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HATMAN
 Post subject: HS 14 W X
PostPosted: Mon Mar 11, 2013 4:25 pm 
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Joined: Wed Apr 30, 2008 9:45 pm
Posts: 694
Location: Saudi Arabia
Human Solvable W X 14

They are Windoku and X

JS used one fish on the first one, 4 on the second and 22 on the third one. SS goes bingo mad on all of them.

On A I avoided the fish, on B I just used the simpler ones on C I needed JS help but avoided the big fish.

B is the main puzzle


14A

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JS Code:
3x3:3:k:3073:14:3848:15:16:2308:2308:2308:3073:3591:3330:3848:17:18:19:20:3330:21:3591:22:5379:23:24:25:5379:3850:3850:3591:26:27:28:29:30:31:32:33:2829:34:35:36:37:38:39:40:41:2829:42:43:44:45:46:47:48:2310:49:50:5379:51:52:53:5379:54:2310:55:3330:56:57:58:1545:1545:3330:2310:3073:2309:2309:2309:3596:3596:59:60:3073:

14B

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JS Code:
3x3:3:k:3073:13:3848:14:15:2308:2308:2308:3073:3591:3330:3848:16:17:18:19:3330:20:3591:21:5379:22:23:24:5379:3850:3850:3591:25:26:27:28:29:30:31:32:33:34:35:36:37:38:39:40:41:42:43:44:45:46:47:48:49:2310:50:51:5379:52:53:54:5379:55:2310:56:3330:57:58:59:1545:1545:3330:2310:3073:2309:2309:2309:3596:3596:60:61:3073:


14C

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JS Code:
3x3:3:k:3073:11:3848:12:13:2308:2308:2308:3073:3591:3330:3848:14:15:16:17:3330:18:3591:19:5379:20:21:22:5379:3850:3850:3591:23:24:25:26:27:28:29:30:31:32:33:34:35:36:37:38:39:40:41:42:43:44:45:46:47:2310:48:49:5379:50:51:52:5379:53:2310:54:3330:55:56:57:1545:1545:3330:2310:3073:2309:2309:2309:58:59:60:61:3073:

Solution:
298763514
617548329
534219678
389625147
765194283
421837956
953471862
876952431
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Andrew
 Post subject: Re: HS 14 W X
PostPosted: Sat Mar 16, 2013 1:54 am 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Thanks HATMAN for another interesting and challenging puzzle.

I can understand that SS won't be able to find step 4; it's probably won't be programmed to look for it. I've never used JSudoku so don't know whether it can find this step. It's probably what makes this a Human Solvable.

I found it hard to find breakthrough steps but eventually managed without using any "chains/fishes". I thought that I'd made a key breakthrough when I found step 17 but found that a lot more work was required.
The final breakthrough in step 30:
was hard to spot since I'm still fairly inexperienced at solving Windoku Killer-Xs.

Here is my walkthrough for HS 14 WX version A:
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) R12C3 = {69/78}
b) R3C89 = {69/78}
c) R56C1 = {29/38/47/56}, no 1
d) R8C67 = {15/24}
e) R9C56 = {59/68}
f) 9(3) cage at R1C6 = {126/135/234}, no 7,8,9
g) 9(3) cage at R6C9 = {126/135/234}, no 7,8,9
h) 9(3) cage at R9C2 = {126/135/234}, no 7,8,9
i) 12(4) disjoint cage at R1C1 = {1236/1245}, no 7,8,9
j) 13(4) disjoint cage at R2C2 = {1237/1246/1345}, no 8,9

1. 12(4) disjoint cage at R1C1 = {1236/1245}, CPE no 1,2 in R5C5 using both diagonals

2. 7 in R9 only in R9C78, locked for N9 and hidden window R159C678, no 7 in R5C678
2a. Hidden killer pair 8,9 in R9C56 and R9C78 for R9, R9C56 contains one of 8,9 -> R9C78 must contain one of 8,9 -> R9C78 = {789}

3. 12(4) disjoint cage at R1C1 and 13(4) disjoint cage at R2C2 both contain 1, each of these cages must have 1 on one of the diagonals -> no other 1 on the diagonals

4. 45 rule on both diagonals 6 innies R4C4 + R5C5 (twice) + R6C6 + R4C6 + R6C4 = 44 can only be 5 + 6 + 7 + 8 + 9 (twice) -> R5C5 = 9, placed for both diagonals, R46C46 = {5678}, locked for N5, clean-up: no 2 in R6C1, no 5 in R9C6

5. 9 in hidden window R678C159 only in R678C1, locked for C1

6. 12(4) disjoint cage at R1C1 must have one of 1,2 in R1 and one of 1,2 in R9 (1,2 cannot be in the same row, because they would clash with 9(3) cage at R1C6 or 9(3) cage at R9C2)
6a. 9(3) cage at R1C6 = {135/234} (cannot be {126} which clashes with 1 or 2 in R1C19), no 6, 3 locked for R1 and hidden window R159C678, no 3 in R5C678
6b. Killer pair 1,2 in R1C19 and 9(3) cage, locked for R1
6c. 9(3) cage at R9C2 = {135/234} (cannot be {126} which clashes with 1 or 2 in R9C19), no 6, 3 locked for R9 and hidden window R159C234, no 3 in R5C234
6d. 3 in N5 only in R46C5, locked for C5

7. 12(4) disjoint cage at R1C1 = {1245} (only remaining combination), no 6
7a. R1C2345 = {6789} (hidden quad in R1)
[HATMAN told me that I’d missed 12(4) disjoint cage at R1C1 = {1245}, locked for hidden window R159C159, no 1,2,4,5 in R19C5 + R5C19, with appropriate clean-ups for R6C1 and R9C6. Then steps 10 and 12 wouldn’t have been needed.]

8. 6 in R9 only in R9C56 = {68}, locked for R9 and N8
8a. Naked pair {79} in R9C78, locked for N9

9. 8 in N9 only in R7C78, locked for R7 and W4, no 8 in R6C678

10. Hidden killer pair 1,2 in 9(3) cage at R1C6 and R5C678 for hidden window R159C678, 9(3) cage contains one of 1,2 -> R5C678 must contain one of 1,2
10a. Hidden killer pair 1,2 in R5C234 and 9(3) cage at R9C2 for hidden window R159C234, 9(3) cage contains one of 1,2 -> R5C234 must contain one of 1,2
10b. Killer pair 1,2 in R5C234 and R5C678, locked for R5, clean-up: no 9 in R6C1
10c. 9 in C1 only in R78C1, locked for N7

11. 8 in hidden window R678C159 only in R68C1, locked for C1, clean-up: no 3 in R6C1

12. Hidden killer pair 4,5 in 9(3) cage at R1C6 and R5C678 for hidden window R159C678, 9(3) cage contains one of 4,5 -> R5C678 must contain one of 4,5
12a. Hidden killer pair 4,5 in R5C234 and 9(3) cage at R9C2 for hidden window R159C234, 9(3) cage contains one of 4,5 -> R5C234 must contain one of 4,5
12b. Killer pair 4,5 in R5C234 and R5C678, locked for R5, clean-up: no 6,7 in R6C1

13. R4C4 + R6C6 + R4C6 + R6C4 contains 8 for one of the diagonals -> 21(4) disjoint cage at R3C3 must contain 8 for the other diagonal = {2478/2568/3468}
13a. Double hidden killer pair 6,7 in R4C4 + R6C6 + R4C6 + R6C4, 21(4) disjoint cage and 13(4) disjoint cage at R2C2 for both diagonals, R4C4 + R6C6 + R4C6 + R6C4 contains both of 6,7, 21(4) disjoint cage contains one of 6,7 -> 13(4) disjoint cage must contain one of 6,7 -> 13(4) disjoint cage = {1237/1246}, no 5
13b. 12(4) disjoint cage at R1C1 and 13(4) disjoint cage at R2C2 both contain 2, each of these cages must have 2 on one of the diagonals -> no other 2 on the diagonals
13c. 21(4) disjoint cage = {3468} (only remaining combination), no 5,7
13d. 21(4) disjoint cage contains 6 -> 13(4) disjoint cage must contain 7 = {1237}, no 4,6

14. 14(3) cage at R2C1 = {167/257/347/356}, R56C1 = [38/65/74] -> combined cage 14(3) + R56C1 = {167}[38]/{257}[38]/{347}[65]/{356}[74], 3,7 locked for C1
14a. 7 in N7 only in R7C2 + R8C23, locked for W3, no 7 in R6C234 + R78C4

15. 7 in hidden window R678C159 only in R78C5, locked for C5 and N8
15a. Naked pair {68} in R19C5, locked for C5
15b. 7 in R1 only in R1C234, locked for hidden window R159C234, no 7 in R5C23

16. R5C19 = {37} (hidden pair in R5), clean-up: no 5 in R6C1
16a. 14(3) cage at R2C1 (step 14) = {167/257/356} (cannot be {347} which clashes with R5C1), no 4

17. 12(4) disjoint cage at R1C1 = {1245}
17a. Hidden killer pair 2,5 in R1249C9 and 9(3) cage at R6C9, 9(3) cage contains one of 2,5 -> R1249C9 must contain one of 2,5
17b. R1249C9 contains one of 2,5 -> R19C1 must contain at least one of 2,5
17c. 14(3) cage at R2C1 (step 16a) = {167/356} (cannot be {257} which clashes with R19C1), no 2, 6 locked for C1 and hidden window R234C159, no 6 in R234C9, clean-up: no 9 in R3C8

18. 6 in C9 only in 9(3) cage at R6C9 = {126}, locked for C9
18a. Naked pair {45} in R19C9, locked for C9 and 12(4) disjoint cage at R1C1, no 4,5 in R19C1
18b. Naked pair {12} in R19C1, locked for C1
[I missed 1,2 also locked for hidden window R678C159, but they are soon eliminated.]

19. 14(3) cage at R2C1 (step 17c) = {356} (only remaining combination), locked for C1 -> R5C1 = 7, R6C1 = 4, R78C1 = [98], R5C9 = 3

20. Naked triple {356} in 14(3) cage at R2C1, locked for hidden window R234C159, no 3,5 in R234C5
20a. Naked triple {124} in R234C5, locked for C5 -> R6C5 = 3
20b. Naked pair {57} in R78C5, locked for N8, clean-up: no 1 in R8C7

21. R8C4 = 9 (hidden single in N8), placed for W3
21a. 9 in N4 only in R4C23, locked for R4 and W1, no 9 in R2C3 + R3C2, clean-up: no 6 in R1C3
21b. 9 in C9 only in R23C9, locked for N2

22. 4 in N1 only in R3C23, locked for R3 and W1, no 4 in R2C4

23. 6 in N7 only in R7C23 + R8C3, locked for W3, no 6 in R6C234

24. 3 in N9 only in R7C78 + R8C8, locked for W4, no 3 in R7C6
24a. 3 in N8 only in R79C4, locked for C4

25. Naked triple {124} in R578C6, locked for C6
25a. R2C5 = 4 (hidden single in N2)
25b. 4 in N5 only in R5C46, locked for R5

26. Hidden killer pair 1,2 in 9(3) cage at R1C6 and R2C78 for N3, 9(3) cage contains one of 1,2 -> R2C78 must contains one of 1,2
26a. Hidden killer pair 1,2 in R2C78 and R4C78 for W2, R2C78 contains one of 1,2 -> R4C78 must contain one of 1,2
26b. R4C78 contains one of 1,2, 4 in R4 only in R4C78 -> R4C78 = {124}
26c. Naked triple {124} in R4C578, locked for R4

27. R7C6 = {124}, R8C67 = {15/24} -> variable combined cage R7C6 + R8C67 = 1{24}/2[15]/4[15], 1 locked for C6, N8 and W4, no 1 in R6C78 + R78C8
[Things would have been more powerful if there wasn’t still a 4 in R7C6 but at this stage the only way I can see to eliminate this is to use a contradiction move. Fortunately step 27 achieves enough after step 30.]

28. 1 in N9 only in R78C9, locked for C9
28a. 1 in R6 only in R6C23, locked for N4 and W3, no 1 in R7C2 + R8C23

29. 13(4) disjoint cage at R2C2 = {1237}, 1 locked for R2
29a. 1 on D\ only in R1C1 + R2C2, locked for N1

30. 9(3) cage at R1C6 (step 6a) = {135} (only remaining combination, cannot be {234} which clashes with R5C6 using hidden window R159C678), locked for R1, 1 also locked for N3 -> R1C1 = 2, placed for D\, R1C9 = 4, placed for D/, R9C1 = 1, R9C9 = 5, placed for D\, R8C8 = 3, placed for D\, clean-up: no 1 in R8C6
30a. 9(3) cage at R1C6 = {135}, 1,5 locked for hidden window R159C678, no 1,5 in R5C78
[Cracked.]

31. R5C6 = 4 (hidden single for hidden window R159C678), R8C67 = [24], R7C6 = 1, R8C2 = 7, placed for D/, R2C2 = 1, R2C8 = 2, R8C5 = 5, R8C3 = 6, R7C3 = 3, placed for D/, clean-up: no 9 in R1C3

32. Naked pair {78} in R12C3, locked for C3 and N1 -> R3C3 = 4

33. Naked pair {68} in R7C78, locked for R7 and W4 -> R6C6 = 7, R7C9 = 2, R6C9 = 6, R5C78 = [28], R7C8 = 6, R3C8 = 7, R3C9 = 8

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

Rating Comment:
I'll rate my walkthrough for HS 14 WX ver A at 1.5. As well as the double-diagonal 45 in step 4, I used other double-diagonal steps and made a lot of use of hidden killer pairs in the hidden windows.
I'll try the next version after I've tried Ed's latest Assassin.
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Andrew
 Post subject: Re: HS 14 W X
PostPosted: Tue Mar 19, 2013 7:47 pm 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
HATMAN wrote:
JS used one fish on the first one, 4 on the second and 22 on the third one. SS goes bingo mad on all of them.

On A I avoided the fish, on B I just used the simpler ones ...

Since I haven't learned fish, I've used several short forcing chains; probably more than were necessary but, since it took me quite a long time to find each of my earlier ones, they are in the order I found them.

Thanks HATMAN for a couple of useful feedback comments (by PM) about my walkthrough for version A. I've noted them at appropriate points in my walkthrough.

Here is my walkthrough for HS 14 WX version B:
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.

I’ve started by using steps from my version A walkthrough, modified where necessary because of the removal of the cage R56C1.

Prelims

a) R12C3 = {69/78}
b) R3C89 = {69/78}
c) R8C67 = {15/24}
d) R9C56 = {59/68}
e) 9(3) cage at R1C6 = {126/135/234}, no 7,8,9
f) 9(3) cage at R6C9 = {126/135/234}, no 7,8,9
g) 9(3) cage at R9C2 = {126/135/234}, no 7,8,9
h) 12(4) disjoint cage at R1C1 = {1236/1245}, no 7,8,9
i) 13(4) disjoint cage at R2C2 = {1237/1246/1345}, no 8,9

1. 12(4) disjoint cage at R1C1 = {1236/1245}, CPE no 1,2 in R5C5 using both diagonals

2. 7 in R9 only in R9C78, locked for N9 and hidden window R159C678, no 7 in R5C678
2a. Hidden killer pair 8,9 in R9C56 and R9C78 for R9, R9C56 contains one of 8,9 -> R9C78 must contain one of 8,9 -> R9C78 = {789}

3. 12(4) disjoint cage at R1C1 and 13(4) disjoint cage at R2C2 both contain 1, each of these cages must have 1 on one of the diagonals -> no other 1 on the diagonals

4. 45 rule on both diagonals 6 innies R4C4 + R5C5 (twice) + R6C6 + R4C6 + R6C4 = 44 can only be 5 + 6 + 7 + 8 + 9 (twice) -> R5C5 = 9, placed for both diagonals, R46C46 = {5678}, locked for N5, clean-up: no 5 in R9C6

5. 9 in hidden window R678C159 only in R678C1, locked for C1

6. 12(4) disjoint cage at R1C1 must have one of 1,2 in R1 and one of 1,2 in R9 (1,2 cannot be in the same row, because they would clash with 9(3) cage at R1C6 or 9(3) cage at R9C2)
6a. 9(3) cage at R1C6 = {135/234} (cannot be {126} which clashes with 1 or 2 in R1C19), no 6, 3 locked for R1 and hidden window R159C678, no 3 in R5C678
6b. Killer pair 1,2 in R1C19 and 9(3) cage, locked for R1
6c. 9(3) cage at R9C2 = {135/234} (cannot be {126} which clashes with 1 or 2 in R9C19), no 6, 3 locked for R9 and hidden window R159C234, no 3 in R5C234
6d. 3 in N5 only in R46C5, locked for C5

7. 12(4) disjoint cage at R1C1 = {1245} (only remaining combination), no 6
7a. 12(4) disjoint cage at R1C1 = {1245}, locked for hidden window R159C159, no 1,2,4,5 in R19C5 + R5C19, clean-up: no 9 in R9C6
7b. R1C2345 = {6789} (hidden quad in R1)
[Thanks HATMAN for pointing out that I’d missed step 7a in my walkthrough for version A.]

8. Naked pair {68} in R9C56, locked for R9 and N8
8a. Naked pair {79} in R9C78, locked for N9

9. 8 in N9 only in R7C78, locked for R7 and W4, no 8 in R6C678

10. 8 in hidden window R678C159 only in R68C1, locked for C1

11. R4C4 + R6C6 + R4C6 + R6C4 contains 8 for one of the diagonals -> 21(4) disjoint cage at R3C3 must contain 8 for the other diagonal = {2478/2568/3468}
11a. Double hidden killer pair 6,7 in R4C4 + R6C6 + R4C6 + R6C4, 21(4) disjoint cage and 13(4) disjoint cage at R2C2 for both diagonals, R4C4 + R6C6 + R4C6 + R6C4 contains both of 6,7, 21(4) disjoint cage contains one of 6,7 -> 13(4) disjoint cage must contain one of 6,7 -> 13(4) disjoint cage = {1237/1246}, no 5
11b. 12(4) disjoint cage at R1C1 and 13(4) disjoint cage at R2C2 both contain 2, each of these cages must have 2 on one of the diagonals -> no other 2 on the diagonals
11c. 21(4) disjoint cage = {3468} (only remaining combination), no 5,7
11d. 21(4) disjoint cage contains 6 -> 13(4) disjoint cage must contain 7 = {1237}, no 4,6

12. 14(3) cage at R2C1 = {167/257/347/356}, R5C1 = {367} -> combined cage 14(3) + R5C1 = {167}[3]/{257}[3or6]/{347}[6]/{356}[7], 7 locked for C1
12a. 7 in N7 only in R7C2 + R8C23, locked for W3, no 7 in R6C234 + R78C4

13. 7 in hidden window R678C159 only in R78C5, locked for C5 and N8
13a. Naked pair {68} in R19C5, locked for C5
13b. 7 in R1 only in R1C234, locked for hidden window R159C234, no 7 in R5C23

14. R5C19 = {37} (hidden pair in R5)
14a. 14(3) cage at R2C1 (step 12) = {167/257/356} (cannot be {347} which clashes with R5C1), no 4
14b. Killer pair 3,7 in 14(3) cage and R5C1, locked for C1

15. 12(4) disjoint cage at R1C1 = {1245}
15a. Hidden killer pair 2,5 in R1249C9 and 9(3) cage at R6C9, 9(3) cage contains one of 2,5 -> R1249C9 must contain one of 2,5
15b. R1249C9 contains one of 2,5 -> R19C1 must contain at least one of 2,5
15c. 14(3) cage at R2C1 (step 14a) = {167/356} (cannot be {257} which clashes with R19C1), no 2, 6 locked for C1 and hidden window R234C159, no 6 in R234C9, clean-up: no 9 in R3C8

16. 6 in C9 only in 9(3) cage at R6C9 = {126}, locked for C9 and hidden window R678C159, no 1,2 in R678C15
16a. Naked pair {45} in R19C9, locked for C9 and 12(4) disjoint cage at R1C1, no 4,5 in R19C1
16b. Naked pair {12} in R19C1, locked for C1

17. 14(3) cage at R2C1 (step 15c) = {356} (only remaining combination), locked for C1 -> R5C1 = 7, R5C9 = 3

18. Naked triple {356} in 14(3) cage at R2C1, locked for hidden window R234C159, no 3,5 in R234C5
18a. Naked triple {124} in R234C5, locked for C5 -> R6C5 = 3
18b. Naked pair {57} in R78C5, locked for N8, clean-up: no 1 in R8C7

19. 9 in N8 only in R7C46 + R8C4, CPE no 9 in R7C2 using W3

20. 4 in N1 only in R3C23, locked for R3 and W1, no 4 in R2C4 + R4C23

21. 6 in N7 only in R7C23 + R8C3, locked for W3, no 6 in R6C234

22. 3 in N9 only in R7C78 + R8C8, locked for W4, no 3 in R7C6
22a. 3 in N8 only in R789C4, locked for C4

[This is how far I could go using (modified) steps from version A. The placement in R6C1 was very helpful in that version.]

23. 5 in N9 only in R7C8 + R8C7 + R9C9, CPE no 5 in R6C6 using W4 and D\

24. 6 in N3 only in R2C7 + R3C78, locked for W2, no 6 in R234C6 + R4C78
24a. 6 in N5 only in R4C4 + R6C6, locked for D\

25. Consider placement for 5 in C6
5 in R1C6 => R2C7 = 5 (hidden single in N3), locked for W2, no 5 in R4C78
or 5 in R234C6, locked for W2, no 5 in R2C7 + R4C78
-> no 5 in R4C78

26. Consider placement for 4 in N9
4 in R7C78 + R8C7, locked for W4, no 4 in R6C78 + R78C6
or 4 in R9C9 => R7C3 = 4 (hidden single on D/)
-> no 4 in R7C6

[I ought to have spotted this one immediately after step 24a]
27. Consider the placement for 6 on D/
6 in R3C7 => R3C89 = {78}, locked for R3 => no 8 in R3C3
or 6 in R7C7 => R12C3 = {78}, locked for C3 => no 8 in R3C3
-> no 8 in R3C3
27a. 21(4) disjoint cage at R3C3 = {3468}, 8 locked for C7

[Just realised that there’s a step fairly similar to a breakthrough step I used for version A.]
28. Consider values in R5C6
R5C6 = 1
or R5C6 = {24} => 9(3) cage at R9C2 (step 6c) = {135} (cannot be {234} which clashes with R5C6 using hidden window R159C678), locked for hidden window R159C678, no 1 in R5C678
-> no 1 in R5C78
28a. Similarly consider values in R5C4
R5C4 = 1
or R5C4 = {24} => 9(3) cage at R9C2 (step 6c) = {135} (cannot be {234} which clashes with R5C4 using hidden window R159C234), locked for hidden window R159C234, no 1 in R5C234
-> no 1 in R5C23
28b. 1 in R5 only in R5C46, locked for N5
28c. 1 in C5 only in R23C5, locked for N2

29. Consider values in R7C6
R7C6 = 1 => R8C67 = {24}, locked for R8 and W4 => R8C8 = 3
or R7C6 = 2 => R8C67 = [15] => R8C8 = 3
or R7C6 = 9 => R7C1 = 4 => R1C9 = 4 (hidden single on D/) => R9C9 = 5 => R8C67 = {24}, locked for R8 and W4
-> no 2 in R6C78 + R78C8
29a. 2 in R7C6 + R8C67, CPE no 2 in R8C4
[These values in R7C6 can be taken a bit further
R7C6 = {12}, naked triple {124} in R578C6, locked for C6
or R7C6 = 9 => R7C1 = 4 => R1C9 = 4 (hidden single on D/)
-> no 4 in R1C6
4 in R1 only in R1C789, locked for N3
However the next step makes this unnecessary.]

[In feedback about my walkthrough for version A, HATMAN commented that R1C19 and R9C19 must each total 6, after the 12(4) disjoint cage at R1C1 has been reduced to {1245}.]
30. R1C19 and R9C19 must be [15/24] (because [14/25] would clash with 9(3) cages at R1C6 and R9C2) -> R1C1 + R9C9 and R1C9 + R9C1 must be [14/25]
30a. R1C1 + R9C9 = [25] (cannot be [14] which clashes with R3C3 + R8C8, ALS block on D\) -> R1C1 = 2, R9C9 = 5, placed for D\, R1C9 = 4, R9C1 = 1, both placed for D/, clean-up: no 1 in R8C6
30b. 1 in R1 only in R1C78, locked for N3
[Cracked.]

31. Naked pair {24} in R8C67, locked for R8 and W4, no 2,4 in R6C78 + R7C678
31a. R2C8 = 2 (hidden single on D/), placed for W2, no 2 in R2C6
31b. R3C3 = 4 (hidden single on D\)
31c. R8C7 = 4 (hidden single in N9), R8C6 = 2
31d. R7C9 = 2 (hidden single in N9)

32. 5 in W4 only in R6C78, locked for R6 and N6 -> R6C4 = 8, placed for D/
32a. Naked pair {36} in R3C7 + R7C3, locked for D/ and 21(4) disjoint cage at R3C3 -> R7C7 = 8, R8C2 = 7, placed for D/, R78C5 = [75], R4C6 = 5, R1C6 = 3
32b. R4C6 = 5, placed for W2, no 5 in R2C7

33. Naked triple {234} in 9(3) cage at R9C2, locked for hidden window R159C234 -> R5C4 = 1, R5C6 = 4, R4C5 = 2, R23C5 = [41]

34. Naked triple {349} in R789C4, locked for C4 and N8 -> R7C6 = 1
34a. Naked triple {67} in R15C4, locked for C4 -> R2C4 = 5, R3C4 = 2

35. R7C2 = 5 (hidden single in N7), R5C3 = 5 (hidden single in N4), R5C7 = 2 (hidden single in R5)

36. R8C1 = 8 (hidden single in C1)
36a. 9 in R8 only in R8C34, locked for W3, no 9 in R6C23 + R7C4
36b. R8C4 = 9 (hidden single in N8)

37. Naked pair {36} in R78C3, locked for C3, N7 and W3 -> R7C4 = 4, R67C1 = [49], 9(3) cage at R9C2 = [423], R6C23 = [21], clean-up: no 9 in R12C3

38. R6C9 = 6, R8C9 = 1, R8C8 = 3, placed for D\, R2C2 = 1, R57C8 = [86], R3C8 = 7, R3C9 = 8, R7C3 = 3, placed for D/, R3C7 = 6

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

Rating Comment:
This puzzle was definitely harder than version A, needing several short forcing chains (or fish for those who know how to do them). I rated version A at 1.5 so I'll rate version B at least Hard 1.5.

HATMAN wrote:
JS used one fish on the first one, 4 on the second and 22 on the third one. SS goes bingo mad on all of them.

... on C I needed JS help but avoided the big fish.

I'll try version C after I've done Pinata's latest puzzle and if there aren't any new puzzles this week.

If nobody has posted a walkthrough for version C in the next week, may I ask HATMAN to post his JS-assisted walkthrough for it. That will avoid it becoming one of the Unsolvables.
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HATMAN
 Post subject: Re: HS 14 W X
PostPosted: Wed Mar 20, 2013 10:25 am 
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Joined: Wed Apr 30, 2008 9:45 pm
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Will do
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Andrew
 Post subject: Re: HS 14 W X
PostPosted: Fri Mar 22, 2013 2:10 am 
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Joined: Wed Apr 23, 2008 6:04 pm
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HATMAN wrote:
JS used one fish on the first one, 4 on the second and 22 on the third one.
Based on that comment, I'd expected version C to be harder than it was.

I'd got as far as step 22 yesterday. When I resumed today:
I found the very useful step 23. I think that R5C6 is the most important and useful cell for this cage pattern.

Here is my walkthrough for HS 14 WX version C:
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.

I’ve started by using steps from my version B walkthrough, modified where necessary because of the removal of the cage R9C56.

Prelims

a) R12C3 = {69/78}
b) R3C89 = {69/78}
c) R8C67 = {15/24}
d) 9(3) cage at R1C6 = {126/135/234}, no 7,8,9
e) 9(3) cage at R6C9 = {126/135/234}, no 7,8,9
f) 9(3) cage at R9C2 = {126/135/234}, no 7,8,9
g) 12(4) disjoint cage at R1C1 = {1236/1245}, no 7,8,9
h) 13(4) disjoint cage at R2C2 = {1237/1246/1345}, no 8,9

1. 12(4) disjoint cage at R1C1 = {1236/1245}, CPE no 1,2 in R5C5 using both diagonals

2. 12(4) disjoint cage at R1C1 and 13(4) disjoint cage at R2C2 both contain 1, each of these cages must have 1 on one of the diagonals -> no other 1 on the diagonals

3. 45 rule on both diagonals 6 innies R4C4 + R5C5 (twice) + R6C6 + R4C6 + R6C4 = 44 can only be 5 + 6 + 7 + 8 + 9 (twice) -> R5C5 = 9, placed for both diagonals, R46C46 = {5678}, locked for N5

4. 9 in hidden window R678C159 only in R678C1, locked for C1

5. 12(4) disjoint cage at R1C1 must have one of 1,2 in R1 and one of 1,2 in R9 (1,2 cannot be in the same row, because they would clash with 9(3) cage at R1C6 or 9(3) cage at R9C2)
5a. 9(3) cage at R1C6 = {135/234} (cannot be {126} which clashes with 1 or 2 in R1C19), no 6, 3 locked for R1 and hidden window R159C678, no 3 in R59C678
5b. Killer pair 1,2 in R1C19 and 9(3) cage, locked for R1
5c. 9(3) cage at R9C2 = {135/234} (cannot be {126} which clashes with 1 or 2 in R9C19), no 6, 3 locked for R9 and hidden window R159C234, no 3 in R5C234
5d. 3 in N5 only in R46C5, locked for C5

6. 12(4) disjoint cage at R1C1 = {1245} (only remaining combination), no 6
6a. 12(4) disjoint cage at R1C1 = {1245}, locked for hidden window R159C159, no 1,2,4,5 in R19C5 + R5C19
6b. R1C2345 = {6789} (hidden quad in R1)
6c. R9C5678 = {6789} (hidden quad in R9)
[Thanks HATMAN for pointing out that I’d missed step 6a in my walkthrough for version A.]

7. R4C4 + R6C6 + R4C6 + R6C4 contains 8 for one of the diagonals -> 21(4) disjoint cage at R3C3 must contain 8 for the other diagonal = {2478/2568/3468}
7a. Double hidden killer pair 6,7 in R4C4 + R6C6 + R4C6 + R6C4, 21(4) disjoint cage and 13(4) disjoint cage at R2C2 for both diagonals, R4C4 + R6C6 + R4C6 + R6C4 contains both of 6,7, 21(4) disjoint cage contains one of 6,7 -> 13(4) disjoint cage must contain one of 6,7 -> 13(4) disjoint cage = {1237/1246}, no 5
7b. 12(4) disjoint cage at R1C1 and 13(4) disjoint cage at R2C2 both contain 2, each of these cages must have 2 on one of the diagonals -> no other 2 on the diagonals
7c. 21(4) disjoint cage = {3468} (only remaining combination), no 5,7
7d. 21(4) disjoint cage contains 6 -> 13(4) disjoint cage must contain 7 = {1237}, no 4,6

8. Killer quad 1,2,4,5 in R19C9 and 9(3) cage at R6C9, locked for C9

9. Consider values in R5C6
R5C6 = 1
or R5C6 = {24} => 9(3) cage at R9C2 (step 6c) = {135} (cannot be {234} which clashes with R5C6 using hidden window R159C678), locked for hidden window R159C678, no 1 in R5C678
-> no 1 in R5C78
9a. Similarly consider values in R5C4
R5C4 = 1
or R5C4 = {24} => 9(3) cage at R9C2 (step 6c) = {135} (cannot be {234} which clashes with R5C4 using hidden window R159C234), locked for hidden window R159C234, no 1 in R5C234
-> no 1 in R5C23
9b. 1 in R5 only in R5C46, locked for N5

[This is how far I could go using (modified) steps from version B. The naked pairs in R9C56 and R9C78 were very helpful in that version, particularly R9C56 = {68} which eliminated 8 from R2345C1. Three of these are eliminated quickly, in step 13, but the one in R5C1 is stubborn.]

10. 9(3) cage at R6C9 = {126/135} (cannot be {234} which clashes with R6C5 using hidden window R678C159), no 4
10a. 9(3) cage = {126/135}, 1 locked for C9 and hidden window R678C159, no 1 in R678C15
10b. 1 in C5 only in R23C5, locked for N2

11. R1C19 and R9C19 must be [15/24] (because [14/25] would clash with 9(3) cages at R1C6 and R9C2)
11a. 4 in C9 only in R19C9 -> 2 must be in R19C1, no 2 in R19C9
11b. R19C9 = {45}, locked for C9 and 12(4) disjoint cage at R1C1
11c. Naked pair {12} in R19C1, locked for C1

12. 9(3) cage at R6C9 (step 10) = {126} (only remaining combination), locked for C9 and hidden window R678C159, no 2,6 in R678C15, clean-up: no 9 in R3C8

13. 14(3) cage at R1C1 = {347/356}, no 8, 3 locked for C1 and hidden window R234C159, no 3 in R4C5 + R24C9
13a. R5C9 = 3 (hidden single in R5), R6C5 = 3 (hidden single in N5)

14. Naked triple {789} in R234C9, locked for hidden window R234C159, no 7,8 in R234C1 + R23C5
14a. 14(3) cage at R1C1 (step 13) = {356} (only remaining combination), locked for C1 and hidden window R234C159, no 5,6 in R23C5
14b. Naked triple {124} in R234C5, locked for C5
14c. 5 in C5 only in R78C5, locked for N8, clean-up: no 1 in R8C7

[Now I can use some more of my steps from my walkthrough for version B.]

15. 4 in N1 only in R3C23, locked for R3 and W1, no 4 in R2C4 + R4C23

16. 6 in N7 only in R7C23 + R8C3, locked for W3, no 6 in R6C234 + R78C4

17. 3 in N9 only in R7C78 + R8C8, locked for W4, no 3 in R7C6
17a. 3 in N8 only in R789C4, locked for C4

18. 5 in N9 only in R7C8 + R8C7 + R9C9, CPE no 5 in R6C6 using W4 and D\

19. 6 in N3 only in R2C7 + R3C78, locked for W2, no 6 in R234C6 + R4C78
19a. 6 in N5 only in R4C4 + R6C6, locked for D\

20. Consider the placement for 6 on D/
6 in R3C7 => R3C89 = {78}, locked for R3 => no 8 in R3C3
or 6 in R7C7 => R12C3 = {78}, locked for C3 => no 8 in R3C3
-> no 8 in R3C3

21. Consider placement for 4 in N9
4 in R7C78 + R8C7, locked for W4, no 4 in R6C78 + R78C6
or 4 in R9C9 => R7C3 = 4 (hidden single on D/)
-> no 4 in R7C6

22. Consider placement for 5 in C6
5 in R1C6 => R2C7 = 5 (hidden single in N3), locked for W2, no 5 in R4C78
or 5 in R234C6, locked for W2, no 5 in R2C7 + R4C78
-> no 5 in R4C78

23. Consider placement for 1 in R5
1 in R5C4, placed for hidden window R159C234 => 9(3) cage at R9C2 = {234}, locked for R9 => R9C9 = 5 => R8C67 = {24}
or 1 in R5C6 => R8C67 = {24}
-> R8C67 = {24}, locked for R8 and W4, no 2,4 in R6C78 + R7C678
23a. 13(4) disjoint cage at R2C2 = {1237}, 2 locked for R2
23b. 21(4) disjoint cage at R3C3 = {3468}, 4 locked for C3
23c. 4 in R6 only in R6C12, locked for N4
23d. 2 on D\ only in R1C1 + R2C2, locked for N1
23e. 2 in R3 only in R3C456, locked for N2

24. Hidden killer pair 1,4 in R5C4 and 9(3) cage at R9C2 for hidden window R159C234, 9(3) cage contains one of 1,4 -> R5C4 = {14}

25. Consider placement for 6 in R8
6 in R8C3 => R3C7 = 6 (hidden single on D/) => no 6 in R9C7
or 6 in R8C9 => no 6 in R7C89 + R9C78
-> no 6 in R9C7

26. Consider placement for 4 in C5
4 in R2C5 => no 4 in R1C6
or 4 in R4C5 => 4 in R5 only in R5C78, locked for hidden window R159C678 => 9(3) cage at R1C6 = {135}
-> no 4 in R1C6
26a. 4 in R1 only in R1C789, locked for N3

27. Consider placements in R5C6
1 in R5C6, placed for hidden window R159C678, no 1 in R1C78 => 9(3) cage at R1C6 = {234}, locked for hidden window R159C678, no 2,4 in R5C78 => R4C78 = {24} (hidden pair in N6), locked for W2 => no 2,4 in R23C6
or {24} in R5C6 => naked pair {24} in R58C6, locked for C6
-> no 2,4 in R23C6
[Cracked.]

28. R2C5 = 4 (hidden single in N2), R4C5 = 2, R3C5 = 1, R3C4 = 2 (hidden single in N2)
28a. Naked pair {14} in R5C46, locked for R5

29. R8C6 = 2 (hidden single in C6), R8C7 = 4, R9C9 = 5, placed for D\, R1C9 = 4, placed for D/
29a. 9(3) cage at R1C6 = {135} (only remaining combination), locked for R1 and hidden window R159C234, no 1,5 in R5C678, 1 also locked for N3 -> R1C1 = 2, R9C1 = 1, R5C6 = 4, R5C4 = 1

30. R3C3 = 4 (hidden single on D\)
30a. R7C6 = 1 (hidden single in N8), placed for W4, no 1 in R6C78 + R8C8
30b. R8C9 = 1 (hidden single in N9)

31. Naked pair {37} in R8C28, locked for R8 and 13(4) disjoint cage at R2C2 -> R2C2 = 1, R2C8 = 2
31a. R5C7 = 2 (hidden single in C7), R67C9 = [62]
31b. R4C4 = 6 (hidden single in N5), placed for W1, no 6 in R2C3 + R3C3, clean-up: no 9 in R1C3

32. Naked pair {89} in R8C14, locked for R8 -> R8C5 = 5, R8C3 = 6, clean-up: no 9 in R2C3
32a. Naked pair {78} in R12C3, locked for C3 and N1 -> R5C3 = 5, R7C3 = 3, placed for D/, R7C7 = 8, placed for D\ and W4, no 8 in R6C8, R3C7 = 6, R6C6 = 7, placed for W4, no 7 in R7C8, R8C2 = 7, R8C8 = 3, R7C5 = 7, clean-up: no 9 in R3C9

33. Naked pair {59} in R6C78, locked for R6, N6 (and W4 but this isn’t necessary) -> R6C4 = 8

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

Rating Comment:
This version was a bit harder than version B, but not a lot harder. I only needed a few more forcing chains so, having rated version B at Hard 1.5 I'll rate my walkthrough for version C at Easy 1.75. Step 27 is my hardest step; it uses the same hidden window twice in one path of the chain.
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