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1. 9/3r8c1 = {135}
-> V7 = {78(6|9)}
-> r7c123 = {24(9|6))

16/3@r6c2 from {169} {259} {268} (Cannot be {358} since at least one of (35) already in W7.)

-> 7 in W7 in r78c4.
Since r8c6 cannot be a 1, 3, or 7 -> 11/3@r6c6 = {146}


2. 19/3@r2c7 is either {379} or {469}
-> n3 is either {456} {379} {128} or {123} {469} {578}

V6 must contain at least one of (46)
-> 12/3@r4c6 cannot be {246}
-> 12/3@r4c6 either {138} or {147} with 1 in r4c78.
-> 6 in W3 must be in n3 in r23c78
-> n3 = {123} {469} {578} - with 6 in r2c78.
-> since 12/3@r4c6 contains a 7 or an 8 -> r3c9 = 7 or 8.


3. 17/3@r7c8 cannot be {368} - No solution for V9
17/3@r7c8 cannot be {359} - Would put V9 = {678} contradicts r3c9 = 7 or 8
-> 17/3@r7c8 either {179} or {269}
-> V9 must contain a 4
-> 19/3@r2c7 = [{46}9]
-> 12/3@r4c6 = {138} with 1 in r4c78
-> r3c789 = [{57}8]
-> r23c6 = [29]


4. V9 cannot contain a 1
-> 1 in n9 in r9c78
-> r1c9 = 1 and r1c78 = {23}
Also 3 in W9 somewhere in c78
-> 12/3@r4c6 = [3{18}]
-> NS 5 in c6 -> r9c6 = 5


5. Given 8 in r4c78 -> V6 must contain a 4 - only place is r5c8.
-> r2c78 = [46]
-> 17/3@r7c8 = [{79}1]
-> r4c78 = [18]
-> 8 in W9 in r78c7
Also r3c78 = [75]
Given 1 in r4c7 -> V6 must contain a 5 - in r56c9
-> HS 5 in W9 -> r7c7 = 5
-> r8c7 = 8
-> in W9: r6c78 = {23}

V6 only contains one of (23) -> Must be 3
-> r6c78 = [23] and r1c78 = [32]
-> r56c9 = {56}
-> HS 6 in n9 -> r9c7 = 6
-> V9 = {234}
-> r4c9 = 7
-> r5c7 = 9


6. Also V7 = {789}
-> r7c123 = {246}
-> r7c9 = 3
Also r7c6 = 1


7. Also 16/3@r6c2 must be {169}
-> r7c123 = [6{24}]
Also 9/3@r8c1 = [1{35}]
Also HS 8 in W7 -> r7c4 = 8
-> r8c4 = 7
-> r78c8 = [79]
-> r7c5 = 9
Also 11/3@r6c6 = [416]


8. 17/3@r2c4 cannot contain a 7 or an 8, or both (29)
-> 17/3@r2c4 = [539]
-> HS 3 in r2 -> r2c1 = 3
-> V1 = {234} or {345}
-> 15/3 @r1c2 cannot contain a 3 or a 4 or both (59) (since they are in 17/3@r2c4) or both (25) (since one of them is in V1)
-> 15/3@r1c2 = [681] or [816]
But whatever goes in r1c2 (6 or 8) must go in W1 in r4c3. Cannot be an 8.
-> 15/3@r1c2 = [681]
-> r1c3 = 9
-> r2c3 = 7
-> HS 5 in n1 -> r1c1 = 5
-> r3c13 = [42]
-> r4c23 = [46]
-> r5c12 = [75] (V4)
Also 16/3@r6c2 = [916]
-> r159c4 = [412]
Also V7 = [978]
etc.

This is a Windoku twin killer. Combinations in cages with totals must use non-consecutive numbers, while those in cages without totals must 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.

1. 9(3) cage at R4C2 = {135} (only combination containing non-consecutive numbers), locked for C2 and N4

2. 11(3) cage at R4C6 = {137/146} (only combinations containing non-consecutive numbers), no 2,5,8,9 1 locked for R4 and W2
2a. 14(3) cage at R2C8 = {248/257} (only remaining combinations containing non-consecutive numbers), no 3,6,9, 2 locked for W2
2b. Killer pair 4,7 in 14(3) cage and 11(3) cage), locked for W2
2c. 45 rule on W2 3 innies R2C67 + R3C6 = 20 = {569} (only remaining combination containing non-consecutive numbers), locked for W2
2d. 11(3) cage at R4C6 = {137} (only remaining combination), locked for R4 and W2 -> R4C2 = 5, placed for W1
2e. Naked triple {248} in 14(3) cage, locked for N3

3. Non-total cage at R1C7 = {567} (only remaining combination of consecutive numbers), locked for R1 and N3 -> R2C7 = 9, placed for W2
3a. Naked pair {56} in R23C6, locked for C6 and N2
3b. Non-total cage at R1C6 = {456} (only remaining combination of consecutive numbers) -> R1C6 = 4, placed for hidden window R159C678
3c. Naked pair {13} in R23C9, locked for C9 and hidden window R234C159
3d. Non-total cage at R2C9 = {123} (only remaining combination of consecutive numbers) -> R4C9 = 2, placed for hidden window R234C159
3e. 5 in N1 only in R23C1, locked for C1

4. 16(3) cage at R1C3 = {169/268} (only remaining combinations containing non-consecutive numbers), no 3,4,7, 6 locked for C3, N1 and W1
4a. 5 in N1 only in R23C1 -> non-total cage at R1C1 = {345} -> R1C1 = 3, placed for hidden window R159C159, R23C1 = {45}, locked for C1, N1 and hidden window R234C159
4b. 1 in N1 only in 16(3) cage = {169}, locked for C3 and N1
4c. Naked triple {278} in R123C2, locked for C2, 7 also locked for W1
4d. Naked triple {469} in R789C2, locked for N7
4e. 7 in N2 only in R23C5, locked for C5

5. 3 in N2 only in R23C4, locked for C4
5a. Non-total cage at R4C4 = {678/789} (only remaining combinations with consecutive numbers, cannot be {456/567} because 5,6 only in R5C4), no 1,2,4,5, 7 locked for R5 and hidden window R159C234
5b. R4C3 = 4 (hidden single in W1)

6. Non-total cage at R1C4 = {123} (only remaining combinations with consecutive numbers) -> R2C4 = 3, R1C45 = {12}, locked for R2 and N2, R1C23 = [89], both placed for hidden window R159C234, R23C9 = [13], R23C3 = [61], R23C6 = [56], R23C1 = [45]
6a. R5C3 = 7, R5C4 = 6, placed for hidden window R159C234, R4C4 = 8 (step 5a), R3C4 = 9, R4C15 = [69]
6b. Naked pair {78} in R23C5, locked for C5

7. R9C2 = 4 -> non-total cage at R9C1 = {234} -> R9C1 = 2, R9C3 = 3
7a. Naked pair {58} in R78C3, locked for C3, N7 and W3 -> R6C3 = 2, placed for W3
7b. Naked triple {147} in R678C4, locked for C4 and W3 -> R1C45 = [21], R9C45 = [56], R56C2 = [13]

8. R5C6 = 2 (hidden single in hidden window R159C678)
8a. Naked pair {45} in R56C5, locked for C5 and N5
8b. Naked pair {17} in R6C46, locked for R6 and N5 -> R4C6 = 3

9. 15(3) cage at R6C6 = {159/168} -> R6C6 = 1, placed for W4
9a. Killer pair 8,9 in R6C1 and 15(3) cage, locked for R6
9b. 4 in N6 only in R56C9, locked for C9

10. 14(3) cage at R7C5 = {248/257} -> R7C5 = 2, R7C67 = [75/84]
10a. Killer pair 5,8 in R7C3 and R7C67, locked for R7

11. R7C8 = 3 (hidden single in R7) -> non-total cage at R7C8 = {123} (cannot be {234/345} because no 4,5 in R9C7) -> R8C8 = 2, R9C7 = 1

12. R8C3 = 3 -> 13(3) cage at R8C4 = {139} (only remaining combination) -> R8C4 = 1, R8C6 = 9, placed for W4
12a. R67C4 = [74], R7C7 = 5, placed for W4, R78C1 = [17], R78C2 = [96], R78C3 = [85], R7C6 = 7

[And finally, since I haven’t used it yet …]
13. R7C9 = 6, R8C9 = 8 -> non-total cage at R7C9 = {678} -> R9C9 = 7

and the rest is naked singles.

I'll rate my walkthrough for CNC 23W at Easy 1.5. The steps were fairly easy; I made frequent use of the hidden windows, hence the rating.

This is a Windoku twin killer. Combinations in cages with totals must use non-consecutive numbers, while those in cages without totals must 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.

1. 9(3) cage at R8C1 = {135} (only combination containing non-consecutive numbers), locked for R8 and N7
1a. Non-total cage at R9C1 = {678/789}, 7,8 locked for R9 and N7
1b. 2,4 in N7 only in R7C123, locked for R7

2. 11(3) cage at R6C6 = {137/146} (only combinations containing non-consecutive numbers), no 2,5,8,9, 1 locked for C6 and W4
2a. 7 of {137} must be in R8C6 -> no 7 in R67C6

3. 19(3) cage at R2C7 = {379/469}, no 1,2,5,8, 9 locked for R2 and N3
3a. Non-total cage at R1C7 = {123/456} (cannot be {234/345/567/678} which clash with 19(3) cage), no 7,8
3b. Killer triple 3,4,6 in non-total cage and 19(3) cage, locked for N3
3c. 8 in N3 only in R3C789, locked for R3

4. 12(3) cage at R4C6 = {138/147/246}, no 5,9

5. 17(3) cage at R7C8 = {179/269/359} (cannot be {368} which doesn’t allow three consecutive candidates in non-total cage at R7C9), no 4,8, 9 locked for C8 and N9
5a. Non-total cage at R7C9 cannot be {123/567} which clash with 17(3) cage -> no 1 in R79C9
5b. 1 in N9 only in R9C78, locked for R9 and hidden window R159C678
5c. Non-total cage at R1C7 (step 3a) = {123/456}
5d. 1 of {123} must be in R1C9 -> no 2,3 in R1C9

6. 15(3) cage at R1C2 = {159/168/249} (cannot be {258/357} which don’t allow three consecutive candidates in non-total cage at R1C1), no 3,7
6a. Non-total cage at R1C1 cannot be {123/456/789} which clash with 15(3) cage -> no 1,9 in R123C1

7. 16(3) cage at R6C2 = {169/259/268} (cannot be {358} which clashes with 9(3) cage at R8C2, ALS block), no 3,4,7
7a. 7 in W4 only in R78C4, locked for C4 and N8
7b. 11(3) cage at R6C6 (step 2) = {146} (only remaining combination), locked for C6 and W4

8. 17(3) cage at R7C8 (step 5) = {179/269/359}
8a. 6 of {269} must be in R9C8 -> no 2 in R9C8
8b. 1,6 of {179/269} must be in R9C8, 9 of {359} must be in R8C8 -> no 9 in R9C8
8c. 17(3) cage = {179/269/359}, 9 locked for W4

9. 12(3) cage at R4C6 (step 4) = {138/147/246}
9a. 2,7 of {147/246} must be in R4C6 -> no 2,7 in R4C78

10. 17(3) cage at R2C4 = {269/359/368}, no 1,4

11. 17(3) cage at R7C8 (step 5) = {179/269/359}, non-total cage at R7C9 (step 5a) = {234/345/456/678}
11a. Hidden killer pair 1,4 in 17(3) cage at R7C8, non-total cage at R7C9 and R9C7 for N9, R9C7 cannot contain both of 1,4 -> 17(3) cage and non-total cage must contain at least one of 1,4 -> 17(3) cage = {179} and/or non-total cage = {234/345/456} -> 17(3) cage = {179/269} (cannot be {359} which clashes with {234/345/456}, locking-out cages), no 3,5
11b. Non-total cage = {234/345/456} (cannot be {678} which clashes with 17(3) cage), no 7,8, 4 locked for C9 and N9
11c. 7 in N9 only in R78C78, locked for W4
11d. 8 in N9 only in R78C7, locked for C7 and W4

12. 16(3) cage at R6C2 (step 7) = {169/268} (cannot be {259} which clashes with R6C78, ALS block), no 5, 6 locked for R6 and W3
12a. Killer pair 2,9 in 16(3) cage and R7C23, locked for W3
12b. Hidden killer pair 2,9 in 16(3) cage and R7C23 for W3 -> R7C23 = {24/49}, 4 locked for R7 and W3
12c. 6 in C6 only in R78C6, locked for N8

13. 4 in C4 only in R159C4, locked for hidden window R159C234

14. Non-total cage at R7C9 (step 11b) = {234/345/456}
14a. Hidden killer pair 1,6 in non-total cage and R9C78 for N9, non-total cage = {456}, R9C8 = {16} and/or R9C7 = {16} -> R9C78 = {16} or non-total cage = {456} -> no 5 in R9C7 (locking-out cages)

15. 15(3) cage at R1C2 (step 6) = {159/168} (cannot be {249} which clashes with R7C2), no 2,4, 1 locked for C2 and N1
15a. Non-total cage at R1C1 (step 6a) = {234/345/678} (cannot be {567} which clashes with 15(3) cage)
15b. Consider combinations for R7C23 (step 12b) = {24/49}
R7C23 = {24} => R7C1 = {69} => non-total cage = {234/345} (cannot be {678} which clashes with R79C1, ALS block)
or R7C23 = {49} => R9C1 = {678} => non-total cage = {234/345} (cannot be {678} which clashes with R9C1)
-> Non-total cage = {234/345}, 3,4 locked for C1 and N1
15c. 7 in N1 only in R123C3, locked for C3
15d. 3 in R8 only in R8C23, locked for W3

16. 4 in W1 only in R4C23, locked for R4
16a. 12(3) cage at R4C6 (step 4) = {138} (only remaining combination), locked for R4 and W2, 1 also locked for N6
16b. R3C9 = 8 (hidden single in R3)
16c. 3 in N4 only in R5C23, locked for R5

17. 4,6 in W2 only in 19(3) cage at R2C7 = {469}, locked for R2 and N3
17a. 1,3 in N3 only in non-total cage at R1C7 = {123} (only remaining combination) -> R1C9 = 1, placed for hidden window R159C159, R1C78 = {23}, locked for R1, N3 and hidden window R159C678
17b. Naked pair {57} in R3C78, locked for R3 and W2 -> R2C6 = 2, R3C6 = 9, placed for W2, R9C6 = 5
17c. R2C9 = 9 (hidden single in R2), placed for R234C159
17d. R5C7 = 9 (hidden single in N6)

18. R4C6 = 3 (hidden single in C6), R4C78 = [18]
18a. R9C8 = 1 (hidden single in R9) -> R78C8 = 16 = {79}, locked for C8 and N9 -> R3C78 = [75]

19. Non-total cage at R7C9 (step 11b) = {234/345} (cannot be {456} which clashes with R9C7), no 6, 3,4 locked for C9 and N9 -> R9C7 = 6, R2C78 = [46], R5C8 = 4
19a. Naked triple {789} in R9C123, locked for R9 and N7
19b. Naked pair {24} in R7C23 and W3 -> R7C1 = 6, R7C6 = 1, R68C6 = [46]
19c. Naked pair {78} in R78C4, locked for C4, N8 and W3
19d. Naked triple {169} in 16(3) cage at R6C2, locked for R6

20. 3 in W1 only in 17(3) cage at R2C4 (step 10) = {359} (only remaining combination) -> R3C4 = 3, R2C4 = 5, placed for W1, R4C4 = 9, R2C1 = 3

21. R9C1 = 9 (hidden single in C1), R9C23= [78], both placed for hidden window R159C234, R2C3 = 7

22. 15(3) cage at R1C2 (step 15) = {168} (only remaining combination, cannot be {159} because 5,9 only in R1C2) -> R1C2 = 6, R23C2 = [81], R3C3 = 2, R13C1 = [54], R1C3 = 9, R7C23 = [24], R4C23 = [46]

23. Non-total cage at R4C2 = {4567} (only remaining combination) -> R5C12 = [75]

[At this stage I couldn’t make further progress so checked HATMAN’s diagram and realised that I’d missed that there was a non-total cage at R5C8, so …]

24. Non-total cage at R5C8 = {3456} (only remaining combination, cannot be {2345} which clashes with R6C7, cannot be cannot be {4567} because 5,7 only in R6C9) -> R5C9 = 6, R6C89 = [35]

and the rest is naked singles.

I'll rate my walkthrough for CNC 22W at 1.5. It's quite a lot harder than CNC 23W, but it's not harder than a 1.5 killer.