Prelims
a) R2C34 = {19/28/37/46}, no 5
b) R2C67 = {16/25/34}, no 7,8,9
c) R8C34 = {49/58/67}, no 1,2,3
d) R8C67 = {29/38/47/56}, no 1
e) 19(3) cage at R1C1 = {289/379/469/478/568}, no 1
f) 8(3) cage at R1C2 = {125/134}
g) 21(3) cage at R1C6 = {489/579/678}, no 1,2,3
h) 19(3) cage at R7C7 = {289/379/469/478/568}, no 1
i) 11(3) cage at R8C8 = {128/137/146/236/245}, no 9
j) 26(4) cage at R6C2 = {2789/3689/4589/4679/5678}, no 1
k) 14(4) cage at R6C6 = {1238/1247/1256/1346/2345}, no 9
1a. 45 rule on C5 1 innie R5C5 = 5, placed for both diagonals
1b. 45 rule on C1234 2 innies R5C34 = 7 = {16/34}
1c. 45 rule on C6789 2 innies R5C67 = 17 = {89}, locked for R5
2a. 8(3) cage at R1C2 = {125/134}, 1 locked for R1
2b. 45 rule on N1 3 innies R1C23 + R2C3 = 8 = {125/134}, 1 locked for N1
2c. 45 rule on N1 2 outie R12C4 = 10 = [19/28/37/46]
3a. 45 rule on R89 2 outies R67C5 = 6 = {24}, locked for C5
3b. 45 rule on R89 2 innies R89C5 = 9 = {18/36}
3c. 45 rule on R12 2 innies R12C5 = 10 = {37}/[91]
3d. 45 rule on R12 2 outies R34C5 = 15 = {69/78}
4a. 45 rule on N3 2 outies R12C6 = 10 = [46/64/73/82/91], no 5, clean-up: no 2 in R2C7
4b. 45 rule on N7 2 outies R89C4 = 12 = {48/57}/[93], no 6 in R8C4, no 1,2,6,9 in R9C4, clean-up: no 7 in R8C3
4c. 45 rule on N9 2 outies R89C6 = 12 = {39/48/57}, no 1,2,6, clean-up: no 5,9 in R8C7
4d. 2 in N8 only in R7C456, locked for R7
4e. 45 rule on R7 3 innies R7C456 = 12 contains 2 = {129/246} (cannot be {237} which clashes with R89C46), no 3,5,7,8
5a. 45 rule on R1234 2 innies R4C19 = 10 = {19/28/37/46}, no 5
5b. 45 rule on R6789 2 innies R6C19 = 11 = {29/38/47/56}, no 1
5c. 1 in R6 only in R6C678, locked for 14(4) cage at R6C6
5d. 14(4) cage contains 1 = {1238/1247/1256/1346}
5e. R7C456 (step 4e) = {246} (only remaining combination), 4,6 locked for R7 and N8, clean-ups: no 9 in R8C3, no 3 in R89C5 (step 3b), no 7 in R8C7
5f. Naked pair {18} in R89C5, locked for C5, 8 locked for N8, clean-ups: no 9 in R1C5 (step 3c), no 5 in R8C3, no 3 in R8C7
5g. Naked pair {37} in R12C5, locked for N2, 7 locked for C5, clean-ups: no 3 in R2C3, no 4 in R2C7
5h. 19(3) cage at R7C7 = {379} (only remaining combination), locked for R7 and N9
5i. Naked triple {158} in 14(3) cage at R7C1, locked for N7, clean-ups: no 5 in R8C4, no 7 in R9C4 (step 4b)
5j. 5 in N2 only in R3C46, locked for R3
5k. 45 rule on R3 3 innies R3C456 = 15 = {159/456} (cannot be {258} because R3C5 only contains 6,9), no 2,8
5l. R3C5 = {69} -> no 6,9 in R3C46
5m. 16(3) cage at R8C1 = {349/367}, no 2, 3 locked for N7
5n. Killer pair 4,6 in 16(3) cage and R8C3, locked for N7
5o. 2 in N7 only in R9C23, locked for R9
5p. 14(3) cage at R9C2 = {239/257}
5q. 16(3) cage at R9C6 = {169/349/457} (cannot be {178} which clashes with R9C5, cannot be {358} which clashes with R9C4, cannot be {367} which clashes with 14(3) cage), no 8
5r. 7,9 only in R9C6 -> R9C6 = {79}, R8C6 = {35} (step 4c), clean-up: no 2,4 in R8C7
5s. Naked triple {279} in R9C236, 7,9 locked for R9
5t. 45 rule on R9 3 innies R9C159 = 15 = {168/348}
5u. 6 of {168} must be in R9C1, 3 of {348} must be in R9C1 -> R9C1 = {36}, no 6 in R9C9
5v. 4 in N7 only in R8C123, locked for R8
5w. 45 rule for N7 1 innie R8C3 = 1 outie R9C4 + 1
5x. Naked pair {35} in R8C6 + R9C4 -> R8C37 = [68/46], 6 locked for R8
6a. 45 rule on R1 3 innies R1C159 = 16 = {349/358/367/457} (cannot be {259/268} because R1C5 only contains 3,7), no 2
[Forgot that I’d already eliminated 5 from R1C19 in step 1a. Doesn’t matter after the next sub-step, which also removed the need to lock 3 for R1.]
6b. 2 in R1 only in 8(3) cage at R1C2 = {125}, 5 locked for R1 and N1, clean-ups: no 6 in R2C4 (step 2c), no 4 in R2C3
6c. Naked triple {125} in R1C23 + R2C3, 2 locked for N1
6d. 21(3) cage at R1C6 = {489/678}, 8 locked for R1
6e. 2 in R3 only in R3C789, locked for N3
7a. R1C159 (step 6a) = {349/367}
7b. 3 of {349/367} must be in R1C5 (cannot be [376/673] which clash with R9C1 using D/) -> R1C5 = 3, R2C5 = 7
[The first fun step.]
7c. 18(3) cage at R3C1 = {378/468} (cannot be {369} which clashes with R3C5), no 9, 8 locked for R3 and N1
8a. 45 rule on N3 1 outie R1C6 = 1 innie R2C7 + 3
8b. 45 rule on N3 3 innies R1C78 + R2C7 = 18 = {189/378/459/468/567} (cannot be {369} = {69}3 which clashes with R1C6 + R2C7 = [63])
8c. 15(3) cage at R1C9 = {159/348/357/456} (cannot be {168} = 6{18} which clashes with R2C34)
8d. 9 of {159} must be in R1C9 -> no 9 in R2C89
8e. 4 of {348} must be in R1C9, 5 of {456} must be in R2C9 -> no 4,6 in R2C9
8f. R1C19 (step 7a) = {49/67}
8g. Consider placements for R9C1 = {36}
8h. R9C1 = 3 => R9C4 = 5 => R8C9 = 5 (hidden single in N9), no 5 in R2C9 => 15(3) cage = {348}
or R9C1 = 6, no 6 in R1C1 and R1C9 + R2C8 using D/ => R1C19 = {49} => 15(3) cage = {159/348}
-> 15(3) cage = {159/348}, no 6,7, clean-up: no 6,7 in R1C1
[Cracked after the second fun step.]
9a. Naked pair {49} in R1C19, locked for R1, clean-ups: no 1,6 in R2C6 (step 4a), no 1,6 in R2C7
9b. 7 in N1 only in 18(3) cage at R3C1 (step 7c) = {378}, 3,7 locked for R3, 3 locked for N1
9c. Naked pair {49} in R1C19, CPE no 4 in R9C9 using D\
9d. 11(3) cage at R8C8 = {128} (only remaining combination), 1,8 locked for N9
9e. R8C7 = 6 -> R8C6 = 5, R8C3 = 4 -> R8C4 = 9, R9C46 = [37], R9C1 = 6, placed for D/, clean-ups: no 4 in R4C9 (step 5a), no 5 in R6C9 (step 5b)
9f. Naked pair {49} in R12C1, locked for C1 and N1, R2C2 = 6, placed for D\, clean-ups: no 1,6 in R4C9 (step 5a), no 2,7 in R6C9 (step 5b)
9g. R3C4 = 5 (hidden single in R3)
9h. R2C9 = 5 (hidden single in C9) -> R1C9 + R2C8 = 10 = [91], both placed for D/, clean-ups: no 1 in R4C1 (step 5a), no 2 in R6C1 (step 5b)
9i. R1C1 = 4, placed for D\, R2C34 = [28], R2C67 = [43], R1C6 = 6, R3C56 = [91], R1C4 = 2, R4C5 = 6, R7C3 = 8, placed for D/, R7C456 = [642], R6C5 = 2
9j. R4C6 = 3, placed for D/, R6C6 = 8, placed for D\, clean-up: no 7 in R4C19 (step 5a)
9k. Naked pair {28} in R4C19, locked for R4
9l. R34C6 = [13] = 4 -> R4C78 = 14 = {59}, locked for N6, 9 locked for R4
9m. R8C2 = 7, placed for D/ -> R6C4 = 4, placed for D/, R5C4 = 1 -> R5C3 = 6 (cage sum), R4C4 = 7, placed for D\
9n. R67C4 = [46] = 10 -> R6C23 = 16 = [97]
9o. R6C67 + R7C6 = [812] -> R6C8 = 3 (cage sum)
and the rest is naked singles, without using the diagonals.