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 Post subject: More Lace Practice
PostPosted: Fri Oct 29, 2010 4:44 pm 
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Here is some more lace practice for you. Both are interesting.

JSudoku uses 17 fishes but if you work the lace fully none are needed. Note that the lace areas overlap at r19c5, R5c19. Remember it is Windoku.

Four Laces Windoku

Image

Fully restrained: it has a single set of solutions. JSudoku uses 50 fishes so you can use it for fish practice. Using the lace it is straightforward. Windoku and X

Three Laces Windoku X

Image


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 Post subject: Re: More Lace Practice
PostPosted: Sun Oct 31, 2010 1:36 pm 
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HATMAN, thanks for the interesting puzzles once again.


2 minor suggestions though:

1) When you want to say "JSudoku uses ?? fishes" I suggest you first disable all the "fishes" techniques and check if JSudoku can solve them at all. As I tested it, the first one could be solved by JSudoku without using any fish. The second one, JSudoku did need to apply a few fishes, but not anywhere close to the number you quote.

2) If you want others to use JSudoku on your puzzle, please do provide the line codes. It is a chore to input the cages manually, and if you have already done the hard work, it would be nice to spare others of it.


Here are some spoilers on solving these two:

spoilers:
For the Three Laces Windoku X, with the 16(2) on D\, R8C8<>{79} --> R8C9<>{46}. Then applying LoL on N9 & the green lace --> R6C8=R8C9. The only common candidate is 5, so 7(2)=[52] & 13(2)=[85]. The rest is easy.

For the Four Laces Windoku, it can also be solved easily using LoL, though through more work.

In a nutshell: First prove via LoL that the 14(4) cannot include {1}, so must be {2345}. Then through innies of N5 can quickly conclude R5C5=1 and R4C56=14=[59/68], and the rest is much easier.


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 Post subject: Re: More Lace Practice
PostPosted: Tue Nov 09, 2010 3:55 am 
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Thanks HATMAN. Four Laces Windoku is a fun puzzle. This time I didn't use Law of Leftovers, finding it easier to use the Laces directly; then I started to make real progress when I realised that the Windows seemed even more useful for my solving path (don't think I'm giving away anything by making those general comments).

My step 13c is possibly some sort of fish. It's probably not needed but I saw that step so kept it in. Steps 14a and 14b are my key breakthrough. After steps 15 and 16 the rest is straightforward.

Here is my walkthrough:
Prelims

a) R1C67 = {14/23}
b) R23C1 = {13}
c) R23C6 = {14/23}
d) R34C5 = {29/38/47/56}, no 1
e) R4C23 = {13}
f) R45C4 = {17/26/35}, no 4,8,9
g) R4C67 = {89}
h) R56C6 = {19/28/37/46}, no 5
i) R6C45 = {39/48/57}, no 1,2,6
j) R6C78 = {12}
k) R78C4 = {15/24}
l) R9C23 = {15/24}
m) Disjoint 14(4) cage at R1C5 = {1238/1247/1256/1346/2345}, no 9

Steps resulting from Prelims
1a. Naked pair {13} in R23C1, locked for C1 and N1
1b. Naked pair {13} in R4C23, locked for R4, N4 and upper-left window, clean-up: no 8 in R3C5, no 5,7 in R5C4
1c. Naked pair {89} in R4C67, locked for R4 and upper-right window, clean-up: no 2,3 in R3C5
1d. Naked pair {12} in R6C78, locked for R6, N6 and lower-right window, clean-up: no 8,9 in R5C6
1e. 8,9 in N3 only in R123C9, locked for C9

2. Naked pair {13} in R3C1 + R4C2, locked for upper-left lace, no 1,3 in R1C5

3. 9 in upper-left lace only in N1 + R2C4, CPE no 9 in R2C3

4. 9 in upper-right lace only in R13C9, locked for C9
4a. 1 in upper-right lace only in R2C6 + N3, CPE no 1 in R2C79
4b. 3 in upper-right lace only in R2C6 + R5C9 + N3, CPE no 3 in R2C9

5. 9 in lower-left lace only in R6C2 + N7, CPE no 9 in R7C2

6. 9 in lower-right lace only in R8C6 + N9, CPE no 9 in R8C7

7. 45 rule on N5 2 outies R3C5 + R4C7 = 1 innie R5C5 + 13
7a. Max R3C5 + R4C7 = 18 -> max R5C5 = 5
7b. Min R3C5 + R4C7 = 14, no 4 in R3C5, clean-up: no 7 in R4C5

8. Disjoint 14(4) cage at R1C5 = {1238/1247/1256/1346/2345}
8a. 1 only in R9C5 -> no 6,7,8 in R9C5

9. R45C4 = {17/26/35}, R78C4 = {15/24} -> combined cage R4578C4 = {17}{24}/{26}{15}/{35}{24}, 2 locked for C4

10. Hidden killer pair 1,2 in R23C6 and R23C78 for upper-right window, R23C6 contains one of 1,2 -> R23C78 must contain one of 1,2
10a. Killer pair 1,2 in R1C78 and R23C78, locked for N3
10b. Hidden killer pair 1,3 in R23C6 and R23C78 for upper-right window, R23C6 contains one of 1,3 -> R23C78 must contain one of 1,3
10c. Killer pair 1,3 in R1C78 and R23C78, locked for N3
10d. 1,2 in C9 only in R789C9, locked for N9

11. Hidden killer pair 1,2 in R78C4 and R78C23 for lower-left window, R78C4 contains one of 1,2 -> R78C23 must contain one of 1,2
11a. Killer pair 1,2 in R78C23 and R9C23, locked for N7

12. 3 in N7 only in R78C23, locked for lower-left window, clean-up: no 9 in R6C5

13. Hidden killer pair 1,3 in R1C46 and R1C78 for R1, R1C78 contains one of 1,3 -> R1C46 must contain one of 1,3
13a. Killer pair 1,3 in R1C46 and R23C6, locked for N2
[I first saw this elimination as
The upper-left and upper-right windows contain two 45(9)s for R234 -> R234C159 must form a hidden window for R234
Naked pair {13} in R23C1, locked for hidden window R234C159, no 1,3 in R2C5
but I then saw that a conventional killer step achieves the same result.]
13b. Hidden killer pair 1,3 in R1C46 and R23C6 for N2, taken with the hidden killer pair in step 13 -> R1C78 and R23C6 must contain the same combination, which is also in R1C7 + R2C6
[With hindsight I could have done this step directly from steps 10 and 10a. Similarly steps 11 and 11a can be used to show that R78C4 and R9C23 must contain the same combination, which is also in R8C4 + R9C3.]
13c. R1C78 = {14}, locked for N3
or R1C78 = {23}, R1C7 + R2C6 = {23} => 1 in upper-right lace only in R2C8 + R3C7, locked for N3
-> no 1 in R3C8

14. 1,2 in C9 only in R789C9
14a. Hidden killer pair 1,2 in R6C8 and R79C9 for lower-right lace, R79C9 must contain at least one of 1,2, R6C8 = {12} -> R79C9 must contain one of 1,2 -> R8C9 = {12}
14b. Killer pair {12} in R6C8 and R79C9, locked for lower-right lace, no 1,2 in R9C5

15. Disjoint 14(4) cage at R1C5 = {2345} (only remaining combination), CPE no 2,3,4,5 in R5C5 -> R5C1 = 1, clean-up: no 7 in R4C4, no 9 in R6C6
15a. 2 in 14(4) cage only in R1C5 + R5C1, locked for upper-left lace
15b. 3 in 14(4) cage only in R5C9 + R9C5, locked for lower-right lace

16. 7 in N5 only in R56C6 = {37} or R6C45 = {57} -> R6C45 = {48/57} (cannot be [93], locking-out cages)

17. R4C6 = 9 (hidden single in N5), R4C7 = 8
17a. 45 rule on N5 one remaining innie R4C5 = 5, R3C5 = 6, clean-up: no 3 in R5C4, no 7 in R6C45

18. Naked pair {26} in R45C4, locked for C4 and N5, clean-up: no 4 in R5C6, no 4,8 in R6C6, no 4 in R78C4
18a. Naked pair {48} in R6C45, locked for R6
18b. Naked pair {37} in R56C6, locked for C6, clean-up: no 2 in R23C6
18c. Naked pair {14} in R23C6, locked for C6, N2 and upper-right window -> R1C5 = 2, clean-up: no 3 in R1C78
18d. Naked pair {14} in R1C78, locked for R1 and N3
18e. Naked pair {14} in R1C7 + R2C6, locked for upper-right lace

19. Naked pair {15} in R78C4, locked for C4, N8 and lower-left window
19a. Naked pair {68} in R78C6, locked for C6, N8 and lower-right window -> R1C6 = 5, R9C6 = 2, clean-up: no 4 in R9C23
19b. Naked pair {15} in R9C23, locked for R9 and N7

20. R1C4 = 3 (hidden single in N2)

21. 5 in disjoint 14(4) cage at R1C5 only in R5C19, locked for R5
21a. 5 in N6 only in R56C9, locked for C9

22. R4C1 = 2 (hidden single in C1), R45C4 = [62], R4C8 = 7, R4C9 = 4

23. Naked quad {6789} in R1239C9, locked for C9
23a. Naked pair {35} in R56C9, locked for N6
23b. Naked pair {69} in R5C78, locked for R5

24. Naked pair {35} in R3C7 + R5C9, locked for upper-right lace -> R2C8 = 6, R5C78 = [69]
24a. Naked pair {89} in R13C9, locked for C9 -> R2C9 = 7, R9C9 = 6, R8C6 = 8, R7C6 = 6
24b. Naked pair {89} in R2C45, locked for R2 and N2 -> R3C4 = 7

25. Naked triple {345} in R5C9 + R8C8 + R9C5, locked for lower-right lace
25a. Naked pair {79} in R79C7, locked for C7
25b. R9C8 = 8 (hidden single in N9)

26. Naked pair {45} in R2C2 + R5C1, locked for upper-left lace
26a. Naked pair {89} in R2C4 + R3C3, locked for upper-left lace
26b. Naked pair {67} in R1C13, locked for R1
26c. Naked pair {89} in R1C2 + R3C3, locked for N1

27. R7C1 = 8 (hidden single in C1)

28. R6C4 = 8 (hidden single in lower-left window)

and the rest is naked singles.

Solution, using my coloured worksheet:
Image


Last edited by Andrew on Thu Nov 18, 2010 11:17 pm, edited 1 time in total.

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 Post subject: Re: More Lace Practice
PostPosted: Sun Nov 14, 2010 12:56 am 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
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Location: Lethbridge, Alberta, Canada
I found Three Laces Windoku-X a lot harder.

It was probably mainly my own fault. In the following position

Image

I'd already done work using the lower-left lace and the lower-left window to find a hidden pair in the lower-left lace.

I could see that R8C9 "sees" all the cells of the lower-right lace except for R6C8 and R9C5. It was only after Ed (many thanks!) told me that R6C8 "sees" all of the cells of N9 except for R8C9 using the lower-right lace AND the lower-right window (I'd forgotten about that :oops: ) that I understood Simon's "spoiler". Then, R6C8 = R8C9 and the only common candidate in these cells is 5 -> 7(2) cage at R6C8 = [52], R8C9 = 5, R8C8 = 8, placed for D\, 11(2) cage at R3C3 = {56}, placed for D\, etc. and the rest is relatively straightforward using quite a lot of hidden singles. I found that the "hidden windows" were useful in making these later eliminations, particularly the one in R159C159 when I got that down to a naked triple and a hidden pair.

I might have found Simon's step myself if I'd also included the four given windows in my diagram. I'm not very good at making thick boundary lines in Excel worksheets; after doing them once several years ago for the basic sudoku grid, I use that again and again. Maybe I'd better try to set up a windoku grid for possible future use.

Now the main reason for this post

Solution, using my coloured diagram:
Image


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 Post subject: Re: More Lace Practice
PostPosted: Tue Dec 14, 2010 4:33 am 
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HATMAN wrote:
.....Fully restrained: it has a single set of solutions.
What does "fully restrained" mean? Both are indeed very interesting puzzles and was totally defeated by the Three laces one. But as Simon's spoiler for Three Laces shows, I used exactly that feature to do the Four Laces!! :bigoops: Must still need Even More Lace Practice.

Walk-through for Four Laces Windoku
10 steps:
1. 3(2) at r6c7 = {12}: both locked for r6, n6 and W4
1a. no 8,9 in r5c6

2. r6c8 sees all of n9 indirectly through Green OL and W4 except r8c9 -> r6c8 = r8c9
2a. r8c9 = {12}

3. r9c5 sees all of n9 indirectly through Green OL except the three cells at r7c8+r8c79
3a. but from step 2, r9c5 sees r8c9 indirectly through r6c8 (Green OL)
3b. -> r9c5 = one of r7c8 or r8c7
3c. no 1,2 in r7c8 or r8c7 -> no 1,2 in r9c5

4. 4(2) at r2c1 = {13}: both locked for n1 and c1
4a. and locked for hidden window in r234 -> no 1,3 in r234c59
4b. no 1,8 in 11(2) at r3c5

Same deal as step 3 around n1
5. since r2c1 = r4c2 -> r1c5 = one of r2c3 + r3c2
5a. no 1,3 in r2c3/r3c2 -> no 1,3 in r1c5

6. remote 14(4) at r1c5 = {2345} only
6a. r5c5 sees all of that 14(4) -> no 2,3,4,5 in r5c5 (CPE)

7. 17(2) at r4c6 = {89}: both locked for r4 and W2
7a. no 2 in r3c5

8. "45" on n5: 3 innies r4c56 + r5c5 = 15
8a. min. r4c56 = 10 -> max. r5c5 = 5
8b. -> r5c5 = 1
8c. no 7 in 8(2)r4c4
8d. no 5,9 in 10(2)r5c6

9. "45" on n5: 2 remaining innies r4c56 = 14 = [59/68]
9a. 11(2)r3c5 = {56}: both locked for c5 and hidden window at r234c159

10. 7 in n5 in 10(2) = {37} or 12(2) = {57} = [3/5..] -> {35} blocked from 8(2)
10a. 8(2) = {26}: both locked for c4 and n5

Cracked

Cheers
Ed


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 Post subject: Re: More Lace Practice
PostPosted: Tue Dec 14, 2010 6:15 am 
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Ed

Restrainted was a slight mis-use of English by one of our European colleagues (I think it was Ruud - perhaps Tarek remembers?) meaning "constrained". We have retained it in its meaning of a puzzle structure with a limited number of solutions - as it has the nice connotation of the puzzle holding itself back.

A fully restrained puzzle has just one set of solutions (i.e. insert 8 clues to make it unique) - Nikoli_freak's Hands is an example.

Maurice


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 Post subject: Re: More Lace Practice
PostPosted: Tue Dec 14, 2010 6:20 am 
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Simon

I've started doing as you said and checking puzzles with fish switched off.

I seem to remember some discusion of re-ordering the application of solution techniques in JSudoku - do you havew any knowledge of this?

Maurice


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 Post subject: Re: More Lace Practice
PostPosted: Tue Dec 14, 2010 12:07 pm 
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HATMAN wrote:
I seem to remember some discusion of re-ordering the application of solution techniques in JSudoku - do you have any knowledge of this?


It is actually quite straight forward, just go to the "Solvers" tab and drag and drop the techniques to re-order them.

I think Para, Pyrrhon & udosuk once talked about this in one of the threads in that forum, they just put all the singles/subsets/intersections at the very top and all the wings/fishes/cycles/chains at the very bottom, or uncheck the inappropriate ones.


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 Post subject: Re: More Lace Practice
PostPosted: Wed Dec 15, 2010 8:37 am 
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Thanks Simon - I'll try it


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 Post subject: Re: More Lace Practice
PostPosted: Thu Dec 16, 2010 10:33 pm 
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HATMAN wrote:
Restrainted was a slight mis-use of English by one of our European colleagues (I think it was Ruud - perhaps Tarek remembers?) meaning "constrained". We have retained it in its meaning of a puzzle structure with a limited number of solutions - as it has the nice connotation of the puzzle holding itself back.
I really don't remember, Ruud, however, did use "restrained" often ....

tarek


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