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PostPosted: Mon Oct 25, 2021 6:19 am 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Here's how I solved Sindoku 25 W:
Prelims
a) For squares with 1 number, delete that number from the rest of that nonet
b) For squares with 1 number, delete the adjacent numbers in the cells covered by those squares

This is a Windoku; placements stated for the windows, remember to make placements for nonets.

Steps Resulting From Prelims
1a. 6 in N1 only in R12C1, locked for C1
1b. 7 in N1 only in R12C3, locked for C3
1c. 8,9 in N1 only in R3C123, locked for R3
1d. 8 in N2 only in R12C6, locked for C6
1e. 4 in N9 only in R89C7, locked for C7
1f. 5 in N9 only in R89C9, locked for C9

2a. 8,9 in N1 only in R3C123
2b. R23C12 contains 2 doublets including at least one of 8,9, no 7 -> R3C12 = {89}, locked for N1, R2C12 = {12/23/34}
2c. R1C1 = 6 (hidden single in N1), placed for WR159C159
2d. R34C23 contains 4 singletons, R3C2 = {89} -> no 8,9 in R4C34

3a. R12C12 contains 6 and 3 consecutive numbers = {1236/2346}, 2,3 locked for N1
3b. R12C56 contains 1 and 3 consecutive numbers including 8 = {1678/1789}, no 3,4,5, 7 locked for N2
3c. R12C45 contains 9 and 3 consecutive numbers = {1239/5679} (cannot be {2349/3459} because R12C5 only contains 1,6,7,9), no 4
3d. 4 in N2 only in R3C456, locked for R3
3e. 7 in R3 only in R3C789, locked for N3

4a. R45C12 contains 3 and 3 consecutive numbers = {3567/3678/3789}, 7 locked for N4
4b. R56C23 contains 2 and 3 consecutive numbers = {2456/2567/2678/2789}
4c. 7 of {2678/2789} must be in R5C2 -> no 8,9 in R5C2

5a. R89C89 contains 5 and 3 consecutive numbers = {5789} (cannot be {1235} because R89C8 only contain 7,8,9), 7,8,9 locked for N9
5b. Naked pair {46} in R89C7, 6 locked for C7 and N9
5c. Naked triple {123} in R7C123, locked for R7
5d. R89C78 contains 4 and 3 consecutive numbers = {4678} -> R89C8 = {78}, locked for N9
5e. R78C89 contains 2 doublets -> R7C89 = {12/23}, 2 locked for N9, R8C89 = [89], R9C89 = [75], 8 placed for WR678C678, 9 placed for WR678C159, 7 placed for WR159C678, 5 placed for WR159C159
5f. R78C67 contains 4 singletons, no 8 and R8C6 = {46} -> R7C6 = 9, placed for WR678C678
5g. R78C67 contains R7C7 = {13}, R8C7 = {46} -> no 2,5 in R8C6
5h. R67C67 contains 4 singletons, R7C13 = {13} -> no 2 in R6C67
5i. 2 in WR678C678 only in R67C8, locked for C8
5j. 5 in WR678C678 only in R6C678, locked for R6
5k. R78C56 contains 2 doublets, R7C6 = 9 -> R7C5 = 8, placed for WR678C159
5l. R78C56 contains 2 doublets, not 4 consecutive numbers -> no 7 in R8C56

6a. 7 in N8 only in R78C6, locked for C6 and WR678C234
6b. 8,9 in WR678C234 only in R6C234
6c. R67C23 contains 2 doublets -> R6C23 = {89}, locked for R6 and N4, R7C23 = {45/56} (not {67} because 2 doublets, not 4 consecutive numbers), 5 locked for R7 and WR678C234
6d. R78C23 contains 2 doublets, R7C23 = {45/56} -> R8C23 = {12/23} (not {34} because 2 doublets, not 4 consecutive numbers), no 4,6, 2 locked for R8, N7 and WR678C234
6e. R56C23 contains 2 and 3 consecutive numbers, R6C23 = {89} -> R5C23 = [72], R45C1 = [53], R4C2 = 6, 5 placed for WR234C159, 6 placed for WR234C234, 3 placed for WR159C159, 2,7 placed for WR159C234
6f. R2C3 = 7 (hidden single in N1)
6g. R23C23 contains 4 singletons, R2C3 = 7 -> R3C12 = [89], 8 placed for WR234C159, 9 placed for WR234C234, R6C23 = [89]
6h. R34C23 contains 4 singletons, R34C2 = [96] -> R34C3 = [14], placeed for WR234C234, R1C3 = 5, placed for WR159C234, R789C3 = [638], 3,6 placed for WR678C234, 8 placed for WR159C234
6i. R23C12 contains 2 doublets, R3C12 = [89] -> R2C12 = [23] (cannot be [43] which clashes with R1C2), 2 placed for WR234C159, 3 placed for WR234C234, 4 placed for WR159C234
6j. R789C2 = [521], 1 placed for WR234C159
6k. R9C1 = 9 (hidden single in C1), placed for WR159C159
6l. R234C4 = [528]
6m. R7C4 = 7 (hidden single in C4) -> R78C1 = [47], 4 placed for WR678C159

7a. R23C45 contains 2 doublets, no 8 -> no 9 in R2C5
7b. R1C4 = 9 (hidden single in N2)
7c. R12C45 contains 9 and 3 consecutive numbers = {5679} -> R12C5 = [76], 6 placed for WR234C159
7d. R23C45 contains 2 doublets, R2C45 = [56], R3C45 = [23], R3C6789 = [4567]
7e. 9 in R2 only in R2C78
7f. R23C78 contains 2 doublets -> R2C78 = [89], 9 placed for WR234C678
7g R12C6 = [81], 1 placed for WR234C678

and the rest is naked singles, without using the windows.

Here's how I solved Sindoku 25 W FNC:
Prelims
a) For squares with 1 number, delete that number from the rest of that nonet
b) For squares with 1 number, delete the adjacent numbers in the cells covered by those squares

This is a Windoku; no initial eliminations for the windows.
FNC: Diagonally adjacent cells are non-consecutive.

Placements stated for the windows; remember to make placements for the nonets.

1a. R89C89 = {5789} (cannot be {1235} because R89C8 only contains 7,8,9), 7,8,9 locked for N9
1b. Naked triple {123} in R7C789, locked for R7
1c. R89C78 contains 4 and 3 consecutive numbers = {4678} -> R89C8 = {78}, locked for N9
1d. R78C89 contains 2 doublets -> R7C89 = {12/23}, 2 locked for N9, R8C89 = [89], R9C89 = [75], R89C7 = [46] (FNC), 4,8 placed for WR678C678, 9 placed for WR678C159, 6,7 placed for WR159C678, 5 placed for WR159159
1e R78C67 contains 4 singletons = {1469/1479} -> R7C67 = [91], placed for W678C678, R8C6 = {67}
1f. R67C67 contains 4 singletons, R7C67 = [91] -> R6C67 = {35/36/37}, 3 locked for R6 and WR678C678
1g. R7C8 = 2 -> R7C9 = 3, placed for WR678C159
1h. R78C56 contains 2 doublets, R7C6 = 9 -> R7C5 = 8, R8C56 = [56] (cannot be {67} because R78C56 contains 2 doublets, not 4 consecutive numbers), 5,8 placed for WR678C159, 6 placed for WR678C678
1i. R6C8 = 5, R6C67 = [37] (FNC)
FNC: no 2,4 in R5C5, no 8 in R5C6, no 2 in R5C7, no 6 in R5C8, no 4,6 in R5C9, no 9 in R6C4, no 1 in R6C9, no 4 in R7C4, no 7 in R8C4, no 4 in R9C4, no 3,4 in R9C6

2a. R7C4 = 7, placed for WR678C234
2b. R8C1 = 7 (hidden single in R8)
2c. R9C5 = 4 (hidden single in N8), placed for WR159C159 -> no 3 in R8C4 (FNC)
2d. R9C4 = 3 (hidden single in N8), placed for WR159C234
2e. 9 in WR678C234 only in R6C23
2f. R67C23 contains 2 doublets -> R6C23 = [89] (FNC)
FNC: no 7 in R5C3, no 8 in R5C4, no 6 in R6C5, no 6 in R7C2, no 2 in R8C3, no 2 in R9C2, no 1,2 in R9C3

3a. R9C3 = 8
3b. R3C12 = [89] (hidden pair in N1), 8 placed for WR234C159, 9 placed for WR234C234, no 7 in R4C2 (FNC)
3c. R9C26 = [12] -> R8C234 = [231], 2 placed for WR678C234
3d. R9C9 = 9, placed for WR159C159
3e. R7C3 = 5 (FNC)
3f. R23C12 contains 2 doublets, R3C12 = [89] -> R2C12 = [23]/{34}, 3 locked for R2 and N1
3g. 6 in N1 only in R1C12, locked for R1
3h. R5C2 = 7 (hidden single in C2), placed for WR159C234
3i. R23C23 contains 4 singletons, R2C2 = {34} -> no 4 in R23C3
FNC: no 6 in R4C13 + R6C3, no 5 in R5C3

4a. 8 in WR234C234 only in R24C4, locked for C4, no 7 in R3C35 (FNC)
4b. R2C3 = 7 (hidden single in N1)
4c. R1C2 = 4 (FNC) -> R2C12 = [23], R4C2 = 6, placed for WR234C234
4d. Naked pair {15} in R13C3, locked for C3, 1 locked for N1
4e. R1C1 = 6 -> R7C13 = [46], 6 locked for WR678C234
4f. R456C1 = [531], R6C459 = [426]
4g. R12345C4 = [95286], 2,5 placed for WR234C234
4h. R34C3 = [14]
FNC: no 1 in R24C5, no 6 in R3C5, no 7 in R4C5

5a. R5C5 = 1, R4C6 = 7, R3C6 = 4
FNC: no 3 in R4C7 (FNC)

and the rest is naked singles, without using FNC.

Solution:
6 4 5 9 7 8 3 1 2
2 3 7 5 6 1 8 9 4
8 9 1 2 3 4 5 6 7
5 6 4 8 9 7 2 3 1
3 7 2 6 1 5 9 4 8
1 8 9 4 2 3 7 5 6
4 5 6 7 8 9 1 2 3
7 2 3 1 5 6 4 8 9
9 1 8 3 4 2 6 7 5


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