Prelims
a) R1C34 = {39/48/57}, no 1,2,6
b) R34C1 = {69/78}
c) R56C7 = {14/23}
d) R7C23 = {19/28/37/46}, no 5
e) R7C45 = {69/78}
f) R89C8 = {16/25/34}, no 7,8,9
g) R9C34 = {17/26/35}, no 4,8,9
h) 10(3) cage at R4C3 = {127/136/145/235}, no 8,9
i) 23(3) cage at R7C7 = {689}
1. Naked triple {689} in 23(3) cage at R7C7, locked for C7 and N9, clean-up: no 1 in R89C8
1a. 1,7 in N9 only in R7C8 + R789C9, CPE no 1,7 in R5C9
2. Killer quad 6,7,8,9 in R7C23, R7C45 and R7C7, locked for R7
2a. 7 in N9 only in R89C9, locked for C9
2b. 16(4) cage at R6C9 contains 7, rest of cage totals 9 -> no 8,9 in R6C9
3. 45 rule on C89 2 outies R14C7 = 12 = {57} (only remaining combination), locked for C7
3a. R1C34 = {39/48} (cannot be {57} which clashes with R1C7), no 5,7
[Ed pointed out that I missed CPE no 5 in R123C9, but I get these eliminations in step 4a.]
4. 45 rule on N69 3 innies R4C789 = 14 = {158/167/257/356} (cannot be {149/239/248} because R4C7 only contains 5,7, cannot be {347} which clashes with R56C7), no 4,9
4a. 45 rule on N69 3 outies R123C9 = 19 = {289/469} (cannot be {568} which clashes with R4C789), no 1,3,5, 9 locked for C9 and N3
5. 16(4) cage at R6C9 contains 7 = {1357} (cannot be {1267/2347} which clash with R123C9), 1,3,5 locked for C9
6. 45 rule on N9 1 outie R6C9 = 1 innie R7C8 + 1 -> R6C9 = {35}, R7C8 = {24}
6a. Killer pair 2,4 in R7C8 and R89C8, locked for C8
7. 25(4) cage at R5C8 = {2689/4678} (cannot be {1789/3589/3679} because R7C8 only contains 2,4, cannot be {4579} which clashes with R4C7), no 1,3,5, 8 locked for N6
7a. R7C8 = {24} -> no 2,4 in R5C9
7b. Killer pair 6,8 in R123C9 and R5C9, locked for C9 -> R4C9 = 2, clean-up: no 8 in R123C9 (step 4a), no 3 in R56C7
8. Naked triple {469} in R123C9, locked for C9 and N3 -> R5C9 = 8
8a. R4C789 (step 4) = {257} (only remaining combination), locked for R4 and N6, clean-up: no 8 in R3C1
8b. Naked pair {14} in R56C7, locked for C7
9. R6C9 = 3, R7C8 = 2 (step 6), clean-up: no 8 in R7C23, no 5 in R89C8
9a. Naked pair {34} in R89C8, locked for C8
10. 19(5) cage at R3C3 must contain 1, locked for R3
11. 45 rule on R1234 2 outies R5C36 = 9 = {27/36/45}, no 1,9
12. 45 rule on N5 2 innies R4C4 + R6C6 = 8 = [17/35/62]
13. 45 rule on N78 1 outie R6C6 = 1 innie R7C1 + 3 -> R6C6 = 7, R7C1 = 4, R4C4 = 1 (step 7), clean-up: no 2 in R5C3 (step 11), no 6 in R7C23, no 7 in R9C3
13a. Killer pair 7,9 in R7C23 and R7C45, locked for R7
14. R4C4 = 1 -> R45C3 = 9 = [36/45/63], clean-up: no 2,5 in R5C6 (step 11)
15. 45 rule on N4578 2 innies R4C12 = 12 = [84/93], clean-up: no 9 in R3C1
15a. Killer pair 3,4 in R4C2 and R45C3, locked for N4
15b. 4 in N4 only in R4C23, locked for R4
16. 45 rule on N7 3 remaining outies R8C4 + R9C45 = 11, no 9 in R8C4 + R9C5, no 7,8 in R9C5 (because no 1 in R89C4)
17. 45 rule on N7 3 remaining innies R8C3 + R9C23 = 14 = {158/257/356} (cannot be {167/239} which clash with R7C23), no 9, 5 locked for N7
17a. 3 of {356} must be in R89C3 (R89C3 cannot be {56} which clashes with R45C3), no 3 in R9C2
17b. R8C3 + R9C23 = {158/257/356}, CPE no 5 in R9C5
17c. 17(3) cage at R8C1 = {269/278/368} (cannot be {179} which clashes with R7C23), no 1
18. 18(3) cage at R4C5 = {369/468}, 6 locked for N5
19. 26(5) cage at R6C6 contains 7 = {13679/14579/23579/24578} (cannot be {14678/23678} which clash with R7C45)
19a. Killer pair 8,9 in 26(5) cage and R7C45, locked for N8
20. R8C4 + R9C45 = 11 (step 16) = {137/146/236/245}
20a. 3 of {137/236} must be in R9C45 (R9C45 cannot total 8 which clashes with R9C34, CCC), no 3 in R8C4
20b. 7 of {137} must be in R8C4 -> no 7 in R9C4, clean-up: no 1 in R9C3
[Ed commented that he saw the elimination in step 20a as
45 rule on N7 2 remaining outies R8C4 + R9C5 = 1 innie R9C3 + 3, IOU no 3 in R8C4.
He often finds IOUs for steps where I’ve found CCCs.]
[There’s probably a better way to make the next elimination.]
21. 17(4) cage at R8C3 = {1268/1358/1367/1457/2348/2357/2456}
21a. R8C4 + R9C45 (step 20) = {146/236/245} (cannot be {137} = [731] because [731] with 17(4) cage = {1367} clashes with R89C8), no 7 in R8C4
[Ed said that he didn’t use this step in his optimised walkthrough but pointed out another way to make this elimination
7 in R7 only in R7C23 = {37} or 7 in R7C45 -> 17(4) cage at R8C3 cannot be {36}[71] and there’s no other way to have 7 in N8 because of R8C4 + R9C45.]
22. 7 in N8 only in R7C45 = {78}, locked for R7 and N8 -> R7C7 = 6, clean-up: no 3 in R7C23
22a. Naked pair {19} in R7C23, locked for R7 and N1 -> R7C9 = 5, R7C6 = 3, clean-up: no 6 in R5C3 (step 11), no 3 in R4C3 (step 14), no 5 in R9C3
23. R8C4 + R9C45 (step 20) = {146/245}, 4 locked for N8
24. R8C3 + R9C23 (step 17) = {257/356}, no 8, 5 locked for 17(4) cage at R8C3, no 5 in R8C4
24a. 6 of {356} must be in R89C3 (R89C3 cannot be [53] which clashes with R5C3), no 6 in R9C2
25. R8C4 + R9C45 (step 23) = {146/245}
25a. 6 of {146} must be in R9C4 -> no 6 in R8C4 + R9C5
25b. 5,6 only in R9C4 -> R9C4 = {56}, clean-up: no 6 in R9C3
25c. Killer pair 2,3 in 17(3) cage at R8C1 and R9C3, locked for N7
26. R8C4 + R9C45 (step 20) = {146/245}
26a. 4 of {146} must be in R8C4, 4 of {245} must be in R8C4 (cannot be [254] because R9C345 = [354] clashes with R9C8, killer combo blocker) -> R8C4 = 4, R89C8 = [34], clean-up: no 8 in R1C3
26b. Killer quad 1,2,5,7 in R9C2, R9C34, R9C5 and R9C9, locked for R9
[With hindsight, if I’d seen steps 28a and 29 earlier, step 26a wouldn’t have been needed but something like step 21a would still have been needed to give the hidden single 7 in C3.]
27. 17(3) cage at R8C1 (step 17c) = {278/368}
27a. 3 in {368} must be in R9C1 -> no 6 in R9C1
27b. 6 in N7 only in R8C123, locked for R8
28. 45 rule on N4578 1 innie R3C1 = 1 outie R4C2 + 3 -> R3C1 + R4C2 = [63/74]
28a. 45 rule on R12 using R123C9 = 19 (step 4a) 4(3+1) outies R3C289 + R4C2 = 23 = {289}4/{568}4/{479}3 (cannot be {389}3 because 3 only in R34C2, cannot be {469}4 because R3C8 only contains 5,7,8, cannot be {578}3 because R3C9 only contains 4,6,9, cannot be {379}4/{478}4/{469}3 which clash with R3C1 + R4C2)
28b. 19(5) cage at R3C3 = {12349/12358/13456} (cannot be {12367} which clashes with R3C1, cannot be {12457} which clashes with R3C289), no 7, 3 locked for R3
29. 7 in N2 only in R1C5 + R2C45, CPE no 7 in R2C3
[Cracked. The rest is fairly straightforward.]
30. R8C3 = 7 (hidden single in C3), R89C9 = [17], R9C2 = 5, R9C4 = 6, R9C3 = 2, R9C5 = 1, R9C6 = 9, R89C7 = [98], R9C1 = 3
31. 18(3) cage at R4C5 (step 18) = {468} (only remaining combination, cannot be {369} because 3,9 only in R4C5) -> R5C6 = 4, R4C56 = {68}, locked for R4 and N5 -> R4C1 = 9, R3C1 = 6, R4C2 = 3 (step 15), R45C3 = [45], R56C7 = [14], R8C12 = [86], clean-up: no 8 in R1C4
32. Naked pair {27} in R5C12, locked for R5 and N4 -> R6C123 = [186], R56C8 = [69]
33. 5 in C1 only in 21(5) cage at R1C1 = {23457} (only remaining combination), no 1,9
33a. R17C2 = {19} (hidden pair in C2)
34. Naked pair {39} in R1C34, locked for R1 -> R1C2 = 1, R7C23 = [91]
34a. R1C2 = 1 -> R1C5 + R2C34 = 21 = {489/579/678}, no 2,3
34b. Naked pair {39} in R15C4, locked for C4
35. R4C2 = 3 -> R3C289 + R4C2 (step 28a) = {479}3 -> R3C8 = 7, R3C9 = 9, R3C2 = 4, R1C7 = 5, R12C8 = [81]
36. R3C6 = 1 (hidden single in R3)
36a. 5 in R3 only in R3C45, locked for N2
37. R8C6 = 5 (hidden single in C6),, R8C5 = 2
38. 2 in C6 only in R12C6, locked for N2 and 18(4) cage at R1C6 -> R2C7 = 3
38a. 18(4) cage at R1C6 contains 2,3 = {2367} (only remaining combination, cannot be {2349} because 4,9 only in R2C5) -> R2C5 = 7, R12C6 = {26}, locked for C6 and N2 -> R1C5 = 4
and the rest is naked singles.
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A routine start to get you excited then just one advanced step (not complicated) and a good few hard to see normal assassinations. So, in short, keep it simple and it will eventually come out. Very satisfying puzzle. It gets a SudokuSolver score of 1.40, which seems to be the score that gives me satisfying puzzles more times than any other score. Ticks all the boxes for a really good Assassin.
