Prelims
a) R23C4 = {14/23}
b) 8(2) cage at R5C4 = {17/26/35}, no 4,8,9
c) 17(2) cage at R5C5 = {89}
d) 10(2) cage at R6C5 = {19/28/37/46}, no 5
e) R6C78 = {15/24}
f) 20(3) cage at R1C1 = {389/479/569/578}, no 1,2
g) 20(3) cage at R2C7 = {389/479/569/578}, no 1,2
h) 19(3) cage at R3C3 = {289/379/469/478/568}, no 1
i) 21(3) cage at R7C2 = {489/579/678}, no 1,2,3
j) 20(3) cage at R7C5 = {389/479/569/578}, no 1,2
k) 21(3) cage at R8C9 = {489/579/678}, no 1,2,3
l) 10(3) cage at R9C5 = {127/136/145/235}, no 8,9
m) 28(4) cage at R1C5 = {4789/5689}, no 1,2,3
n) 13(4) disjoint cage at R1C3 = {1237/1246/1345}, no 8,9
o) 13(4) cage at R2C2 = {1237/1246/1345}, no 8,9
p) 18(5) cage at R1C7 = {12348/12357/12456}, no 9
1. 45 rule on N3 1 innie R3C7 = 7
1a. 20(3) cage at R2C7 = {389/569}, no 4
2. 45 rule on N7 1 innie R7C3 = 3
3. Naked pair {89} in 17(2) cage at R5C5, locked for N5
3a. 45 rule on N5 2 innies R5C4 + R6C5 = 3 = {12}, locked for N5
3b. 8(2) cage at R5C4 = [17/26]
3c. 10(2) cage at R6C5 = [19/28]
3d. Naked pair {89} in R67C4, locked for C4
3e. Killer pair 1,2 in R23C4 and R5C4, locked for C4
3f. Killer pair 1,2 in R6C5 and R6C78, locked for R6
3g. Killer pair 8,9 in R7C4 and 20(3) cage at R7C5, locked for R7
3h. Min R89C4 = 8 (cannot be {34} which clashes with R23C4) -> max R8C5 = 6
4. 28(4) cage at R1C5 = {4789/5689}, 8,9 locked for N2
5. 45 rule on N14 2 innies R16C3 = 8 = [17/26]
5a. 45 rule on N89 2 innies R7C49 = 10 = [82/91]
5b. R1C3 + R7C9 = {12} -> 13(4) disjoint cage at R1C3 = {1237/1246}, no 5
5c. R1C3 + R7C9 = {12}, CPE no 1,2 in R1C9
6. Hidden killer pair 1,2 in R1C3 and R1C78 for R1, R1C3 = {12} -> R1C78 must contain one of 1,2 -> R23C9 must contain one of 1,2
6a. Killer pair 1,2 in R23C9 and R7C9, locked for C9
7. 45 rule on N2 3 innies R1C4 + R3C56 = 12 = {147/156/237} (cannot be {246/345} which clash with R23C4) -> R1C4 = {67}, R3C56 = {14/15/23}, no 6
7a. 13(4) disjoint cage at R1C3 (step 5b) = {1237/1246} -> R6C9 = {34}
7b. Max R89C4 = 12 (cannot be {67} which clashes with R1C4) -> min R8C5 = 2
8. 45 rule on N6 3 innies R45C7 + R6C9 = 14 = {239/248/356} (cannot be {149} which clashes with R6C78, cannot be {158} because R6C9 only contains 3,4), no 1
8a. R6C9 = {34} -> no 3,4 in R45C7
8b. Killer pair 2,5 in R45C7 and R6C78, locked for N6
9. 15(4) cage at R7C8 = {1239/1248/1257/1347/1356/2346}
9a. 8,9 of {1239/1248} must be in N9 (R7C8 + R8C78 cannot be {124/125} which clash with R7C9) -> no 8,9 in R8C6
9b. Hidden killer pair 8,9 in R7C4 and R7C56 for N8, R7C4 = {89} -> R7C56 must contain one of 8,9
9c. Killer pair 8,9 in R7C4 and R7C56, locked for R7
9d. 20(3) cage at R7C5 = {479/569/578}
9e. 4 of {479} must be in R7C7 -> no 4 in R7C56
10. 13(4) cage at R2C2 = {1237/1246/1345}
10a. 6,7 of {1237/1246} must be in N1 (R2C23 + R3C2 cannot be {123/124} which clash with R1C3) -> no 6,7 in R4C2
11. 45 rule on N9 3 innies R7C79 + R9C7 = 1 outie R8C6 + 9
11a. Min R7C79 + R9C7 = 10 cannot be [622] -> min R9C7 = 3
11b. Max R7C79 + R9C7 = 13 -> max R8C6 = 4
11c. 10(3) cage at R9C5 = {136/145/235} (cannot be {127} because 1,2,7 only in R9C56), no 7
[I’m a bit out of practice with Assassins, so maybe it’s a bit early to try a forcing chain …]
12. 20(3) cage at R7C5 = {479/569/578}, 10(3) cage at R9C5 (step 11c) = {136/145/235}
12a. Consider combinations for 14(3) cage at R8C4 = {257/347/356}
14(3) cage = {257/347}, 7 locked for N8 => 20(3) cage = {569}
or 14(3) cage = {356}, locked for N8 -> 10(3) cage = {14}5 => 20(3) cage = {479} (cannot be {78}5)
-> 20(3) cage = {479/569}, 9 locked for R7
12b. R7C4 = 8 -> R6C5 = 2, R5C4 = 1 -> R6C3 = 7, 17(2) cage at R5C5 = [89], clean-up: no 4 in R23C4, no 4 in R6C78
12c. Naked pair {23} in R23C4, locked for C4 and N2
12d. Naked pair {15} in R6C78, locked for R6 and N6
12e. 14(3) cage at R8C4 = {347/356} -> R8C5 = 3
12f. Killer pair 6,7 in R1C4 and R89C4, locked for C4
12g. R6C3 = 7 -> R1C3 = 1 (step 5) -> R7C9 = 2
12h. 10(3) cage at R9C5 (step 11c) = {136/145/235}
12i. 3 of {136} must be in R9C7 -> no 6 in R9C7
13. 13(4) cage at R2C2 = {1237/1246/1345} -> R4C2 = 1
13a. 45 rule on N1 2 remaining innies R3C13 = 12 = [39/48/84]
13b. 2 in N1 only in 13(4) cage = {1237/1246}, no 5
13c. Killer pair 3,4 in 13(4) cage and R3C13, locked for N1
14. 15(4) cage at R7C8 = {1248/1257}, no 6,9 -> R8C6 = 2
14a. 9 in N9 only in 21(3) cage at R8C9 = {489/579}, no 6
14b. R7C7 = 6 (hidden single in N9) -> R7C56 = 14 = {59}, locked for R7 and N8
14c. 14(3) cage at R8C4 = {347} (only remaining combination), 4,7 locked for C4 and N8 -> R1C4 = 6, R6C9 = 4 (cage sum), R4C4 = 5
14d. Naked pair {16} in R9C56, locked for R9, R9C7 = 3 (cage sum)
15. 45 rule on N2 2 remaining innies R3C56 = 6 = {15}, locked for R3 and N2, R3C7 = 7 -> R45C7 = 10 = [82]
16. 8 in R6 only in 16(3) cage at R5C2 = {358} (only possible combination) -> R5C2 = 5, R6C12 = {38}, locked for R6 and N4 -> R6C6 = 6, R9C56 = [61], R3C56 = [15], R7C56 = [59]
17. R1C78 + R2C9 = [421] (hidden triple in N3)
17a. 28(4) cage at R1C5 = {4789}, 4 locked for R2
17b. R2C7 = 9 (hidden single in C7) -> R1C5 = 9 (hidden single in N2)
17c. 20(3) cage at R1C1 = {578} (only remaining combination), locked for N1, 5 also locked for C1 -> R3C13 (step 13a) = [39]
17d. R3C3 = 9 -> R45C3 = 10 = {46}, locked for C3 and N4, R2C23 = [62], R3C3 = 4
17e. R7C2 = 7 -> R8C23 = 14 = [95]
17f. R1C9 = 3 (hidden single in R1) -> R3C9 = 8 (cage sum)
and the rest is naked singles.