SudokuSolver Forum

and those annoying diagonal cages also make for a very hard puzzle. Takes me a really unusual move (but NOT complicated) which my optimised walk-through gets on step 12...but then many more steps to get it fully cracked. This cage structure ended up quite non-symetrical to get a nice balance between progress and stuckness.

Assassin 203 [edit to correct number! ]
Note: this is an X-killer...1-9 cannot repeat on the diagonals. Thanks to Børge for the pics.

Cheers
Ed

Thanks Ed for an interesting and fun Assassin!

Yes, it was certainly difficult to colour. I managed to do it with 4 colours but then added a 5th colour for one cage, which made the cage pattern a lot clearer to work with.

I've no idea whether I found Ed's unusual step. A few of my steps were interesting and unusual.


Here is my walkthrough for A203. While checking it, I found a flaw in one step but I've retained a comment about it because it would have been an interesting step. Fortunately I didn't need to do much re-work to get back to my original solving path. I've added two comments, one prompted by Ed's feedback; thanks Ed.

Prelims

a) R1C12 = {29/38/47/56}, no 1
b) R12C3 = {17/26/35}, no 4,8,9
c) R12C7 = {12}
d) R12C9 = {18/27/36/45}, no 9
e) R2C12 = {69/78}
f) 12(2) cage at R6C6 = {39/48/57}, no 1,2,6
g) 8(2) cage at R7C8 = {17/26/35}, no 4,8,9
h) R8C12 = {17/26/35}, no 4,8,9
i) R89C3 = {69/78}
j) R9C12 = {15/24}
k) 18(5) cage at R3C1 = {12348/12357/12456}, no 9

Steps resulting from Prelims
1a. Naked pair {12} in R12C7, locked for C7 and N3, clean-up: no 7,8 in R12C9
1b. 18(5) cage at R3C1 = {12348/12357/12456}, CPE no 1,2 in R456C1

2. 45 rule on N1 3 innies R3C123 = 11 = {128/137/146/236/245}, no 9

3. 45 rule on N3 2 innies R3C79 = 15 = {69/78}

4. 45 rule on N8 1 innie R7C6 = 1 outie R9C7, no 1,2 in R7C6

5. 9 in N1 only in R1C12 = {29} or R2C12 = {69} -> R1C12 = {29/38/47} (cannot be {56}, locking-out cages), no 5,6
5a. R12C3 = {17/35} (cannot be {26}, locking cages), no 2,6
5b. R3C123 (step 2) = {128/146/245} (cannot be {236}, locking cages, cannot be {137} which clashes with R12C3), no 3,7

6. R8C12 = {17/26/35}, R9C12 = {15/24} -> combined cage R89C12 = {17}{24}/{26}{15}}/{35}{24}, 2 locked for N7

7. 45 rule on C89 2 outies R56C7 = 10 = {37/46}, no 5,8,9

8. 12(3) cage in N6 cannot contain 2 (because 2+10(2) clashes with R56C7=10, CCC)
8a. 12(3) cage = {138/147/156/345}, no 9
8b. 6 of {156} must be in R6C7 -> no 6 in R4C9 + R5C8

9. 15(3) cage at R3C9 = {168/249/267/348/357/456} (cannot be {159/258} because R5C7 only contains 3,4,6,7)
9a. 1,2 of {168/249/267} must be in R4C8, 5 of {357/456} must be in R4C8, 8 of {348} must be in R3C9 -> no 6,7,8,9 in R4C8
[I first saw those eliminations as Min R3C9 + R5C7 = 9 -> max R4C8 = 5 because 15(3) cage cannot be [663], however I’ve listed the combinations because I’m now going to look at one of them.]
9b. 15(3) cage cannot be {249} = [924] because R3C79 = [69] (step 3) clashes with R56C7 = [46] (step 7)
-> 15(3) cage = {168/267/348/357/456}, no 9, clean-up: no 6 in R3C7 (step 3)
9c. 4 of {348/456} must be in R5C7 (15(3) cage = {348} cannot be [843] because R3C79 = [78] (step 3) clashes with R56C7 = [37], step 7) -> no 4 in R4C8
[I realised later that the analysis parts of steps 9b and 9c can be seen more clearly as
R3C79 = hidden 15(2) cage, R56C7 = hidden 10(2) cage -> R3C9 cannot be 5 more than R5C7. It’s a long time since I’ve used that sort of logic in a walkthrough.]
10. 45 rule on N2 3(2+1) outies R3C7 + R4C56 = 19
10a. Max R3C7 + R4C6 = 17 -> min R4C5 = 2

11. 45 rule on C1234 1 outie R5C5 = 2, placed for both diagonals, clean-up: no 9 in R1C2, no 6 in R8C1, no 4 in R9C2
[I ought to have spotted this 45 a lot sooner. I also found step 7 hard to spot.]

12. Caged X-Wing for 2 in 18(5) cage at R3C1 (2 only in R3C1 + R46C2) and combined cage R89C12 (step 6), no other 2 in C12, clean-up: no 9 in R1C1
[That’s what I saw. Much simpler, as Ed pointed out, is 2 in C3 only in R46C3, locked for 25(5) cage at R3C2, no 2 in R3C2. Then 2 in 18(5) cage at R3C1 only in R3C1.]
13. R3C1 = 2 (hidden single in N1), clean-up: no 6 in R8C2

14. 9 in N1 only in R2C12 = {69}, locked for R2 and N1, clean-up: no 3 in R1C9

15. R9C2 = 2 (hidden single in N7), R9C1 = 4, placed for D/, clean-up: no 7 in R1C2, no 5 in R2C9, no 4 in R7C6 (step 4)

16. 1 in C1 only in R78C1, locked for N7, clean-up: no 7 in R8C1

17. 1 on D/ only in R4C6 + R6C4, locked for N5

18. 45 rule on N7 3 innies R7C123 = 16 = {169/178/358} (cannot be {367} which clashes with R89C3)
18a. 1 of {169/178} must be in R7C1 -> no 6,7 in R7C1

19. 18(5) cage at R3C1 = {12348/12357/12456}
19a. 25(4) cage in N4 = {1789/3589/3679/4579} (cannot be {4678} because R456C1 are common peers of the 18(5) cage so cannot be {678}), 9 locked for N4
19b. 1,4 of {1789/4579} must be in R5C2, 6 or 9 of {3679} must be in R5C2 (R456C1 cannot be {369/679} which clash with R2C1) -> no 7 in R5C2

20. 45 rule on N4 2 remaining innies R46C3 = 1 outie R7C1 + 4 and R46C3 must contain 2
20a. Max R46C3 = 10 -> no 8 in R7C1
20b. R7C1 = {135} -> R46C3 = 5,7,9 = {23/25/27}, no 1,4,6,8

21. R12C3 = {17/35}, R46C3 (step 20b) = {23/25/27} -> variable combined cage R1246C3 = {17}{23}/{17/25}/{35}{27}, 7 locked for C3, clean-up: no 8 in R89C3

22. Naked pair {69} in R89C3, locked for C3 and N7

23. 8 in N7 only in R7C23, locked for R7, clean-up: no 4 in R6C6, clean-up: no 8 in R9C7 (step 4)

24. Variable hidden killer pair 4,8 in 18(5) cage at R3C1 and 25(4) cage in N4, 25(4) cage (step 19a) cannot contain both of 4,8 -> 18(5) cage must contain at least one of 4,8 -> 18(5) cage at R3C1 = {12348/12456}, no 7, 4 locked for N4

Original step 25 deleted. Here I thought I’d deleted 6 from the 16(3) cage in N9. I thought that I’d eliminated {169} because of clashes with R2C2 using D\ or with R9C3 but later realised that R89C8 can still be {69}; {367} clashes with the 8(2) cage.
I’ve rearranged the next few steps to get back to my original solving path.

25. 45 rule on N6 2 outies R37C9 = 1 innie R4C7 + 4
25a. Max R37C9 = 13, min R3C9 = 6 -> max R7C9 = 7

26. 17(3) cage at R9C5 = {179/359/368}
26a. Killer pair 6,9 in R9C3 and 17(3) cage, locked for R9

27. 16(3) cage in N9 = {178/358/457} (cannot be {169/349} because 4,6,9 only in R8C8, cannot be {367} which clashes with the 8(2) cage), no 6,9

28. 6 on D\ only in R2C2 + R4C4, CPE no 6 in R4C2
28a. 18(5) cage at R3C1 (step 24) = {12348/12456}
28b. 6 of {12456} must be in R6C2 -> no 5 in R6C2

[Now I’m back to my original solving path.]

29. 9 in N9 only in R789C7, locked for C7, clean-up: no 6 in R3C9 (step 3)
29a. 9 in N3 only in R13C8, locked for C8
29b. R3C7 + R4C56 = 19 (step 10)
29c. Max R3C7 + R4C5 = 17 -> no 1 in R4C6

30. Naked pair {78} in R3C79, locked for R3 and N3, CPE no 7 in R5C7, clean-up: no 1 in R3C23 (step 5b)
30a. Naked pair {45} in R3C23, locked for R3 and N1, CPE no 5 in R46C3, clean-up: no 7 in R1C1, no 3 in R12C3
30b. Naked pair {38} in R1C12, locked for R1
30c. Naked pair {17} in R12C3, locked for C3
30d. 1 in R3 only in R3C456, locked for N2
[I added the CPE to step 30a later. That’s why I didn’t use the naked pair in R46C3 next. The next three steps, before I used the naked pair, are very powerful.]

31. 18(3) cage in N3 = {369/459}
31a. R2C8 = {35} -> no 5 in R1C8, no 3 in R3C8

32. 3 in N3 only in R2C89, locked for R2
32a. 5 in N5 only in R1C9 + R2C8, locked for D/, clean-up: no 3 in R8C1

33. Naked triple {378} in R3C7 + R7C3 + R8C2, locked for D/, 3 also locked for N7 -> R2C8 = 5, R1C9 = 6, placed for D/, R13C8 = [49], R2C9 = 3, R4C6 = 9, R6C4 = 1, clean-up: no 3 in R7C7, no 2 in R7C8, no 9 in R9C7 (step 4)

34. Naked pair {23} in R46C3, locked for C3, N4 and 25(5) cage at R3C2, no 3 in R5C4 -> R7C3 = 8, placed for D/, R3C7 = 7, placed for D/, R3C9 = 8, R8C2 = 3, R8C1 = 5, R7C12 = [17], R1C2 = 8, R1C1 = 3, placed for D\, clean-up: no 5 in R6C6, no 9 in R7C7, no 3 in R7C8, no 1,7 in R8C9

35. 8(2) cage at R7C8 = [62]

36. Naked pair {45} in R4C2 + R5C3, locked for N4 -> R6C2 = 6, R2C2 = [69], R5C2 = 1

37. R46C3 = {23} = 5, R7C2 = 7 -> R3C2 + R5C4 = 13 = [58], R3C3 = 4, placed for D\, R6C6 = 7, placed for D\, R7C7 = 5, placed for D\

and the rest is naked singles.

Your step 21 (my step 12). Thanks to Andrew for posting a really nice walk-through. Love the rating! Here's my optimised walk-through which basically follows Andrew's way but without his step 9. Unusual for Andrew and I to follow the same path so perhaps it's the only one. Thanks Andrew for some corrections and additions.

A203 WT
Cheers
Ed