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I effectively finished this before I started on A115 but only tidied up my walkthrough this evening with the re-work of steps 20 and 24.

The walkthroughs by Afmob and udosuk, plus the partial one by Mike, were all interesting. I particularly liked the grouped X-Wings that used the two diagonals. I've never looked for a grouped X-Wing on diagonals; something to remember for future Killer-Xs.

I also used a couple of short chains, the first one being my key breakthrough, so I'll rate A114V2 at 1.5 the way I solved it.

Here is my walkthrough. I've given eliminations on the diagonals; it's so easy for those of us doing manual eliminations to overlook them.

Prelims

a) R1C123 = {126/135/234}, no 7,8,9
b) R123C4 = {126/135/234}, no 7,8,9
c) R123C5 = {589/679}, 9 locked for C5 and N2
d) R1C789 = {289/379/469/478/568}, no 1
e) R3C123 = {389/479/569/578}, no 1,2
f) R3C789 = {128/137/146/236/245}, no 9
g) R456C8 = {389/479/569/578}, no 1,2
h) R5C456 = {489/579/678}, no 1,2,3
i) R7C123 = {789}, locked for R7 and N7
j) R789C4 = {689} -> R7C4 = 6, R89C4 = {89}, locked for C4 and N8
k) R7C789 = {125/134}, 1 locked for R7 and N9
m) R8C789 = {489/579/678}, no 1,2,3

1. R123C4 = {135/234}, 3 locked for C4 and N2
1a. 7 in C4 locked in R456C4, locked for N5

2. 9 in C6 locked in R456C9
2a. 45 rule on C6 3 innies R456C6 = 19 = {289/469}, no 1,3,5
2b. 3 in N5 locked in R46C5, locked for C5

3. R456C4 = {157} (only remaining combination, cannot be {247} which clashes with R456C6), locked for C4 and N5
3a. Naked triple {234} in R123C4, locked for N2
3b. 1 in N2 locked in R123C6, locked for C6

4. 45 rule on R8 3 innies R8C456 = 15 = {159/249/258/348} (cannot be {357} because R8C4 only contains 8,9), no 7

5. 7 in N8 locked in R9C56, locked for R9
5a. 45 rule on R9 3 innies R9C456 = 17 = {179/278} (cannot be {467} because R9C4 only contains 8,9), no 3,4,5

6. R8C789 must contain 7 = {579/678}, no 4

7. R789C6 must contain 3 = {237} (only remaining combination, cannot be {345} because R9C6 only contains 2,7) -> R9C6 = 7, R78C6 = {23}, locked for C6 and N8 -> R9C5 = 1, R9C4 = 9 (step 5a), R8C4 = 8, R78C5 = {45}, locked for C5, clean-up: no 8 in R123C5 (prelim c), no 8 in R456C6 (step 2a), no 6 in R8C789 (step 6)
7a. Naked triple {679} in R123C5, locked for C5 and N2 -> R5C5 = 8, locked for both diagonals
7b. R5C5 = 8 -> R5C46 = 13 = [76]
7c. R4C456 = {129/345}
7d. R6C456 = {129/345}

8. R1C123 = {126/135} (cannot be {234} which clashes with R1C4), no 4, 1 locked for R1 and N1

9. Naked triple {579} in R8C789, locked for R8 and N9 -> R8C5 = 4, R7C5 = 5, clean-up: no 2 in R7C789 (prelim k)
9a. Naked triple {134} in R7C789, locked for R7 and N9 -> R7C6 = 2, R8C6 = 3
9b. Naked triple {126} in R8C123, locked for N7

10. 45 rule on R1 3 innies R1C456 = 17 = {278/359/368} (cannot be {269/467} because R1C6 only contains 5,8, cannot be {458} because 5,8 only in R1C6), no 4
10a. 45 rule on R2 3 innies R2C456 = 14 = {149/257/356} (cannot be {158} because 1,5,8 only in R2C6, cannot be {167} because 6,7 only in R2C5, cannot be {239/347} which clash with R1C456, cannot be {248} because 2,4 only in R2C4), no 8
10b. Similarly 45 rule on R3 3 innies R3C456 = 14 = {149/257/356}, no 8
10c. R1C6 = 8 (hidden single in C6), R1C45 (step 10) = [27/36], no 9

11. 4,9 in R1 locked in R1C789 = {469}, locked for R1 and N3 -> R1C5 = 7, R1C4 = 2 (step 10)
11a Naked triple {135} in R1C123, locked for N1

12. R3C123 = {479} (only remaining combination), locked for R3 and N1 -> R3C45 = [36], R3C6 = 5 (step 10b), R2C456 = [491]
12a. Naked triple {268} in R2C123, locked for R2

13. R456C7 = {138/147/156/237/246/345} (cannot be {129} which clashes with R3C7), no 9
13a. R456C9 = {139/148/157/238/247} (cannot be {256} which clashes with R9C9, cannot be {346} which clashes with R456C7), no 6
13b. R456C7 (step 13) = {138/147/156/237/246} (cannot be {345} which clashes with R456C9)
13c. Killer pair 1,2 in R3C7 and R456C7, locked for C7

14. R456C2 = {138/147/237} (cannot be {129/156} which clash with R28C2, cannot be {246} which clashes with R2C2, cannot be {345} which clashes with R9C2), no 5,6,9

15. R456C3 = {269/359/368/458} (cannot be {179} which clashes with R7C3, cannot be {278} which clashes with R456C2, cannot be {467} which clashes with R37C3), no 1,7

16. R456C1 = {169/259/358/457} (cannot be {268} which clashes with R2C1, cannot be {178/349/367} which clash with R456C2)
16a. R456C3 (step 15) = {269/368/458} (cannot be {359} because R456C1 cannot be {268} and because R456C2 cannot be {246})
16b. 3 of {368} must be in R5C3 -> no 3 in R46C3

17. 1 on D\ locked in R1C1 + R4C4, CPE no 1 in R4C1

18. R456C3 = {269/368/458} (cannot be {359} which clashes with R379C3)

19. Killer pair 1,2 in R28C2 and R456C2, locked for C2

20. R4C456 (step 7c) = {129/345}
20a. R6C456 (step 7d) = {129/345}
20b. -> R4C4 + R6C6 = [14/59], R4C6 + R6C4 = [41/95] (other permutations clash with R4C456 and R6C456)
20c. No 4 in R7C7 because it forces a clash with step 20b
R7C7 = 4 => R6C6 = 9 => R3C3 = 7 => R8C8 = 5 => R4C4 = 1 => R4C4 + R6C6 = [19] clashes with step 20b -> R7C7 = 3, locked for D\
20d. Naked pair {15} in R1C1 + R4C4, locked for D\
[I originally did step 20c as
20c. R4C4 + R6C6 = [41] => R7C7 = 3 => R1C1 = 5
20d. R4C4 + R6C6 = [59] => R8C8 = 7 => R3C3 = 4 => R7C7 = 3
20e. -> R7C7 = 3, locked for D\ and no 5 in R8C8
but I reworked it because I know that Mike prefers chains to start with “no …” which in this case also gave a simpler step.]

21. R456C7 (step 13b) = {147/156/246}, no 8
21a. R9C7 = 8 (hidden single in C7)
21b. R456C9 (step 13a) = {139/157/238/247} (cannot be {148} which clashes with R7C9)

22. R456C8 = {389/569/578} (cannot be {479} which clashes with R8C8), no 4
22a. Killer pair 7,9 in R456C8 and R8C8, locked for C8
22b. R7C3 = 7 (hidden single on D/), R8C8 = 7 (hidden single on D\)

23. R456C8 (step 22) = {389/569}, 9 locked for N6

24. R456C9 (step 21b) = {157/238/247}
24a. R1C9 cannot be 4 because of clashes in C9
R1C9 = 4 => R7C9 = 1 => R3C9 = {28} -> no valid combinations for R456C9
[Another step that I reworked with “no …” and found that it was simpler]
24b. 4 on D/ locked in R4C6 + R9C1, CPE no 4 in R4C1

25. 8 in C9 locked in R3C9 and R46C9
25a. If R456C9 = {238} => R3C9 = 1
25b. -> no 2 in R3C9

26. Hidden killer pair 3,7 in R2C9 and R456C9 for C9 -> R2C9 = {37}

27. R456C1 (step 16) = {358/457} (cannot be {169} which clashes with R278C1, cannot be {259} which clashes with R1278C1), no 1,2,6,9, 5 locked for C1 and N4 -> R1C1 = 1, locked for D\ -> R4C4 = 5, R6C6 = 9 (step 20b), locked for D\, R3C3 = 4, R4C6 = 4, R6C4 = 1, both locked for D/, R9C1 = 3, locked for D/, R2C8 = 5, R3C7 = 2 , locked for D/, R8C2 = 6, locked for D/, R2C2 = 2, locked for D\, R2C79 = [73], R8C13 = [21], R9C23 = [45], R9C89 = [26], R4C5 = 3 (step 7c), R6C5 = 2, R1C23 = [53], R1C9 = 9, R8C79 = [95], clean-up: no 8 in R46C1 (step 16), no 7 in R46C2 (step 14), no 8 in R46C3 (step 15), no 4 in R56C7 (step 21), no 6 in R46C8 (step 23), no 1,8 in R45C9 (step 24)

and the rest is naked singles

I wonder what that rating was based on. Did the rest of us miss something? The grouped X-Wings using diagonals deserve at least a solid 1.25 while, as Mike has pointed out, any chains rate at least 1.5.

Were they the grouped X-Wings or did SS find some other good moves along the diagonals?

I suspect Afmob also meant moves like the following generalized Swordfish involving the diagonals:




Neat, isn't it? I seem to remember that JSudoku also found this move (or a similar one).

_________________
Cheers,
Mike

For the record, Børge has now added a diagram for this as A114 V3 in the images thread. That post also includes the code string for the diagram.

Edit. I had a quick look at this variant and only managed a few early steps. Then I couldn't find any way to get "into" this puzzle so I won't waste any more time. I can imagine that it needs lots of T&E.