Many thanks to Nasenbaer for the latest challenging puzzle.
As Afmob said, it was a very demanding killer and the moves were very hard to find. On Tuesday and Wednesday I think I only found 6 or 7 moves each day but I never ground to a complete halt. Then today I found steps 33 and 34, after which it was fairly straightforward even though the first placement didn't come until step 43.
I didn't find this one quite as difficult as Maverick 1, which most people rated as a Hard 1.5, so I'll also rate Maverick 4 as a Hard 1.5. I didn't feel that my combination analysis justified a higher rating; it was fairly routine after the heavy analysis used for some recent puzzles.
I'll be interested to see how Afmob solved it. My walkthrough looks a lot longer.
Here is my walkthrough. Some of the key moves were steps 11a, which I added today, 26, 33, 34 and the simpler 36.
Nasenbaer wrote:Sadly the diagonals are only there because of uniqueness this time, sorry for that.
Now that I've finished the puzzle I must disagree with that. The diagonals were very helpful from step 42 onward.
Thanks Afmob for the comments. I've corrected steps 17 and 26b and simplified step 41. I've also re-phrased step 10b and added a couple of clean-ups for step 43 which allowed me to simplify the remaining steps.
This is a Killer-X. I've included eliminations on the diagonals because it's easy to overlook them.
Prelims
a) R23C2 = {17/26/35}, no 4,8,9
b) R23C8 = {14/23}
c) R8C2 + R9C1 = {16/25/34}, no 7,8,9
d) R8C8 + R9C9 = {69/78}
e) R234C1 = {489/579/678}, no 1,2,3
f) 20(3) cage in N6 = {389/479/569/578}, no 1,2
g) 19(3) cage in N7 = {289/379/469/478/568}, no 1
h) 15(5) cage in N8 = {12345}, locked for N8
1. 45 rule on R1 2 outies R23C5 = 8 = {17/26/35}, no 4,8,9
2. 45 rule on R123 2 outies R4C19 = 9 = {45}/[63/72/81], no 9, no 6,7,8 in R4C9
3. 45 rule on R89 3 innies R8C159 = 22 = {589/679}, 9 locked for R8, clean-up: no 6 in R9C9
4. 45 rule on N3 2 innies R23C7 = 1 outie R4C9 + 12, min R23C7 = 13, no 1,2,3
5. 45 rule on N7 1 innie R7C3 = 1 outie R6C1 + 2, no 8,9 in R6C1, no 1,2 in R7C3
6. 45 rule on N9 1 outie R6C9 = 1 innie R7C7 + 4, no 1,2,3,4 in R6C9, no 6,7,8,9 in R7C7
7. 45 rule on C12 2 innies R49C2 = 1 outie R1C3 + 11
7a. Min R49C2 = 12, no 1,2
7b. Max R49C2 = 17 -> max R1C3 = 6
8. 45 rule on C89 2 innies R49C8 = 1 outie R1C7
8a. Max R49C8 = 9, no 9
8b. Min R49C8 = 3 -> min R1C7 = 3
9. 45 rule on N5 2 outies R78C5 = 2 innies R6C46
9a. Min R78C5 = 13 -> min R6C46 = 13, no 1,2,3
10. 45 rule on C789 4 innies R2367C7 = 17
10a. Min R23C7 = 13 (step 4) -> max R67C7 = 4 -> R67C7 = {12/13}, 1 locked for C7, clean-up: no 8,9 in R6C9 (step 6)
10b. Min R67C7 = 3 -> max R23C7 = 14
-> no 3,4,5 in R4C9 (step 4), clean-up: no 4,5,6 in R4C1 (step 2)
10c. Max R67C7 = 4 -> min R67C6 = 15, no 4,5
11. 45 rule on N6 3 innies R4C9 + R6C79 = 9 = {126/135} (cannot be {234} because no 2,3,4 in R6C9), no 7, 1 locked in R4C9 + R6C7 for N6, clean-up: no 3 in R7C7 (step 6)
11a. 2 of {126} must be in R4C9 (cannot be [126] which would give R7C7 = 2 (step 6) when R6C7 clashes with R7C7) -> no 2 in R6C7
12. 12(3) cage in N9 = {138/147/156/237/246/345} (cannot be {129} which clashes with R7C7), no 9
12a. 1 of {138} must be in R9C8 -> no 8 in R9C8
12b. 7 of {237} must be in R89C7 (cannot be {23}7 which clashes with R67C7) -> no 7 in R9C8
13. 45 rule on N58 4 outies R67C37 = 11
13a. R67C7 = 3,4 (steps 10b and 10c) -> R67C3 = 7,8, no 8,9, no 6,7 in R6C3, clean-up: no 6,7 in R6C1 (step 5)
14. 45 rule on N1 2 innies R23C3 = 1 outie R4C1 + 4, min R4C1 = 7 -> min R23C3 = 11, no 1
15. R234C9 = {129/138/147/237/246} (cannot be {156} which clashes with R6C9, cannot be {345} because R4C9 only contains 1,2), no 5
16. 20(3) cage in N6 = {389/479/578} (cannot be {569} which clashes with R6C9), no 6
17. 16(3) cage in N6 = {268/349
/358/457} (cannot be
{259/367} which clash with
20(3) cage and with R4C9 + R6C79)
17a. 6 of {268} must be in R4C78 (cannot be {28}6 which clashes with R4C19) -> no 6 in R5C7
18. R67C3 = 7,8 -> R67C4 = 14,15, no 4 in R6C4
19. R1C123 = {129/138/147/246/345} (cannot be {156/237} which clash with R23C2), if {246/345} R23C2 = {17} -> R1C123 + R23C2 must contain one of 7,8,9
19a. R234C1 = {489/579/678} -> R23C1 must contain one of 7,8,9
19b. Hidden killer triple 7,8,9 in R1C123 + R23C2, R23C1 and R23C3 for N1 -> R23C3 must contain one of 7,8,9
19c. R4C1 = {78} -> R23C3 = 11,12 (step 14), no 6 in R23C3
20. 45 rule on N9 4 innies R7C789 + R8C9 = 18 = {1269/1278/2349/2358/2457} (cannot be {1368/1467/2367} which clash with 15(2) cage, cannot be {1359/1458} which clash with 22(4) cage at R6C9 which would be 5{359}/5{458}, cannot be {3456} because R7C7 only contains 1,2), 2 locked for R7 and N9
21. 12(3) cage in N9 (step 12) = {138/147/156/345}
21a. 1 of {156} must be in R9C8 -> no 6 in R9C8
22. 45 rule on N7 4 innies R7C123 + R8C1 = 19 = {1369/1378/1468/1567/3457} (cannot be {1459} which clashes with 7(2) cage)
22a. 3 of {1369} must be in R7C12 (3 cannot be in R7C3 which would make 17(4) cage at R6C1 1{169} -> 6 of {1369} must be at R7C3 and 9 at R8C1 -> no 9 in R7C12
23. 19(3) cage in N7 = {289/379/469/478} (cannot be {568} which clashes with R7C123 + R8C1), no 5
24. R23C3 = 11,12 (step 14) -> R23C4 = 10,11
24a. 45 rule on C123 4 outies R2367C4 = 25 = {1789/2689/3589/3679/4579/4678}
24b. 5 of {3589/4579} must be in R6C4 (cannot make R23C4 = 10,11 including 5) -> no 5 in R23C4
25. 45 rule on N3 4 innies R23C79 = 24 = {1689/2589/2679/3579/3678/4569/4578} (cannot be {3489} which clashes with R23C8)
25a. 4 of {4569} must be in R23C9 because no {156} in R234C9 (step 15)
25b. 4 of {4578} must be in R23C9 (only way to make R234C9 total 12)
25c. -> no 4 in R23C7
26. R4C19 (step 2) = [72/81]
26a. 45 rule on N4 3 innies R4C1 + R6C13 = 13 = {148/157/238/247}
26b. Cannot be 7{15} which clashes with R4C9 + R6C79 = [21
6]
26c. Cannot be 8{23} which clashes with R4C9 + R6C79 = [135]
26d. -> R4C1 + R6C13 = {148/247}, no 3,5, 4 locked for R6 and N4, clean-up: no 5,7 in R7C3 (step 5)
27. R67C3 (step 13a) = 7,8 = [16/26/43], no 4 in R7C3, clean-up: no 2 in R6C1 (step 5)
28. R7C123 + R8C1 (step 22) = {1369/1567/3457} (cannot be {1378/1468} which would make 17(4) cage at R6C1 1{178}/4{148}), no 8
28a. 6 of {1567} must be in R7C3 -> no 6 in R7C12 + R8C1
29. 8 in N7 locked in 19(3) cage = {289/478}, no 3,6
30. R23C3 must contain one of 7,8,9 (step 19b)
30a. 45 rule on C123 4 innies R2367C3 = 19 = {1369/1468/1567/2368/2467/3457} (cannot be {1279/1378} which contain two of 7,8,9, cannot be {2458} because R7C3 only contains 3,6, cannot be {1459/2359} which aren’t consistent with R67C3 = [16/26/43])
30b. 2 of {2368/2467} must be in R6C3 -> no 2 in R23C3
31. 45 rule on N1 4 innies R23C13 = 25 = {3589/4579/4678} (cannot be {3679} which clashes with R23C2)
31a. 9 of {3589/4579} must be in R23C1 -> no 9 in R23C3
32. R1C123 (step 19) = {129/138/147/246} (cannot be {345} which clashes with R23C13), no 5
33. R67C37 = 11 (step 13)
33a. R67C3 (step 27) = [16/26/43]
33b. If R67C3 = [26] => R67C7 = 3 = [12]
33c. If R67C3 = [43] => R6C1 = 1 (step 26d)
33d. -> 1 in R6 locked in R6C137, no 1 in R6C5
34. R67C3 (step 27) = [16/26/43]
34a. R7C123 + R8C1 (step 28) = {1369/1567/3457}
34b. 6 of {1369/1567} must be in R7C3 -> R7C37 cannot be [61] => R67C7 = [12]
34c. -> no 1 in R6C3
35. R2367C3 (step 30a) = {2368/2467/3457}
35a. 19(3) cage (step 29) = {289/478}
35b. 4 of {478} must be in R89C3 (because R89C3 = {78} would clash with R23C3) -> no 4 in R9C2
36. Killer pair {24} in R6C3 and R89C3, locked for C3
37. R2367C3 (step 35) = {2368/3457} (cannot be {2467} because 2,4,6 only in R67C3), 3 locked for C3
37a. R23C3 = {38/57}
38. R1C123 (step 32) = {129/138/147/246}
38a. R1C3 = {16} -> no 1,6 in R1C12
39. R23C3 = {38/57} (step 37a)
39a. R23C13 (step 31) = {3589/4579} (cannot be {4678} which clashes with R23C3), 9 locked in R23C1, locked for C1 and N1, 5 locked for N1, clean-up: no 3 in R23C2
39b. R23C1 = {49/59}, no 6,7,8
40. Hidden killer quad 1,3,5,6 in R1C3, R23C3, R45C3 and R7C3
for C3 -> R45C3 must contain one of 1,5,6
40a. 18(3) cage in N4 = {189/369/567} (cannot be {378} which clashes with R4C1)
40b. R45C3 cannot be {56} -> no 7 in R4C2
41.
17(4) cage at R6C1 = {1457} (only remaining combination), no 3, 5,7 locked for N7, clean-up: no 2 in 7(2) cage, no 4 in R89C3 (step 29)
[Step 41 simplified at Afmob’s suggestion. I originally used the remaining combinations for R7C123 + R8C3.]
42. Killer pair 3,6 in R7C3 and 7(2) cage, locked for D/, clean-up: no 2 in R3C8
43. R6C3 = 4 (hidden single in C3), R7C3 = 3 (step 34), R6C1 = 1, R6C7 = 3, R7C7 = 1 (hidden single in C7, locked for D\), clean-up: no 7 in R3C2
, no 8 in R23C3 (step 37a), no 4 in 7(2) cage in N7
43a. R9C1 = 6, R8C2 = 1, locked for D/, clean-up: no 7 in R2C2, no 4 in R3C8
44. R1C3 = 1 (hidden single in C3)
44a. Naked pair {26} in R23C2, locked for C2 and N1
44b. Naked pair {57} in R23C3, locked for C3, N1 and 22(4) cage
44c. Naked pair {49} in R23C1, locked for C1 and N1
44d. Naked pair {38} in R1C12, locked for R1
44e. Naked pair {57} in R78C1, locked for C1 and N7 -> R7C2 = 4, R4C1 = 8, R1C12 = [38], 3 locked for D\, R5C1 = 2, R9C2 = 9, R4C9 = 1 (step 2), R6C9 = 5 (step 11), R6C2 = 7, clean-up: no 6 in R8C8
45. Naked pair {89} in R6C48, locked for R6 -> R6C56 = [26], 6 locked for D\, R7C6 = 9 (cage sum), R23C2 = [26], R23C8 = [41], 4 locked for D/, R23C1 = [94], clean-up: no 6,7 in R2C5
46. Naked pair {78} in R8C8 + R9C9, locked for N9 and D\ -> R3C3 = 5, locked for D\, R5C5 = 9, locked for D/, R2C3 = 7, R45C3 = [96], R4C2 = 3 (step 40a), R5C2 = 5, R4C4 = 4, R6C4 = 8, locked for D/, R3C7 = 7, R1C9 = 2, R3C5 = 3, R2C5 = 5 (step 1)
and the rest is naked singles
3 8 1 6 4 7 9 5 2
9 2 7 1 5 8 6 4 3
4 6 5 9 3 2 7 1 8
8 3 9 4 7 5 2 6 1
2 5 6 3 9 1 8 7 4
1 7 4 8 2 6 3 9 5
5 4 3 7 8 9 1 2 6
7 1 2 5 6 3 4 8 9
6 9 8 2 1 4 5 3 7
In my previous message, I mentioned that I'd used 20 different "45" tests which are all included above. In addition I eventually looked at another 5 of them which never led to any candidate eliminations, although some produced combination eliminations.
This walkthrough was posted before I went through Afmob's walkthrough. Some comments on that and Mike's walkthrough are given in my later message including pointing out a couple of 45s that I missed, one of which I ought to have seen and the other was a less obvious one.
So, if my counting is correct, that's at least 27 45s in this puzzle! That must be some sort of record.