SudokuSolver Forum

OK, here's the first one! I had another go at A20 V2. When it first appeared I was still using insertion solving and didn't manage to finish it. I started again, this time using elimination solving.

I'll rate A20 V2 as 1.25.

Here is my walkthrough. It's fairly similar to Ed's one in the Assassin Archive & Rating Update thread but I think there's enough different to post it. Step 23a is a fun move but unnecessary after I found step 24; I left it in for interest.

Prelims

a) R1C67 = {17/26/35}, no 4,8,9
b) R1C34 = {13}, locked for R1, clean-up: no 5,7 in R1C67
c) R23C3 = {19/28/37/46}, no 5
d) R23C7 = {15/24}
e) R56C6 = {15/24}
f) R56C4 = {18/27/36} (cannot be {45} which clashes with R56C6), no 4,5,9
g) R89C3 = {17/26/35}
h) R78C2 = {79}, locked for C2 and N7, clean-up: no 1 in R89C3
i) R78C8 = {14/23}
j) R89C7 = {69/78}
k) R9C12 = {16/34} (cannot be {25} which clashes with R89C3)
l) R9C89 = {69/78}
m) 9(3) cage at R3C1 = {126/135/234}, no 7,8,9
n) R678C1 = {128/137/146/236/245}, no 9
o) R678C9 = {127/136/145/235}, no 8,9
p) 26(4) cage in N1 = {2789/3689/4589/4679/5678}, no 1

1. Naked quad {6789} in R8C7 + R9C789, locked for N9

2. Naked pair {26} in R1C67, locked for R1

3. Killer pair 3,6 in R89C3 and R9C12, locked for N7

4. 45 rule on C1234 2 innies R89C4 = 9 = {18/27/36/45}, no 9
4a. 45 rule on C5 2 innies R89C5 = 8 = {17/26/35}, no 4,8,9
4b. 45 rule on C6789 2 innies R89C6 = 11 = {29/38/47/56}, no 1

5. 45 rule on N1 1 outie R4C2 = 1 innie R1C3 -> R4C2 = {13}

6. 45 rule on N3 1 innie R1C7 = 1 outie R4C8 + 1 -> R4C8 = {15}

7. 45 rule on N7 1 innie R7C3 = 1 outie R6C1 + 3, R6C1 = {125}, R7C3 = {458}

8. 45 rule on N9 1 outie R6C9 = 1 innie R7C7, no 6,7 in R6C9

9. R678C9 = {145/235}, 5 locked for C9

10. 45 rule on R1234 2 innies R4C19 = 13 = [49/58/67/76/94], no 1,2,3, no 8 in R4C1

11. 17(3) cage at R3C8 = {179/359/458} (cannot be {269/278/368/467} because R4C8 only contains 1,5), no 2,6
11a. R4C8 = {15} -> no 1,5 in R3C89

12. 45 rule on C12 1 outie R5C3 = 1 innie R6C2 + 1, no 1,8 in R5C3

13. 45 rule on C89 1 outie R5C7 = 1 innie R6C8 + 2, no 1,2 in R5C7, no 8,9 in R6C8

14. 6 in R7 locked in R7C456, locked for N8, clean-up: no 3 in R89C4 (step 4), no 2 in R89C5 (step 4a), no 5 in R89C6 (step 4b)
14a. Hidden killer pair 7,9 in R7C2 and R7C456 for R7 -> R7C456 must contain 7 or 9
14b. 45 rule on N8 3 innies R7C456 = 17 = {269/467}, no 1,3,5,8
14c. 8 in R7 locked in R7C13, locked for N7

15. R678C1 = {128/245}, 2 locked for C1
15a. 8 of {128} must be in R7C1 -> no 1 in R7C1

16. 45 rule on N7 3 innies R7C13 + R8C1 = 14 = {158/248}
16a. 1 of {158} must be in R8C1 -> no 5 in R8C1
16b. 5 of {158} must be in R7C3 (R78C1 cannot be [51] which clashes with R678C1) -> no 5 in R7C1
16c. 5 in N7 locked in R789C3, locked for C3, clean-up: no 4 in R6C2 (step 12)

17. 1,3 in R7 locked in R7C789, locked for N9, clean-up: no 2,4 in R7C8

18. 3 in C7 locked in R4567C7, CPE no 3 in R6C8, clean-up: no 5 in R5C7 (step 13)

19. 45 rule on R89 4 innies R8C1289 = {1259/1457} -> R8C1 = 1, R8C9 = 5, R67C1 = [28] (step 15), R7C3 = 5 (step 16), clean-up: no 3,6 in R5C3 (step 12), no 7 in R5C4, no 4 in R5C6, no 4 in R5C7 (step 13), no 1 in R6C2, (step 12), no 2 in R7C7 (step 8), no 3 in R89C3, no 6 in R9C12, no 8 in R9C4 (step 4), no 3,7 in R9C5 (step 4a)
19a. R8C9 = 5 -> R67C9 = {14/23} (step 9)
19b. 2 of {23} must be in R7C9 -> no 3 in R7C9

20. Naked pair {26} in R89C3, locked for C3, clean-up: no 4,8 in R34C3
20a. Killer pair 1,3 in R1C3 and R23C3, locked for C3 and N1
20b. 4,8 in C3 locked in R456C3, locked for N4, clean-up: no 9 in R4C9 (step 10), no 9 in R5C3 (step 12)

21. 9(3) cage at R3C1 = {126/234} (cannot be {135} because 1,3 only in R4C2), no 5 -> R3C2 = 2, clean-up: no 4 in R2C7

22. Naked pair {34} in R9C12, locked for R9, clean-up: no 5 in R8C4 (step 4), no 7,8 in R8C6 (step 4b)

23. R7C456 (step 14b) = 6{29/47} -> R89C456 = 1358{29/47}
23a. 9 can only be in R89C6 -> 2 can only be in R89C6 (step 4b) -> no 2 in R89C4, clean-up: no 7 in R89C4 (step 4)

24. 25(4) cage at R6C2 = {3589} (only remaining combination, cannot be {4579} because R6C2 only contains 3,6) -> R6C2 = 3, R6C3 = 8, R7C4 = 9, R78C2 = [79], R9C12 = [34], R4C2 = 1, R1C3 = 1 (step 5), R1C4 = 3, R3C1 = 6 (step 21), R4C8 = 5, R5C3 = 4 (step 12), clean-up: no 9 in R23C3, no 7,8 in R4C9 (step 10), no 1,6 in R5C4, no 6 in R6C4, no 4 in R7C56 (step 14b), no 2 in R7C9 (step 19a), no 2 in R89C6 (step 4b), no 6 in R9C7

25. Naked pair {79} in R4C13, locked for R4 and N4 -> R5C12 = [56], R4C1 = 7 (cage sum), R4C3 = 9, R4C9 = 6 (step 10), clean-up: no 1 in R6C6, no 9 in R9C8

26. Naked quad {6789} in R9C6789, locked for R9 -> R89C3 = [62], clean-up: no 9 in R9C7

27. Naked pair {78} in R89C7, locked for C7 and N9 -> R9C89 = [69]

28. Naked triple {134} in R7C789, locked for N9 -> R8C8 = 2, R7C8 = 3

29. R6C56 = [65] (hidden pair in R6), R5C6 = 1, R6C4 = 7, R5C4 = 2, R7C5 = 2, R7C6 = 6, R1C67 = [26]
29a. R5C5 = 9 (hidden single in N5), R5C7 = 3, R6C8 = 1 (step 13), R6C79 = [94], R7C79 = [41], R4C7 = 2

30. Naked pair {78} in R15C9, locked for C9 -> R23C9 = [23], R3C8 = 9 (cage sum), R23C3 = [37]

31. R2C4 = 6 (hidden single in C4)
31a. R2C4 + R4C3 = 15 -> R34C4 = 9 = [18/54], no 4,8 in R3C4

32. R2C6 = 9 (hidden single in C6), R12C1 = [94]
32a. R2C6 + R4C7 = 11 -> R34C6 = 11 = [83], R89C6 = [47], R8C4 = 8, clean-up: no 5 in R9C4 (step 4)

and the rest is naked singles

9 5 1 3 7 2 6 4 8
4 8 3 6 1 9 5 7 2
6 2 7 5 4 8 1 9 3
7 1 9 4 8 3 2 5 6
5 6 4 2 9 1 3 8 7
2 3 8 7 6 5 9 1 4
8 7 5 9 2 6 4 3 1
1 9 6 8 3 4 7 2 5
3 4 2 1 5 7 8 6 9