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HATMAN
 Post subject: HS 17 - CNC W X 59
PostPosted: Tue Nov 19, 2013 11:05 am 
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Joined: Wed Apr 30, 2008 9:45 pm
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HS 17 - CNC W X 59

All Cages are Non-Consecutive.
It is X.
It is Windoku.
Note the disjoint 23(4) cage in N1.

This one came out well and I think you will find it interesting. After you remove impossible values from the cages JS uses about 25 fishes. When you do the same with SS it finds something similar to my solution.

Image
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JS Code:
3x3:3:k:5897:5897:3078:3078:15:3847:3847:5130:5130:5897:16:3078:17:18:19:3847:5130:20:3077:3077:5897:21:22:23:5130:3080:3080:3077:24:25:26:27:28:29:30:3080:31:4109:4109:4109:32:4878:4878:4878:33:2818:34:35:36:37:38:39:40:2817:2818:2818:3596:41:42:43:3595:2817:2817:44:3596:2820:45:46:47:2819:3595:48:3596:49:2820:2820:50:2819:2819:3595:51:

Solution

294768513
761453298
385291746
179346852
526819374
438527961
612985437
947632185
853174629


Last edited by HATMAN on Wed Nov 27, 2013 5:40 pm, edited 1 time in total.

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Andrew
 Post subject: Re: HS 17 - CNC W X 59
PostPosted: Thu Nov 21, 2013 3:14 am 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
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Thanks HATMAN for another enjoyable and challenging puzzle!

Since JSudoku used about 25 fishes, I'm not surprised that I used a difficult step for my key breakthrough.

Here is my walkthrough for Human Solvable 17 CNC WX 59:
The Windows at R2C2, R2C6, R6C2 and R6C6 are numbered W1, W2, W3 and W4

In the following walkthrough I’ve used Windoku properties, the four given windows and five hidden ones, as in my post in the Standard Techniques forum here.

Prelims

a) 12(3) cage at R1C3 = {138/147/246}, no 5,9
b) 15(3) cage at R1C6 = {159/168/249/258/357}
c) 12(3) cage at R3C1 = {138/147/246}, no 5,9
d) 12(3) cage at R3C8 = {138/147/246}, no 5,9
e) 16(3) cage at R5C2 = {169/259/268/358}, no 4,7
f) 19(3) cage at R5C6 = {379/469}, no 1,2,5,8
g) 11(3) cage at R6C1 = {137/146}, no 2,5,8,9
h) 11(3) cage at R6C9 = {137/146}, no 2,5,8,9
i) 14(3) cage at R7C3 = {149/158/248/257}, no 3,6
j) 14(3) cage at R7C7 = {149/158/248/257}, no 3,6
k) 11(3) cage at R8C3 = {137/146}, no 2,5,8,9
l) 11(3) cage at R8C7 = {137/146}, no 2,5,8,9
m) 23(4) disjoint cage at R1C1 = {2579}
n) 20(4) cage at R1C8 = {1379/1469/2468}, no 5

1. Naked quad {2579} in 23(4) disjoint cage at R1C1, locked for N1

2. 19(3) cage at R5C6 = {379/469}, 9 locked for R5 and hidden window R159C678
2a. 16(3) cage at R5C2 = {268/358}, no 1, 8 locked for R5 and hidden window R159C234
2b. Killer pair 3,6 in 16(3) cage and 19(3) cage, locked for R5

3. 45 rule on R5 3 innies R5C159 = 10 = {127/145}
3a. 1 in R5 only in R5C159, locked for hidden window R159C159

4. Caged X-Wing for 1 in 11(3) cage at R6C1 and 11(3) cage at R6C9, no other 1 in R67
4a. 1 in R6 only in R6C19, locked for hidden window R678C159

5. Caged X-Wing for 1 in 11(3) cage at R8C3 and 11(3) cage at R8C7, no other 1 in R89
5a. 1 in N8 only in R9C46, locked for R9

6. 14(3) cage at R7C3 = {248/257}, no 9, 2 locked for N7 and D/
6a. 20(4) cage at R1C8 = {1379/1469/2468}
6b. 2 of {2468} must be in R1C8 -> no 8 in R1C8

7. 14(3) cage at R7C7 = {248/257}, no 9, 2 locked for N9
7a. 14(3) cage at R7C7 = {248/257}, CPE no 2 in R6C8 using W4
7b. 9 in N9 only in R89C9, locked for C9
7c. 9 in R7 only in R7C456, locked for N8

8. 12(3) cage at R1C3 = {138/147/246}
8a. 2,7 of {147/246} must be in R1C4 -> no 4,6 in R1C4
8b. 8 of {138} must be in R2C3 -> no 3 in R2C3

9. 12(3) cage at R3C1 = {138/147/246}
9a. 2,7 of {147/246} must be in R4C1 -> no 4,6 in R4C1

10. R7C12 + R89C3 = {13467}, 14(3) cage at R7C3 (step 6) = {248/257}
10a. Killer pair 4,7 in R7C12 + R89C3 and 14(3) cage, locked for N7

11. 9 in N7 only in R8C1 + R9C2
11a. 45 rule on N7 2 innies R8C1 + R9C2 = 2 outies R6C1 + R9C4 + 9
11b. R6C1 + R9C4 cannot total 3 or 6 (R6C1 + R9C4 must contain 1 because both 11(3) cages contain 1) -> no 3,6 in R8C1 + R9C2
11c. R8C1 + R9C2 = {59/89} -> R6C1 + R9C4 = {14/17} (must contain 1 because both 11(3) cages contain 1), no 3,6 in R6C1 + R9C4

12. 9 in N9 only in R89C9
12a. Hidden killer pair 5,8 in 14(3) cage at R7C7 and R89C9 for N9, 14(3) cage contains one of 5,8 -> R89C9 must contain one of 5,8 = {59/89}
12b. 45 rule on N9 2 innies R89C9 = 2 outies R6C9 + R9C4 + 9
12c. R6C9 + R9C6 must contain 1 because both 11(3) cages contain 1 -> R6C9 + R9C6 = {14/17}, no 3,6 in R6C9 + R9C6

13. 2 in hidden window R678C159 only in R678C5, locked for C5

14. 45 rule on N3 2 outies R1C6 + R4C9 = 1 innie R2C9 + 2, IOU no 2 in R1C6
14a. 2 in hidden window R159C678 only in R1C78 + R9C8, CPE no 2 in R3C8

15. 9 in N3 only in R2C78 + R3C7, locked for W2
15a. 20(4) cage at R1C8 = {1379/1469/2468}
15b. 9 in 20(4) cage = {1379/1469}, 1 locked for N3 or in R2C7 -> no 1 in R2C7 (blocking cages)
15c. 15(3) cage at R1C6 = {159/168/258/357} (cannot be {249} = [429] which clashes with 20(4) cage), no 4

16. 20(4) cage at R1C8 = {1379/1469/2468}, 15(3) cage at R1C6 (step 15c) = {159/168/258/357}
16a. 9 in N3 only in 20(4) cage = {1379/1469} or in R2C7 => 15(3) cage + 20(4) cage = {15}9 + 2{468}
16b. Consider combinations for 12(3) cage at R1C3 = {138/147/246}
12(3) cage = {138} => R1C34 = {13}, locked for R1 => 15(3) cage cannot be {15}9 => 20(4) cage = {1379/1469}
or 12(3) cage = {147}, R1C4 = 7 => 20(4) cage = {1379/1469} (cannot be {2468} because 15(3) cage + 20(4) cage = {15}9 + 2{468} (step 16a) clashes with R1C12, ALS block)
or 12(3) cage = {246}, R1C4 = 2 => 20(4) cage = {1379/1469}
-> 20(4) cage = {1379/1469}, no 2,8, 1,9 locked for N3, 9 also locked for D/
16c. 1 in C9 only in R456C9, locked for N6

17. 12(3) cage at R3C8 = {138/246} (cannot be {147} which clashes with 20(4) cage at R1C8, no 7
17a. 1 of {138} must be in R4C9 -> no 3,8 in R4C9

18. 20(4) cage at R1C8 (step 16b) = {1379/1469}, 12(3) cage at R3C8 (step 17) = {138/246} each contain either 3 or {46} -> no other 3 in N3, no 4,6 in R2C9
18a. 4 in N3 must be in 20(4) cage or in 12(3) cage at R3C89 (locking cages) -> no 4 in R4C9

19. 2 in hidden window R159C678 only in R1C7 + R9C8, CPE no 2 in R7C7
19a. 2 in N9 only in R89C8, locked for C8

20. 12(3) cage at R3C1 and 12(3) cage at R3C8 must have different combinations -> 12(3) cage at R3C1 = {147/246} or 12(3) cage at R3C8 = {246} (locking cages), 4 locked for R3

21. Consider placement for 9 in R9
R9C2 = 9
or R9C9 = 9, placed for D\, R8C1 = 9 (hidden single in R8) => R1C2 = 9 (hidden single in N1)
-> 9 in R19C2, locked for C2
21a. 9 in N4 only in R46C3, locked for C3

22. 12(3) cage at R1C3 and 12(3) cage at R3C1 must have different combinations -> 12(3) cage at R1C3 = {147/246} or 12(3) cage at R3C1 = {147/246} (locking cages), 4 locked for N1

23. 14(3) cage at R7C7 (step 7) = {248/257}
23a. Consider combinations for R89C9 (step 12a) = {59/89}
R89C9 = {59}
or R89C9 = {89}, locked for N9 => 14(3) cage = {257}, naked quad {2579 in R1C1 + R3C3 + R7C7 + R8C8, locked for D\ => R9C9 = 8
-> no 8 in R8C9

24. 15(3) cage at R1C6 (step 15c) = {168/258/357}
24a. 1,3 of {168/357} must be in R1C6 -> no 6,7 in R1C6

[Maybe there’s a simpler way to continue than this rather heavy step, which cracks the puzzle.]
25. 12(3) cage at R1C3 = {138/147/246}, 12(3) cage at R3C1 = {138/147/246}, 12(3) cage at R3C8 (step 17) = {138/246}
25a. Consider combinations for 15(3) cage at R1C6 (step 24) = {168/258/357}
15(3) cage = {168/357}=> R1C6 = {13} => 12(3) cage at R1C3 = {147/246} (cannot be {138} = {13}8 which clashes with R1C6)
or 15(3) cage = {258} = 5{28} => 12(3) cage at R3C8 = {246}, 4 locked for R3 => 12(3) cage at R3C1 = {138} => 12(3) cage at R1C3 = {147/246}
or 15(3) cage = {258} = 8{25} => 12(3) cage at R3C8 = {246} (the hard part, cannot be {138} = {38}1, R2C9 = 7, R6C9 = 4 gives clash between 6 in R1C9 and 6 in R7C9), 4 locked for R3 => 12(3) cage at R3C1 = {138} => 12(3) cage at R1C3 = {147/246}
-> 12(3) cage at R1C3 = {147/246}, no 3,8, 4 locked for C3 and N1
25b. 2,7 of {147/246} only in R1C4 -> R1C4 = {27}

26. 12(3) cage at R3C1 = {138} (only remaining combination)
26a. Caged X-Wing for 1 in 12(3) cage and 11(3) cage at R6C1, no other 1 in C12

27. 12(3) cage at R3C8 (step 17) = {246} (only remaining combination, cannot be {138} which clashes with 12(3) cage at R3C1), 4 locked for N3, 2 locked for C9
27a. 20(4) cage at R1C8 (step 16b) = {1379} (only remaining combination), locked for N3
27b. 15(3) cage at R1C6 (step 24) = {168/258}, no 3

28. 6 on D/ only in R4C6 + R6C4, locked for N5

29. R2C2 = 6 (hidden single in D\)
29a. Naked pair {14} in R12C3, locked for C3 and N1, R1C4 = 7 (cage sum), R1C9 = 3, placed for D/ and hidden window R159C159, R1C8 = 1, placed for hidden window R159C678, R12C3 = [41]
29b. Naked pair {38} in R3C12, locked for R3, R4C1 = 1, placed for hidden window R234C159

30. Naked pair {79} in R2C8 + R3C7, locked for D/ and W2
30a. 14(3) cage at R7C3 (step 6) = {248} (only remaining combination), locked for N7 and D/
30b. Naked pair {56} in R4C6 + R6C4, locked for N5 -> R5C5 = 1

31. 15(3) cage at R1C6 = {258} (only remaining combination), no 6
31a. R3C89 = {46} (hidden pair in N3), 6 locked for R3 and 12(3) cage at R3C8 -> R4C9 = 2, placed for hidden window R234C159

32. R9C4 = 1 (hidden single in R9), R89C3 = 10 = {37}, locked for C3 and N7
32a. R7C12 = [61], R6C1 = 4 (cage sum), placed for hidden window R678C159
32b. R6C9 = 1 (hidden single in R6), R7C89 = 10 = [37], 3 placed for W4, 7 placed for hidden window R678C159

33. 14(3) cage at R7C7 (step 7) = {248} (only remaining combination), locked for N9 -> R89C7 = [16], R9C6 = 4 (cage sum), 4,6 placed for hidden window R159C678

34. Naked triple {379} in 19(3) cage at R5C6, locked for R5
34a. 16(3) cage at R5C2 = {268}, only remaining combination, locked for R5 and hidden window R159C234 -> R5C1 = 5, placed for hidden window R159C159, R9C9 = 9, placed for D\, R1C1 = 2, placed for D\
34b. Naked pair {48} in R7C7 + R8C8, locked for D\ -> R4C4 = 3, R6C6 = 7

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

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

Rating Comment:
I'll rate my walkthrough for HS17 at (very) Hard 1.5, for step 25a.
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HATMAN
 Post subject: Re: HS 17 - CNC W X 59
PostPosted: Wed Nov 27, 2013 8:58 pm 
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Joined: Wed Apr 30, 2008 9:45 pm
Posts: 694
Location: Saudi Arabia
Andrew after your 12 (approx.) I did I/O on HW at r1c234r5c234r9c234 this eliminates 8 at r2c3 and means that the 12(3) at r3c12r4c2 = 138 - it rolls out from there.
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Andrew
 Post subject: Re: HS 17 - CNC W X 59
PostPosted: Fri Nov 29, 2013 4:07 am 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
HATMAN wrote:
Andrew after your 12 (approx.) I did I/O on HW at r1c234r5c234r9c234 this eliminates 8 at r2c3 and means that the 12(3) at r3c12r4c2 = 138 - it rolls out from there.

Maurice. Thanks for pointing that out. It shows that I've still got things to learn about Windokus. I've never thought about trying a 45 on a hidden window.
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