This is a Windoku twin killer. Combinations in killer cages must use non-consecutive numbers, while the cages in HATMAN’s diagram with red borders use consecutive numbers (not necessarily in order).
The four windows are numbered W1, W2, W3 and W4; the
hidden windows will give their cells, for example hidden window R159C159.
Prelims
a) 10(3) killer cage at R1C1 = {136} (only possible combination, other combinations contain consecutive numbers)
b) 18(3) killer cage at R1C9 = {279/369/468} (other combinations contain consecutive numbers), no 1,5
c) 12(3) killer cage at R7C3 = {138/147/246} (other combinations contain consecutive numbers), no 5,9
d) 20(3) killer cage at R7C7 = {479} (only possible combination, other combinations contain consecutive numbers)
Steps resulting from Prelims
1a. Naked triple {136} in 10(3) cage at R1C1, locked for N1 and D\
1b. Naked triple {479} in 20(3) cage at R7C7, locked for N9 and D/
2. 5 on both diagonals only in N5 -> R5C5 = 5
2a. Naked pair {28} in R4C4 + R6C6, locked for N5
3. 18(3) killer cage at R1C9 = {279/369} (cannot be {468} which clashes with 12(3) killer cage at R7C3), no 4,8, 9 locked for N3 and D/
3a. 12(3) killer cage at R7C3 = {138/147} (cannot be {246} which clashes with 18(3) killer cage), no 2,6, 1 locked for N7 and D/
3b. Killer pair 3,7 in 18(3) killer cage and 12(3) killer cage, locked for D/
3c. Naked pair {46} in R4C6 + R6C4, locked for D/ and N5
3d. 18(3) killer cage = {279} (only remaining combination), locked for N3
3e. 12(3) killer cage = {138} (only remaining combination), locked for N7
4. R2C2 + R3C3 = {136} -> Remban group R23C23 = {1234/3456} (other combinations only contain one of 1,3,6), 3,4 locked for N1 and W1
5. Remban group R4C234 = {678/789} -> R4C4 = 8, placed for W1, R4C23 = {67/79}, 7 locked for R4, N4 and W1
5a. R6C6 = 2, placed for W4
6. R7C3 + R8C2 = {138} -> Remban group R78C78 = {1234}, locked for N7 and W3 -> R6C4 = 6, R4C6 = 4, placed for W2
6a. R9C1 = 8, placed for hidden window R159C159
6b. 7 in W3 only in R78C4, locked for C4 and N8
6c. 8 in W3 only in R6C23, locked for R6 and N4
6d. 3,4 in C1 only in R456C1, locked for N4
6b. 8 in N1 only in R1C23, locked for R1
7. R7C7 + R8C8 = {479} -> Remban group R78C78 = {4567/6789} (other combinations only contain one of 4,7,9), 6,7 locked for N9 and W4
8. Remban group R23C23 (step 4) = {3456} (cannot be {1234}, locked for W1 because R23C4 = {59} clashes with R78C4, ALS block), locked for N1 and W1 -> R1C1 = 1, placed for hidden window R159C159
8a. Naked pair {79} in R4C23, locked for R4, N4 and W1
8b. Naked pair {12} in R23C4, locked for C4 and N4
8c. Naked pair {58} in R6C23, locked for R6, N4 and W3
8d. Naked pair {79} in R78C4, locked for C4 and N8 -> R5C4 = 3, R4C5 = 1, placed for hidden window R234C159
8e. 1 in N4 only in R5C23, locked for R5
8f. 5 in C1 only in R78C1, locked for N7
9. 5 in hidden window R234C159 only in R234C9, locked for C9
10. 3 in hidden window R159C159 only in R19C5, locked for C5
[It’s getting a bit harder now. At first I analysed the Remban group at R1C6, but I’ve left that until a bit later after finding the next step …]
11. Consider placements for R9C4
11a. R9C4 = 4 => R9C9 = 9, R7C7 + R8C8 = {47} => Remban group R78C78 = {4567}, locked for N9 => R9C6 = 5 (hidden single in R9)
or R9C4 = 5
-> 5 must be in R9C46, locked for R9 and N8
11b. 5 in N9 only in Remban group R78C78 = {4567}, locked for N9 and W4 -> R9C9 = 9
12. Naked pair {67} in R9C23, locked for N7 and hidden window R159C234, no 7 in R1C23, no 6 in R5C23
12a. Naked pair {59} in R78C1, locked for C1
12b. Naked pair {27} in R23C1, locked for C1, N1 and hidden window R234C159, no 7 in R23C5
12c. Naked pair {89} in R1C23, locked for R1
13. R1C9 = 2 (hidden single in R1), placed for hidden window R159C159
13a. Naked pair {79} in R2C8 + R3C7, locked for W2
13b. 9 in N2 only in R23C5, locked for C5 -> R6C5 = 7, R5C6 = 9
14. R1C6 = 7 (hidden single in N2) -> Remban group at R1C6 = [789], R2C7 = 8, placed for W2, R3C7 = 9
14a. R23C5 = [98] (hidden pair in N2)
and the rest is naked singles, with using the windows.
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