> R2C78 = [79]
7k. R7C278 (step 1d) = {578} (only possible combination because R7C7 only contained 3,8 and R7C8 only contained 5,7) = [587], R9C78 = [25], R8C7 = 3 -> R8C6 = 5 (cage sum), R8C45 = [26], R8C23 = {48}, locked for N7, clean-up: no 6 in R56C2
7l. Naked pair {29} in R7C13, 9 locked for R7 and N7 -> R9C3 = 6
7m. Naked pair {29} in R37C3, locked for C3
7n. 11(3) cage at R4C3 = {137} (only remaining combination) -> R4C4 = 1, R45C3 = {37}, locked for N4, 3 locked for C3, clean-up: no 8 in R5C2
7o. 1 in N8 only in R7C56 -> 13(3) cage at R6C6 = {139} (only remaining combination) -> R6C6 = 9, R7C56 = {13}, 3 locked for R7, R7C4 = 4, R4C67 = [69], R19C6 = [28], clean-up: no 2 in R5C2
7p. 7 in R6 only in R6C45, locked for N5
7q. 15(3) cage at R5C4 = {357} (only possible combination), 3,5 locked for N5 -> R5C6 = 4
7r. 45 rule on the whole grid R56C6 + R67C3 + R7C4 = 28, R56C6 = [64], R6C3 = 5, R7C4 = 4 -> R7C3 = 9
7s. R23C3 = [82], R4C2 = 4 -> R3C2 = 6 (cage sum)
and the rest is naked singles.