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HATMAN
 Post subject: Windoku X Solo Killers
PostPosted: Fri May 05, 2023 4:31 pm 
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I've always liked Windoku X interactions for Killers. But too much information is given, so either you do zero killers with very few cages, or KiMos.

On the players forum Hajime came up with the Solo idea for Windoku: http://forum.enjoysudoku.com/windoku-solo-t41273.html
It is excellent as leaving out the nonets makes the information level more reasonable.
It works very well for killers adding an interesting twist, but not as different as jigsaws.

Windoku X Solo Killer 1

Reasonably hard about 1.0 on the assassin scale.
This is an estimate as I do not know how to enter these in Sudoku Solver.
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Windoku X Solo Killer 2

Harder about 1.2 on the assassin scale.
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Andrew
PostPosted: Sun May 14, 2023 10:31 pm 
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Thanks HATMAN for an enjoyable puzzle. I'd put it a touch harder than 1.0 unless there's a simpler alternative to the interaction analysis I used in my step 3. I've stated all the placements in and locked numbers for windows, for those who aren't familiar with Windoku puzzles.

Here's how I solved Windoku X Solo Killer 1:
I’ve identified the four given windows as W1 (R234C234), W2 (R234C678), W3 (R678C234) and W4 (R678C678). As always with Windokus there are five hidden windows WR159C234, WR159C678, WR234C159, WR678C159 and WR159C159.

Prelims

a) R12C5 = {18/27/36/45}, no 9
c) R3C12 = {19/28/37/46}, no 5
d) R4C12 = {16/25/34}, no 7,8,9
e) R5C12 = {17/26/35}, no 4,8,9
f) R5C89 = {19/28/37/46}, no 5
g) R6C89 = {17/26/35}, no 4,8,9
h) R7C89 = {15/24}
i) R89C5 = {89}
j) 11(3) cage at R1C6 = {128/137/146/236/245}, no 9
k) 21(3) cage at R3C9 = {489/579/678}, no 1,2,3
l) 26(4) cage at R1C8 = {2789/3689/4589/4679/5678}, no 1
m) 26(4) cage at R6C6 = {2789/3689/4589/4679/5678}, no 1
n) 11(4) cage at R8C8 = {1235}

1a. Naked pair {89} in R89C5, locked for C5, clean-up: no 1 in R12C5
1b. 45 rule on R12 1 innie R2C7 = 4, placed for W2, clean-up: no 5 in R1C5
1c. 45 rule on C89 1 innie R3C8 = 8, placed for W2, R3C7 = 2 (cage sum), placed for W2 and D/, clean-up: no 2 in R5C9
1d. 45 rule on C12 1 innie R7C2 = 6, placed for W3, clean-up: no 4 in R3C1, no 1 in R4C1, no 2 in R5C1
1e. 45 rule on R89 1 innie R8C3 = 4, placed for W3, R7C3 = 3 (cage sum), placed for W3 and D/
1f. 11(3) cage R1C6 = {128/137/146/236} (cannot be {245} because 2,4 only in R1C6), no 5
1g. 2,4 of {128/146/236} only in R1C6 -> no 6,8 in R1C6
1h. 21(3) cage at R3C9 = {489/579/678}
1i. 8 of {489/678} only in R4C9 -> no 4,6 in R4C9
1j. Combined cages R89C89, R7C89 and R6C89 = {1235}{15}{26}/{1235}{24}{17}/{1235}{24}/{35}, caged X-Wing for 2, no other 2 in C89, clean-up: no 8 in R5C9

2a. 45 rule on R1234 1 outie R5C7 = 1 innie R4C5 + 3, no 1,7 in R4C5, no 1,3 in R5C7
2b. 45 rule on R6789 1 outie R5C3 = 1 innie R6C5 + 2, no 1,2 in R5C3, no 1,2 in R6C5
2c. 45 rule on C1234 1 innie R5C4 = 1 innie R7C5, no 3,6,8,9 in R5C4
2d. 45 rule on C6789 1 innie R5C6 = 1 innie R3C5 + 3, no 7 in R3C5, no 1,2,3,5 in R5C6
2e. 3 in R5 only in R5C12 = {35} or R5C89 = {37} -> R5C12 = {35}/[62] (cannot be {17}, locking-out cages), no 1,7

[Time to start using the hidden windows]
3a. 2 in R5 only in R5C24, locked for WR159C234
3b. 4 on D/ only in R1C9 + R5C5 + R9C1, locked for WR159C159, clean-up: no 5 in R2C5, no 6 in R5C8
3c. R34567C5 = {145}{27}/{145}{36}
3d. R3C5 + R5C6 (step 2d) = [14/47/58/69] (cannot be [36] which clashes with all 6s in C5), no 3 in R3C5, no 6 in R5C6
3e. R34567C5 = {145}{27} gives 2,7 both in 22(5) cage at R4C5 (because R5C4 = R7C5, step 2c) and no 3,6 in 22(5) cage
3f. R34567C5 = {145}{36} gives 3 in R46C5 and no 2,7 in 22(5) cage (because R5C4 = R7C5, step 2c)
3g. 22(5) cage must therefore contain both of 2,7 but not 3,6 or 3 but not 2,7 = {12478/13459/13468} (cannot be {12379/12469/12568/13567/23458/23467}, 1 locked for R5, clean-up: no 9 in R5C89
3h. 8,9 only in R5C6 -> R5C6 = {89}, R3C5 = {56} (step 2d)
3i. Killer pair 3,6 in R5C12 and R5C89, locked for R5, clean-up: no 3 in R4C5 (step 2a), no 4 in R6C5 (step 2b)
3j. 7 of {12478} only in R6C5 -> no 7 in R5C45, clean-up: no 7 in R7C5 (step 2c)
3k. 3,5 of {13459} must be in R6C5 and R4C5 (cannot be 4{15}93 which clashes with R5C3 + R6C5 = [53], step 2b) -> no 5 in R5C45 + R6C5, clean-up: no 7 in R5C3 (step 2b), no 5 in R7C5 (step 2c)
3l. 3 of {13468} must be in R6C5 -> no 6 in R6C5, clean-up: no 8 in R5C3 (step 2b)
3m. 1 in R5 only in R5C45, CPE no 1 in R46C4 using diagonals
3n. 8 in R6 only in R5C67, locked for hidden window WR159C678
3o. 5 in C5 only in R34C5, locked for hidden window WR234C159, clean-up: no 2 in R4C2
3p. 1 in C89 only in combined cages R89C89, R7C89 and R6C89 (step 1j) = {1235}{15}{26}/{1235}{24}{17}, no 3,5 in R6C89

4a. 27(5) cage at R3C5 = {13689/15678} -> R5C7 = 8, R5C6 = 9, placed for hidden window WR159C678, R4C5 = 5 (step 2a), R3C5 = 6, placed for hidden window WR234C159, R5C3 = 5, placed for hidden window WR159C234, R6C5 = 3 (step 2b), placed for hidden window R678C159, clean-up: no 4 in R3C2, no 2 in R4C1, no 1 in R4C2, no 3 in R5C12
4b. R5C12 = [62], 6 placed for hidden window WR159C159, clean-up: no 4 in R5C8, no 2 in R7C5 (step 2c)
4c. Naked pair {34} in R4C12, locked for R4
4d. 3,5 of 27(5) cage only in R3C6 -> R3C6 = {35}
4e. 27(5) cage = {13689/15678}, 1 locked for R4 and W2
4f. 3 in W2 only in R23C6, locked for C6
4g. Caged X-Wing for 3 in R5C89 and 11(4) cage at R8C8, no other 3 in C89
4h. 3 in C9 only in R59C9, locked for hidden window WR159C159
4i. 25(5) cage at R5C3 = {12589/14578}
4j. 25(5) cage = [52]{89}1/[51]{78}4 (R7C45 cannot be [21/14] which clash with R7C89) -> R6C3 = {12}, R67C4 = {78/89}, 8 locked for C4 and W3
4k. Killer pair 1,2 in R6C3 and R6C89, locked for R6
4l. Killer pair 1,4 in R7C4 and R7C89, locked for R7

5a. 21(3) cage at R3C9 = [498/768] -> R4C9 = 8, placed for hidden window WR234C159
5b. R2C8 = 6 (hidden single on D/), R4C8 = 9, R3C9 = 4 (cage sum), placed for hidden window WR234C159, R4C12 = [34], clean-up: no 7 in R3C2, no 2 in R6C9, no 2 in R7C8
5c. Naked pair {17} in R4C67, 7 locked for R4 and W2 -> R23C6 = [35]
5d. 26(4) cage at R1C8 = {4679} (only remaining combination) -> R1C8 = 4, placed for hidden window WR159C678, R12C9 = {79}, 7 locked for C9, R5C89 = [73], 7 placed for hidden window WR159C678, clean-up: no 1 in R6C89, no 2 in R7C9
5e. R6C89 = [26], 2 placed for W4, naked pair {15} in R7C89, locked for R7, R7C5 = 4, R5C45 = [41], 1 placed for both diagonals, R4C67 = [71], 7 placed for D/, R1C9 = 9, placed for D/
5f. R1C7 = 6, R2C6 = 3 -> R1C6 = 2 (cage sum), 6 placed for hidden window WR159C678
5g. R67C6 = [48] = 12 -> R67C7 = 14 = [59], 9 placed for D\, R67C4 = [87], 8 placed for D/, 7 placed for W3
5h. R9C678 = [135], R9C9 = 2, placed for D\
5i. R3C3 = 7, placed for D\ and W1, R4C34 = [26], 2 placed for W1, R3C4 = 3 (cage sum)

and the rest is naked singles, not using the diagonals or windows.

Solution:
5 3 8 1 7 2 6 4 9
1 8 9 5 2 3 4 6 7
9 1 7 3 6 5 2 8 4
3 4 2 6 5 7 1 9 8
6 2 5 4 1 9 8 7 3
7 9 1 8 3 4 5 2 6
2 6 3 7 4 8 9 1 5
8 5 4 2 9 6 7 3 1
4 7 6 9 8 1 3 5 2
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Andrew
PostPosted: Mon May 15, 2023 8:00 pm 
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And now the second one. I was a bit slower getting going on this one but then I found it the easier of the two; just one short forcing chain.

Here's how I solved Windoku X Solo Killer 2:
I’ve identified the four given windows as W1 (R234C234), W2 (R234C678), W3 (R678C234) and W4 (R678C678). As always with Windokus there are five hidden windows WR159C234, WR159C678, WR234C159, WR678C159 and WR159C159.

Prelims

a) R12C7 = {29/38/47/56}, no 1
c) R1C89 = {19/28/37/46}, no 5
d) R34C4 = {69/78}
e) R3C56 = {19/28/37/46}, no 5
f) R45C3 = {17/26/35}, no 4,8,9
g) R4C67 = {59/68}
h) R56C7 = {89}
i) R6C34 = {49/58/67}, no 1,2,3
j) 22(3) cage at R1C3 = {589/679}
k) 11(3) cage at R6C1 = {128/137/146/236/245}, no 9
l) 27(4) cage at R1C1 = {3789/4689/5679}, no 1,2
m) 12(4) cage at R1C5 = {1236/1245}, no 7,8,9
n) 12(4) cage at R2C8 = {1236/1245}, no 7,8,9
o) 13(4) cage at R5C8 = {1237/1246/1345}, no 8,9

1a. Naked pair {89} in R56C7, locked for C7, clean-up: no 2,3 in R12C7, no 5,6 in R4C6
1b. R12C7 = {47} (cannot be {56} which clashes with R4C7), locked for C7
1c. 45 rule on C89 3 outies R378C7 = 6 = {123}, locked for C7
1d. 12(4) cage at R2C8 = {1236/1245}, CPE no 1,2 in R2C6 using W2
1e. 12(4) cage at R1C5 and 12(4) cage at R2C8 must have different combinations because R2C6 ‘sees’ all of 12(4) cage at R2C8
1f. 45 rule on R123 2 innies R3C49 = 14 = [68/86/95], clean-up: no 8 in R4C4
1g. 45 rule on C123 2 innies R16C3 = 15 = {69/78}, clean-up: no 8,9 in R6C4
1h. 21(4) cage at R7C7 = {1389/2379}, 3 locked for C7 and W4, R78C8 = {79/89}, 9 locked for C8, clean-up: no 1 in R1C9
1i. 45 rule on C1234 4 innies R5789C4 = 10 = {1234}, 4 locked for C4, clean-up: no 9 in R6C3, no 6 in R1C3
1j. 45 rule on R789 1 outie R6C6 = 1 innie R7C1 + 2, no 1,2 in R6C6, no 1,7,8 in R7C1
1k. 45 rule on C789 3 outies R489C6 = 21 = {489/579/678}, no 1,2,3
1l. 4 in W1 only in R234C2 + R23C3, CPE no 4 in R1C2
1m. 9 in W2 only in R34C6, locked for C6
1n. 45 rule on R789 3 outies R6C126 = 13 = {148/238/247/346} (cannot be {157/256} which clash with R6C34), no 5, clean-up: no 3 in R7C1 (step 1j)
1o. 11(3) cage at R6C1 = {128/146/236/245} (cannot be {137} because no 1,3,7 in R7C1), no 7
1p. 45 rule on R6789 4 innies R6C5789 = 19 contains 9 for R6 = {1279/1369/1459/2359}, no 8 -> R6C7 = 9, placed for W4, R5C7 = 8, placed for hidden window WR159C678, clean-up: no 2 in R1C9
1q. R9C8 = 9 (hidden single in C8)

2a. 45 rule on C123 1 innie R1C3 = 1 outie R6C4 + 2
2b. R1C3 + R126C4 = 7{69}5/8{59}6/9{58}7, no 7 in R12C4
2c. 7 in C4 only in R46C4, CPE no 7 in R5C5 using diagonals
2d. Hidden killer pair 8,9 in R2C1 and R2C234 for R2, R2C234 cannot contain both of 8,9 (clashes with R34C4 in W1) -> R2C1 = {89}, R2C234 contains one of 8,9
2e. Killer pair 8,9 in R2C234 and R34C4, locked for W1
2f. 27(4) cage at R1C1 = {3789/4689/5679}, 9 locked for C1

3a. 45 rule on R123 R4C4 = R3C9 + 1
3b. Consider placements for R3C9 = {568}
R3C9 = 5 => R4C4 = 6, R4C67 = [95]
or R3C9 = {68} => max R4C89 = 9, no 9 in R4C9
-> no 9 in R4C9
3c. 9 in R4 only in R4C456, CPE no 9 in R5C5 using diagonals
[Cracked. The rest is fairly straightforward.]
3d. R5C2 = 9 (hidden single in R5), placed for hidden window WR159C234 -> 18(4) cage at R4C1 = {1269/1359/2349}, no 7,8
3e. 22(3) cage at R1C3 = {589/679} -> R2C4 = 9, R2C1 = 8, placed for hidden window WR234C159, R3C4 = 8 (hidden single in W1) -> R4C4 = 7, placed for W1 and D\, R8C8 = 8, placed for W4 and D\, R3C9 = 6, placed for hidden window R234C159, clean-up: no 4 in R1C8, no 2,4 in R3C56, no 1 in R5C3, no 6 in R6C3, no 5,6 in R7C1 (step 1j)
3f. Naked pair {78} in R16C3, locked for C3, clean-up: no 1 in R4C3
3g. R89C8 = [89] = 17 -> R78C7 = 4 = {13}, 1 locked for C7 and W4, R3C7 = 2, placed for W2 and D/
3h. R3C9 = 6 -> R4C89 = 9 = {45}, locked for R4, R4C7 = 6, placed for W2, R4C6 = 8, placed for D/, clean-up: no 2 in R1C8, no 2,3 in R5C3
3i. R9C8 = 5, placed for hidden window WR159C678 -> R89C7 = 13 = {67}, locked for C7
3j. R6C6 = 4, placed for W4 and D\, R7C1 = 2 (step 1j), placed for hidden window WR678C159, R7C6 = 5, placed for W4, R2C6 = 3, placed for W2
3k. R3C6 = 9 (hidden single in C6) -> R3C5 = 1, placed for hidden window WR234C159
3l. R4C1 = 3, R4C23 = [12], both placed for W1, R5C2 = 9 -> R5C1 = 5 (cage sum), R5C3 = 6, placed for hidden window WR159C234, R1C4 = 5, R6C4 = 6, placed for W3 and D/, R6C3 = 7, placed for W3, R1C3 = 8
3m. R67C1 = [12], both placed for hidden window WR678C159, R6C2 = 8 (cage sum)

4a. R5C5 = 3, placed for both diagonals, R46C5 = [95], 5 placed for hidden window WR678C159, R456C5 = 17 -> R5C46 = 6 = [42], 4 placed for hidden window WR159C234, R7C7 = 1, placed for D\, clean-up: no 7 in R1C8
4b. R23C3 = [45], R2C2 = 6, placed for D\, R1C2 = 2 (cage sum), placed for hidden window WR159C234
4c. R6C6 = 4, R7C4 = 3, placed for W3, R7C6 = 5 -> R7C5 = 7 (cage sum), placed for hidden window WR678C159

and the rest is naked singles, not using the diagonals or windows.

Solution:
9 2 8 5 6 1 4 3 7
8 6 4 9 2 3 7 1 5
7 3 5 8 1 9 2 4 6
3 1 2 7 9 8 6 5 4
5 9 6 4 3 2 8 7 1
1 8 7 6 5 4 9 2 3
2 4 9 3 7 5 1 6 8
6 5 1 2 4 7 3 8 9
4 7 3 1 8 6 5 9 2
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HATMAN
PostPosted: Mon May 22, 2023 11:10 am 
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Andrew
On the first one at your step three JSudoku goes into a couple of turbofish. So although convoluted yours is preferred as it is a killer style solution.
I had hoped that there would be a neater way of using the centre cross.
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