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 Post subject: TENS NCwrap 1
PostPosted: Thu Mar 28, 2013 2:40 pm 
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Grand Master
Grand Master

Joined: Wed Apr 30, 2008 9:45 pm
Posts: 693
Location: Saudi Arabia
TENS NCwrap 1

This is the ten by ten: 0 to 9.

It is Non-Consecutive and it wraps so 0 cannot be next to 9
- did not make much use of this property.

Note that it has symetrical cages hence the solution is symetrical - I just used this to speed up solving as I did not see anything clever to do.

Medium hard I think - grateful for your views.
Remember the 14 hidden windows (see previous posts for a description). I found that they helped a lot. (Moderator Note): See here.





Image
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JS Code for the extra groups (set design: latin square, 0-9 and then paste in as extra groups):

1x10::k:11521:11521:11521:11521:11529:11528:11522:11522:11522:11522:11521:11521:11521:11525:11529:11528:11528:11522:11522:11522:11521:11521:11525:11525:11529:11528:11528:11528:11522:11522:11521:11525:11525:11525:11529:11528:11528:11528:11528:11522:11525:11525:11525:11525:11529:11530:11530:11530:11530:11530:11529:11529:11529:11529:11529:11530:11527:11527:11527:11527:11524:11526:11526:11526:11526:11530:11527:11527:11527:11523:11524:11524:11526:11526:11526:11530:11527:11527:11523:11523:11524:11524:11524:11526:11526:11530:11527:11523:11523:11523:11524:11524:11524:11524:11526:11530:11523:11523:11523:11523:

JS Killer Cages:

1x10:4:k:17:2313:2313:18:2309:2566:19:4109:4109:20:4110:21:22:23:2309:2566:24:25:26:2316:4110:27:28:29:2309:2566:30:31:32:2316:33:34:35:36:37:38:39:40:41:42:1539:1539:1539:43:44:45:46:3847:3847:3847:3844:3844:3844:47:48:49:50:1544:1544:1544:51:52:53:54:55:56:57:58:59:60:2315:61:62:63:2562:2305:64:65:66:4112:2315:67:68:69:2562:2305:70:71:72:4112:73:4111:4111:74:2562:2305:75:2314:2314:76:

Solution:

5182036974
7408269531
9635714208
3961480752
0247953186
6813597420
2570841693
8024175369
1359628047
4796302815


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 Post subject: Re: TENS NCwrap 1
PostPosted: Sun Feb 26, 2017 11:59 pm 
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Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
After my recent Anti-kNight walkthroughs in this forum, I was left with a choice between this almost four years old Decidoku and the one posted last month. I decided to try the older one first, since it appeared to have easier rules to apply; but maybe it wasn’t the easier of the two to solve, I’ll discover that once I’ve tried the other one.

As HATMAN said, remember the 14 hidden windows. It’s an easy start using them but would probably be extremely difficult to solve without them. Things got harder after I’d made all possible use of the hidden windows. Definitely at least medium hard. It might have been a bit easier if I'd been prepared to use symmetry in my forcing chains.

Here is my walkthrough for TENS NCwrap 1:
Decidoku, candidates 0-9. Non-consecutive (NC) including 9 and 0 NC.
I’ve numbered the rows and columns 0 to 9, with the decidoku windows (decets) DR0C0, etc. Hidden decets, as in wellbeback’s diagram will be HR0C4, etc.
Decidoku has hidden cages, as in previous decidoku puzzle.

Prelims

a) R0C12 = {09/18/27/36} (cannot be {45} because of NC)
b) R0C78 = {79}
c) R12C0 = {79}
d) R12C9 = {09/18/27/36} (cannot be {45} because of NC)
e) R78C0 = {09/18/27/36} (cannot be {45} because of NC)
f) R78C9 = {79}
g) R9C12 = {79}
h) R9C78 = {09/18/27/36} (cannot be {45} because of NC)
i) 6(3) cage at R4C0 = {015/024} (cannot be {123} because of NC)
j) 6(3) cage at R5C7 = {015/024} (cannot be {123} because of NC)
k) 9(3) cage at R0C4 cannot contain 9
l) 9(3) cage at R7C5 cannot contain 9

Steps resulting from Prelims
1a. Naked pair {79} in R0C78, locked for R0 and D0C6, clean-up: no 0,2 in R0C12 + R12C9
1b. Naked pair {79} in R12C0, locked for C0 and D0C0, clean-up: no 0,2 in R78C0
1c. Naked pair {79} in R78C9, locked for C9 and D6C9, clean-up: no 0,2 in R9C78
1d. Naked pair {79} in R9C12, locked for R9 and D0C6
1e. Naked pair {79} in R0C78 -> no 8 in R0C69 + R1C78 (NC)
1f. Naked pair {79} in R12C0 -> no 8 in R03C0 + R12C1 (NC)
1g. Naked pair {79} in R78C9 -> no 8 in R69C9 + R78C8 (NC)
1h. Naked pair {79} in R9C12 -> no 8 in R8C12 + R9C03 (NC)
1i. 6(3) cage at R4C0 = {015/024}, 0 locked for R4 and DR1C3
1j. 6(3) cage at R5C7 = {015/024}, 0 locked for R5 and DR5C6
[NC effects on the placements in the 6(3) cages have been omitted because of the next step.]

[As HATMAN said the hidden windows helped a lot. I agree, without them this step wouldn’t get me into the puzzle quickly.]
2. Hidden decet DR0C5 contains R0123C5 + R4C012345
This hidden window contains 10(3) cage at R0C5, 6(3) cage at R4C0 and R3C5 + R4C345
2a. 45 rule on hidden window 4 remaining cells R3C5 + R4C345 = 29 = {5789} -> 6(3) cage = {024}, locked for R4 and DR1C3, 10(3) cage = {136}, locked for C5 and DR0C5
2b. Similarly for one of the hidden decets at R5C4 containing R5C456789 + R6789C4 which contains 6(3) cage at R5C7, 10(3) cage at R7C4 and R5C456 + R6C4
45 rule on hidden window 4 remaining cells R5C456 + R6C4 = 29 = {5789} -> 6(3) cage = {024}, locked for R5 and DR5C6, 10(4) cage = {136}, locked for C4 and DR6C1
2c. 9(3) cage at R0C4 = {027/045}, 0 locked for C4
2d. 4,5 of {045} must be in R02C4 because of NC -> no 4,5 in R1C4
2e. 9(3) cage at R7C5 = {027/045}, 0 locked for C5
2f. 4,5 of {045} must be in R79C5 because of NC -> no 4,5 in R8C5
2g. 8 in R0 only in R0C123, locked for DR0C0
2h. 8 in R9 only in R9C678, locked for DR6C9
2i. R3C5 + R4C345 = {5789} -> 5 must be in R4C45 and 8 in R3C5 + R4C3 because of NC, no 5 in R3C5 + R4C3, no 8 in R4C45, 5 locked for R4
2j. R5C456 + R6C4 = {5789} -> 5 must be in R5C45 and 8 in R5C6 + R6C4 because of NC, no 5 in R5C6 + R6C4, no 8 in R5C45, 5 locked for R5
2k. Grouped X-Wing for 5 in R4C45 and R5C45, no other 5 in C45

3. 15(3) cage at R4C7 = {168}, locked for R4 and DR4C5
3a. 15(3) cage at R5C0 = {168}, locked for R5 and DR0C4
3b. R4C6 = 3 (hidden single in R4) -> no 2,4 in R3C6 (NC)
3c. R5C3 = 3 (hidden single in R5) -> no 2,4 in R6C3 (NC)
3d. 9(3) cage at R0C4 = {027}, locked for C4
3e. 9(3) cage at R7C5 = {027}, locked for C5
3f. R3C4 = 4 (hidden single in C4) -> no 5 in R3C3 + R4C4 (NC)
3g. R6C4 = 8 (hidden single in C4) -> no 9 in R5C4 + R6C5, no 7,9 in R6C3 (NC)
3h. R4C45 = [95], R5C45 = [59]
3i. R4C3 = 7 -> no 6,8 in R3C3 (NC)
3j. R3C5 = 8 -> no 7,9 in R3C6 (NC)
3k. R5C6 = 7 -> no 6 in R6C6 (NC)
3m. R6C5 = 4 -> no 5 in R6C6 (NC)
3n. R0C4 = {02} -> no 1 in R0C35 (NC)
3o. R9C5 = {02} -> no 1 in R9C46 (NC)
3p. 7 in R3 only in R3C78, locked for DR05
3q. 7 in R6 only in R6C12, locked for DR6C1

[Looks like there’s nothing more to get from the hidden windows.]

4. R0C12 = {18} (cannot be {36} which clashes with R0C5), locked for R0 and DR0C0
4a. R9C78 = {18} (cannot be {36} which clashes with R9C4), locked for R9 and DR6C9
4b. 1,8 in C3 only in R123C3, locked for DR1C3
4c. 8 in R12C3 -> no 9 in R12C3 (NC)
4d. 1,8 in C6 only in R678C6, locked for DR5C6
4e. 8 in R78C6 -> no 9 in R78C6 (NC)

[Unless I’m missing something it looks like it’s now time to nibble away using interactions and NC.]

5. Consider placements for R0C5 = {36}
R0C5 = 3 => no 2 in R0C46 (NC)
or R0C5 = 6 => R12C5 = {13} => no 2 in R12C4 (NC) => R0C4 = 2
-> R0C45 = [03/26], no 2 in R0C6
5a. Similarly R9C45 = [03/26], no 2 in R9C3 (NC)

6. Taking steps 3p and 3q further
6a. 7 in R3 only in R3C78 -> R4C78 must contain 1 (cannot both be {68} because of NC) -> no 1 in R4C9
6b. 1 in C9 only in R123C9, locked for DR0C6
6c. Killer pair 6,8 in R12C9 and R4C9, locked for C9
6d. 7 in R6 only in R6C12 -> R5C12 must contain 1 (cannot both be {68} because of NC) -> no 1 in R5C0
6e. 1 in C0 only in R678C0, locked for DR6C0
6f. Killer pair 6,8 in R5C0 and R78C0, locked for C0
6g. 4 in R4 must be in R4C12 (R4C12 cannot be {02} which clashes with 1 in R5C12), no 4 in R4C0
6h. 4 in R5 must be in R5C78 (R5C78 cannot be {02} which clashes with 1 in R4C78), no 4 in R5C9
6i. 6 in R3 only in R3C12, locked for DR1C1
6j. 6 in R3 only in R3C12 -> no 5 in R3C12 (NC)
6k. 6 in R6 only in R6C78, locked for DR5C6
6l. 6 in R6 only in R6C78 -> no 5 in R6C78 (NC)

7. Consider placements for 8 in C3
R1C3 = 8 => no 7 in R1C4 (NC) => R2C4 = 7 (hidden single in C4) => R12C0 = [79]
or R2C3 = 8 => no 9 in R2C2 + R3C3 (NC)
-> no 9 in R2C2
7a. 9 in DR1C3 only in R3C123, locked for R3
7b. R2C2 = {35} -> no 4 in R1C2 + R2C1 (NC)
7c. Similarly no 9 in R7C7, 9 in DR5C6 only in R6C678, locked for R6
7d. R7C7 = {35} -> no 4 in R7C8 + R8C7 (NC)

8. Consider placements for R3C3 = {19}
R3C3 = 1 => R3C12 = {69} (hidden pair in DR1C1) => R2C2 = 3 (hidden single in DR1C1)
or R3C3 = 9 => R3C12 = {36} => R2C2 = 5 (hidden single in DR1C1) => no 6 in R3C2 => R3C12 = [63]
-> 3 in R23C2, locked for C2 and DR1C1
8a. Similarly 3 in R67C7, locked for C2 and DR5C6

[I wasn’t happy with this step, which cracks this puzzle. It only stops just short of being a contradiction, but I couldn’t see any other forcing chain to achieve this result.
There is a long forcing chain based on the placement of 1 in R4C78 but it seems to depend on symmetry and, while the puzzle clearly has symmetry, it’s not easy to prove.]
9. Consider combinations for R12C9 = {18/36}
R12C9 = {18}, locked for DR0C6
or R12C9 = {36} => R4C9 = 8, R3C9 = 1 (hidden single in C9) => no 0,2 in R3C8 (NC), R3C8 = {57} => no 6 in R4C8 => R4C8 = 1 => R9C8 = 8
-> no 8 in R2C8
9a. 8 in DR0C6 only in R12C9 = {18}, locked for C9
9b. R3C3 = 1 (hidden single in R3), naked pair {58} in R12C3, locked for C3 and DR1C3, R2C2 = 3
9c. R2C2 = 3 -> no 2 in R1C2 + R2C1 (NC)
9d. R6C3 = 0 -> no 9 in R7C3 (NC wrap)
9e. R8C3 = 9 (hidden single in C3) -> R78C9 = [97]
9f. R7C5 = 7 (hidden single in C5) -> no 6 in R7C4, no 8 in R7C6 (both NC)
9g. R8C6 = 8 (hidden single in C6)
9h. Similarly considering combinations for R78C0 = {36}/[81] and using NC where necessary -> no 8 in R7C1 -> R78C1 = [81], R6C6 = 1, R7C67 = [53], R3C6 = 0, R1C6 = 9, R12C0 = [79], R2C4 = 7, R12C3 = [85], R12C9 = [18], also no 6 in R2C6, no 2 in R7C8 + R8C7 (NC)

10. R2C5 = 1 -> no 2 in R2C6 (NC)
10a. R2C67 = [42]
10b. R0C6 = 6 -> no 7 in R0C7 (NC)
10c. R0C5 = 3 -> no 2 in R0C4 (NC)
10d. R0C78 = [97], R3C8 = 5
10e. R3C7 = 7 -> no 6,8 in R4C7 (NC)
10f. R4C7 = 1 -> no 0 in R5C7 (NC)
10g. R9C78 = [81] -> no 0,2 in R8C8 + R9C9 (NC)
10h. Similarly R7C234 = [241], R9C34 = [63], R9C12 = [79], R6C12 = [57], R5C2 = 1, R0C12 = [18], no 0,2 in R0C0 + R1C1, no 0 in R4C2 (NC)

and the rest is naked singles, without using non-consecutive or hidden groups.


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