Weekly Assassin - Aug 11

[nd]

No-one posting walkthroughs anymore? Here's one.

Step 1. R7C89 = {79}. Innie-outie difference on N9 -> R7C7 = 1, R9C6 = 9. 45 rule on N8 -> R9C4 = 5. 45 rule on N7 -> R7C3 = 2, R7C12 = {35}, R7C456 = {468}, R89C5 = {27}, R8C46 = {13}.

Step 2. In C5 the 1 is blocked from R12789C5. It also cannot go in the 17(3) cage as this would make it {179} (and 7 is already blocked). So R3C5 = 1; 45 rule on C5 -> R7C5 = 6, 5 is locked in N5 in the 17(3) cage. Since {59} is now blocked from R6C6, R6C67 = {68}. 45 rule on N6 -> R46C7 = 14 -> R4C7 = {68}, R4C89 = {59}, R6C34 = {19|37}. 45 rule on N4 -> R46C3 = [19] or {37}.

Step 3. In N3, the 8 cannot go in the 9(2) cage (because {18} is blocked) nor in the 10(3) cage of course, & it's blocked from R123C7, so R2C8 = 8. 45 rule on R12 -> R2C46 = 10 = {37|46}, producing a hidden {34} pair in N2 in conjunction with the 12(2) cage (which is {39|48}! 45 rule on N2 -> R1C46 = 9 = {27} (since {134} are blocked). R2C46 = {46}, R12C5 = {39}, R3C46 = [85], R1C3 = 8.

Step 4. 45 rule on N123 -> R3C37 = 11. So we have two 11(2) cages in R3, neither of which can contain a 6 (because {56} is blocked}, so R3C89 = {36}. The 1 in N3 must go in the 10(3) cage (can't go in a 26(4) cage). 45 rule on N3 -> R1C6 = R3C7 = {27}, so the 10(3) cage cannot contain {127} -> the only possibility is that the 10(3) cage contains {145} -> R2C7 = {27}, R1C7 = 9, R12C5 = [39]. 6 is locked in R1 in the 10(3) cage in N1 -> R1C12 = {16}, R2C1 = 3, R7C12 = [53], R1C89 = {45}, R2C9 = 1.

Step 5. Basically mopping up from here on in. R8C7 = 5 -> remaining two cells in the 23(4) cage = 9 = {36} -> R9C7 = 3, R8C8 = 6, R3C89 = [36], R5C7 = 4, R56C8 = {17}, R56C9 = {23}, R7C89 = [97], R4C89 = [59], R1C89 = [45], R9C8 = 2, R89C9 = {48}, R89C5 = [27]. In N7 the 1 cannot go in the 17(3) cage as this would create {179} and {79} is blocked from two of its cells -> R9C3 = 1, R46C3 = R6C4 = {37}, R56C8 = [71], R56C9 = [32], R8C23 = [89].... and you carry on.

[sudokuEd]

And a nice walkthrough it is too. I missed that hidden pair in your step 3 - but some 'hidden' singles in N9 and '45' on c89 made big inroads at that point as well - so no real harm done.

And only one typo this time (step 4)! You must have been typing before midnight? I'm sure it won't lead anyone astray.

And thanks Ruud for a very enjoyable puzzle.

[nd]

Ed--made the small fix (N2 -> N3) in step 4....!