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Prelims

a) R1C23 = {29/38/47/56}, no 1
b) R1C56 = {17/26/35}, no 4,8,9
c) R56C1 = {19/28/37/46}, no 5
d) R5C23 = {39/48/57}, no 1,2,6
e) R67C7 = {49/58/67}, no 1,2,3
f) R67C8 = {18/27/36/45}, no 9
g) R9C78 = {15/24}
h) 20(3) cage at R3C2 = {389/479/569/578}, no 1,2
i) 29(4) cage at R1C4 = {5789}
j) 23(6) cage at R6C2 = {123458/123467}, no 9

1. Naked quad {5789} in 29(4) cage at R1C4, locked for N2, clean-up: no 1,3 in R1C56
1a. Naked pair {26} in R1C56, locked for R1 and N2, clean-up: no 5,9 in R1C23
1b. Naked triple {134} in R2C56 + R3C6, CPE no 1,3,4 in R3C8

2. 45 rule on C9 2 outies R1C78 = 17 = {89}, locked for R1 and N3, clean-up: no 3 in R1C23
2a. Naked pair {47} in R1C23, locked for R1 and N1 -> R1C4 = 5
2b. R1C78 = 17 -> R123C9 = 14 = {167/347/356} (cannot be {257} because R1C9 only contains 1,3), no 2
2c. R1C9 = {13} -> no 1,3 in R23C9

3. 45 rule on N1 2 innies R3C23 = 11 = {38/56}/[92], no 1,9 in R3C3

4. 30(7) cage at R2C5 = {1234569/1234578}
4a. Killer pair 8,9 in R1C8 and 30(7) cage, locked for C8, clean-up: no 1 in R67C8

5. Hidden killer pair 8,9 in 16(3) cage at R4C9 and 15(3) cage at R7C9, neither cage can contain both of 8,9 -> 16(3) cage and 15(3) cage must each contain one of 8,9
5a. Killer pair 8,9 in 16(3) cage and 30(7) cage at R2C5 (which must contain one of 8,9 in R45C8), locked for N6, clean-up: no 4,5 in R7C7
5b. 15(3) cage contains one of 8,9 -> no 7

6. 45 rule on R1234 1 outie R5C8 = 1 innie R4C9 + 6 -> R5C8 = {789}, R4C9 = {123}
6a. 16(3) cage at R4C9 contains one of 8,9 (step 5) = {169/178/259/268/349/358}
6b. R4C9 = {123} -> no 1,2,3 in R56C9
6c. 16(3) cage = {169/259/349/358} (cannot be {178/268} which clash with R4C9 + R5C8, IOD block), no 7

7. 7 in C9 only in R123C9, locked for N3
7a. R123C9 (step 2b) = {167/347}, no 5

8. 15(3) cage at R7C9 contains one of 8,9 (step 5) = {159/168/249/348} (cannot be {258} which clashes with R9C78)
8a. Killer pair {14} in 15(3) cage and R9C78, locked for N9, clean-up: no 5 in R6C8
8b. 5 in C9 only in 16(3) cage at R4C9 = {259/358} or in 15(3) cage = {159} -> 16(3) cage (step 6c) = {259/349/358} (cannot be {169}, locking-out cages), no 1,6, clean-up: no 7 in R5C8 (step 6)
8c. Naked pair {89} in R15C8, locked for C8
8d. Killer pair 1,4 in R123C9 and 15(3) cage, locked for C9
8e. 16(3) cage (step 8b) = {259/358}, 5 locked for C9 and N6, clean-up: no 8 in R7C7
8f. 30(7) cage at R2C5 = {1234569/1234578}, 5 locked for N3
8g. 1 in N6 only in R4C78 + R5C7, CPE no 1 in R2C7

9. Killer triple 5,8,9 in R5C23, R5C8 and R5C9, locked for R5, clean-up: no 1,2 in R6C1

10. 45 rule on N2369 2 outies R48C6 = 1 innie R5C7 + 10
10a. Min R48C6 = 11, no 1 in R48C6

11. 15(3) cage at R8C6 = {249/258/267/348/357/456}
11a. 4 of {249} must be in R8C6 -> no 9 in R8C6
11b. 4 of {348} must be in R8C6, 8 of {258} must be in R8C7 (R8C78 cannot be {25} which clashes with R9C78) -> no 8 in R8C6

12. 45 rule on R89 4(1+3) outies R6C2 + R7C129 = 11
12a. Max R7C129 = 10, no 8,9 in R7C129
12b. Min R7C129 = 6 -> max R6C2 = 5

13. 7 in N9 only in R78C78
13a. 45 rule on N9 4 innies R78C78 = 24 = {2679/3579/3678}
13b. 15(3) cage at R8C6 (step 11) = {249/258/267/348/357} (cannot be {456} because R78C78 only contains one of 5,6)

14. 45 rule on N23 2 outies R45C8 = 2 innies R3C67 + 8
14a. Min R3C67 = 3 -> min R45C8 = 11, no 1 in R4C8

15. 45 rule on N23 4(2+2) outies R4C67 + R45C8 = 26
15a. 30(7) cage at R2C5 = {1234569/1234578} -> max R45C8 = 15 -> min R4C67 = 11, no 2,3 in R4C6, no 1 in R4C7
15b. R5C7 = 1 (hidden single in N6), clean-up: no 9 in R6C1, no 5 in R9C8

16. 30(7) cage at R2C5 = {1234569/1234578}, 1 locked for R2
16a. 1 in N1 only in R13C1, locked for C1

17. 45 rule on N1 and R4 5 outies for N1 R4C12345 = 25 -> 4 innies for R4 R4C6789 = 20 = {2369/2378/2468/2567/3467} (cannot be {2459/3458} because 5,8,9 only in R4C6)
17a. R6C78 cannot be [62/73] (because of 13(2) and 9(2) cages at R6C7 and R6C8) -> R4C789 must contain at least one of 2,6 and at least one of 3,7 -> R4C6789 = {2369/2378/2567/3467} (cannot be {2468} which doesn’t contain 3 or 7)
17b. 5,9 of {2369/2567} must be in R4C6, 6 of {3467} must be in R4C78 (because R4C789 must contain one of 2,6) -> no 6 in R4C6

18. R48C6 = R5C7 + 10 (step 10)
18a. R5C7 = 1 -> R48C6 = 11 = [47/56/74/83/92], no 5 in R8C6

19. 30(7) cage at R2C5 = {1234569/1234578}, R5C8 = R4C9 + 6 (step 6) -> R4C9 + R5C8 = [28/39] -> R4C89 + R5C8 = [728/x39] (where x is one of 2,4,6) -> no 3 in R4C8
19a. 30(7) cage at R2C5 = {1234569/1234578}, 3 locked for R2

20. Double hidden killer pair 1,3 in R1C9, 30(7) cage and R3C67 for N23, R1C9 = {13}, 30(7) cage contains both of 1,3 -> R3C67 must contain one of 1,3
[Alternatively hidden killer pair 1,3 for N1, then hidden killer pair 1,3 for R3.]
20a. R45C8 = R3C67 + 8 (step 14)
20b. R45C8 cannot be [48] = 12 because R3C67 cannot be 4 = [13], R45C9 cannot be [49] = 13 because R3C67 = 5 = [14/32] leaves 4 in N2 in R2C56 which is in the same cage at R4C8 -> no 4 in R4C8
20c. 30(7) cage at R2C5 = {1234569/1234578}, 4 locked for R2

21. R45C8 = R3C67 + 8 (step 14)
21a. R45C8 = [29/69/78] (cannot be [28] because min R3C67 = 3) = 11,15 -> R3C67 = 3,7 = [12/16/34/43]
21b. Consider placements for R4C9
R4C9 = 2
or R4C9 = 3 => R1C9 = 1 => 1 in R2 only in R2C56, locked for N2 => R3C67 = {34} = 7 => R45C8 = 15 = [69/78]
-> no 2 in R4C8
21c. 30(7) cage at R2C5 = {1234569/1234578}, 2 locked for N3
21d. R4C8 = {67} -> no 6 in R2C78 + R3C8

22. R45C8 = R3C67 + 8 (step 14), R45C8 (step 21b) = [69/78] = 15 -> R3C67 = 7 = [16]/{34}
22a. Consider combinations for R3C67
R3C67 = [16] => R67C7 = [49], no 4 in R9C7
or R3C67 = {34}, 1 in N2 only in R2C56 => R9C8 = 1 (hidden single in C8)
-> R9C78 = [24/51]

23. Consider combinations for R67C7 = [49]/{67}
R67C7 = [49] => R1C78 = [89], R5C8 = 8, R4C8 = 7 (step 21b) => R8C7 = 7 (hidden single in N9)
or R67C7 = {67}
-> 7 in R678C7, locked for C7
23a. R3C67 = 7 (step 22) -> R4C67 = 11 = [56/74/83/92], no 4 in R4C6, clean-up: no 7 in R8C6 (step 18a)

24. 15(3) cage at R8C6 (step 13b) = {249/258/267/348/357}
24a. 3 of {357} must be in R8C6, 8 of {348} must be in R8C7 -> no 3 in R8C7

25. Consider placements for 3 in C7
R2C7 = 3 => R3C3 = 3 (hidden single in N2)
or R34C7 = 3
-> 18(4) cage at R3C6 must contain 3
25a. 18(4) cage at R3C6 = {1368/2349/3456} (cannot be {1359/2358/2367} because R3C67 must total 7, step 22), no 7, clean-up: no 4 in R4C7 (step 23a), no 4 in R8C6 (step 18a)
25b. 4 in N6 only in R6C78, locked for R6, clean-up: no 6 in R5C1
25c. 6 in R5 only in R5C456, locked for N5

26. 15(3) cage at R8C6 (step 13b) = {258/267/357}, no 9
26a. 3 of {357} must be in R8C6 -> no 3 in R8C8

27. R4C6789 (step 17a) = {2369/2378/2567}, 2 locked for R4 and N6, clean-up: no 7 in R7C8

28. Hidden killer triple 7,8,9 in R7C7, 15(3) cage at R7C9 and 15(3) cage at R8C6 for N9, 15(3) cage at R7C9 contains one of 8,9, 15(3) cage at R8C6 contains one of 7,8 -> R7C7 = {79}, clean-up: no 7 in R6C7
28a. 7 in C7 only in R78C7, locked for N9
28b. 15(3) cage at R8C6 contains one of 7,8 -> R8C7 = {78}

29. R4C6789 (step 17a) = 20, R4C67 (step 23a) = 11 -> R4C89 = 9 = [63/72]
29a. Consider combinations for 18(4) cage at R3C6 (step 25a) = {1368/2349/3456}
18(4) cage = [1368/3456}, 6 locked for C7
or 18(4) cage = {2349} = {34}[92] => R4C89 = [63]
-> 6 in R34C7 + R4C8, CPE no 6 in R6C7
29b. R6C7 = 4, R7C7 = 9, R1C78 = [89], R8C7 = 7, R5C8 = 8, R4C9 = 2 (step 6), R4C8 = 7, clean-up: no 9 in R4C6 (step 23a), no 4 in R5C23, no 2,5 in R7C8, no 2 in R8C6 (step 18a)
29c. Naked pair {36} in R67C8, locked for C8

30. Naked pair {36} in R34C7, locked for C7 and 18(4) cage at R3C6, no 3 in R3C6
30a. Naked pair {25} in R2C7 + R3C8, locked for N3

31. R56C1 = [28/46] (cannot be {37} which clashes with R5C23), no 3,7 in R56C1

32. R8C1 = 9 (hidden single in R8)

33. 9 in R9 only in 15(3) cage at R9C4 = {159/249}
33a. Naked quad {12459} in 15(3) cage + R9C78, locked for R9

34. 7 in R9 only in R9C123, locked for N7
34a. 27(5) cage at R7C1 contains 7,9 = {23679} (only remaining combination, cannot be {245} because 4,5 only in R7C1) -> R7C1 = 2, R9C123 = {367}, locked for R9 and N7 -> R9C9 = 8, R5C1 = 4, R6C1 = 6, R67C8 = [36], R34C7 = [36], R4C6 = 5 (step 17a), R3C6 = 4 (cage sum), R8C6 = 6 (step 18a), R8C8 = 2 (cage sum), R9C7 = 5, R9C8 = 1, R2C78 = [24], R3C8 = 5, clean-up: no 6,8 in R3C23 (step 3)
34b. R3C2 = 9, R4C12 = {38}, locked for R4 and N4, clean-up: no 9 in R5C3
34c. Naked pair {57} in R5C23, locked for R5 and N4
34d. R3C3 = 2, R46C3 = {19}, locked for C3 and N4 -> R6C2 = 2

35. R6C2 + R7C129 = 11 (step 12)
35a. R6C2 = 2, R7C1 = 2 -> R7C29 = 7 = [43]

36. R7C4 = 1 (hidden single in R7), R6C3 = 9, R7C3 = 8 (cage sum)

and the rest is naked singles.

I'll rate my walkthrough for Pinata 44 at Hard 1.5.