something I just noticed with XYChains

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something I just noticed with XYChains

Postby stumble » Sat Feb 23, 2008 4:43 pm

I just figured out another Sudoku fact I was unaware of. Probably you guys are well aware of it, but maybe there’s a few innocents out there.
Here’s the BrainBasher 2-22-08SuperHard original
Code: Select all
.------------------.------------------.------------------.
| 4     379   239  | 9     6     8    | 129   179   5    |
| 1269  8     269  | 7     149   5    | 1249  3     24   |
| 19    79    5    | 2     1489  3    | 6     1479  478  |
:------------------+------------------+------------------:
| 39    2     4    | 1     37    6    | 8     5     3    |
| 7     36    368  | 5     238   28   | 14    146   9    |
| 36    5     1    | 4     38    9    | 7     2     36   |
:------------------+------------------+------------------:
| 2569  469   7    | 8     29    1    | 3     469   246  |
| 2569  1     269  | 3     279   4    | 259   8     267  |
| 8     3469  2369 | 69    5     27   | 249   4679  1    |
'------------------'------------------'------------------'

Here it is after I lay down my pencil and turn on the computer.
Code: Select all
.---------------.---------------.---------------.
| 4    37   23  | 9    6    8   | 12   17   5   |
| 26   8    69  | 7    1    5   | 49   3    24  |
| 1    79   5   | 2    4    3   | 6    79   8   |
:---------------+---------------+---------------:
| 9    2    4   | 1    7    6   | 8    5    3   |
| 7    6    8   | 5    3    2   | 14   14   9   |
| 3    5    1   | 4    8    9   | 7    2    6   |
:---------------+---------------+---------------:
| 5    49   7   | 8    29   1   | 3    6    24  |
| 26   1    69  | 3    29   4   | 5    8    7   |
| 8    349  23  | 6    5    7   | 249  49   1   |
'---------------'---------------'---------------'

With SudoCue I usually then look for any Xwings I missed, any AICs I can make work and then, if there’s enough bivalue cells, try to make XYChains work. Here’s my first XYChain on 4: r9c8-r3c8-r3c2-r7c2=>r9c2<>4
Code: Select all
.---------------.---------------.---------------.
| 4    37   23  | 9    6    8   | 12   17   5   |
| 26   8    69  | 7    1    5   | 49   3    24  |
| 1    79*  5   | 2    4    3   | 6    79*  8   |
:---------------+---------------+---------------:
| 9    2    4   | 1    7    6   | 8    5    3   |
| 7    6    8   | 5    3    2   | 14   14   9   |
| 3    5    1   | 4    8    9   | 7    2    6   |
:---------------+---------------+---------------:
| 5    49*  7   | 8    29   1   | 3    6    24  |
| 26   1    69  | 3    29   4   | 5    8    7   |
| 8    39-4 23  | 6    5    7   | 249  49*  1   |
'---------------'---------------'---------------'

I’m reasonably sure that is correct, and agrees with solution.

For my next trick I schemed to eliminate one of the 2’s in box 7 with another XYChain: r1c3-r1c2-r3c2… at this point in chain r3c2 is 9. But where do I go now? I already eliminated that 4 from r9c2 with the first chain so now I am faced with jumping to EITHER r7c2 or or r9c2 in clm 2. Ungood and illegal.
Code: Select all
.---------------.---------------.---------------.
| 4    37*  23* | 9    6    8   | 12   17   5   |
| 26   8    69  | 7    1    5   | 49   3    24  |
| 1    79*  5   | 2    4    3   | 6    79   8   |
:---------------+---------------+---------------:
| 9    2    4   | 1    7    6   | 8    5    3   |
| 7    6    8   | 5    3    2   | 14   14   9   |
| 3    5    1   | 4    8    9   | 7    2    6   |
:---------------+---------------+---------------:
| 5    49   7   | 8    29   1   | 3    6    24  |
| 26   1    69  | 3    29   4   | 5    8    7   |
| 8    39   23  | 6    5    7   | 249  49   1   |
'---------------'---------------'---------------'

I never had realized this was possible before when I was wrestling with XYChains. It seems once you eliminate a candidate with one chain, the puzzle is kind of illegal.
The chain I should have tried first was r2c7-r3c8-r1c8-r5c8=>r5c7<>4, which broke the puzzle.
stumble
 
Posts: 52
Joined: 29 October 2007

Re: something I just noticed with XYChains

Postby hobiwan » Sat Feb 23, 2008 6:49 pm

stumble wrote:Here’s my first XYChain on 4: r9c8-r3c8-r3c2-r7c2=>r9c2<>4
Code: Select all
.---------------.---------------.---------------.
| 4    37   23  | 9    6    8   | 12   17   5   |
| 26   8    69  | 7    1    5   | 49   3    24  |
| 1    79*  5   | 2    4    3   | 6    79*  8   |
:---------------+---------------+---------------:
| 9    2    4   | 1    7    6   | 8    5    3   |
| 7    6    8   | 5    3    2   | 14   14   9   |
| 3    5    1   | 4    8    9   | 7    2    6   |
:---------------+---------------+---------------:
| 5    49*  7   | 8    29   1   | 3    6    24  |
| 26   1    69  | 3    29   4   | 5    8    7   |
| 8    39-4 23  | 6    5    7   | 249  49*  1   |
'---------------'---------------'---------------'

I’m reasonably sure that is correct, and agrees with solution.

It is correct, but with that chain you can also eliminate 4 from r7c9, which solves the puzzle.
stumble wrote:For my next trick I schemed to eliminate one of the 2’s in box 7 with another XYChain: r1c3-r1c2-r3c2… at this point in chain r3c2 is 9. But where do I go now? I already eliminated that 4 from r9c2 with the first chain so now I am faced with jumping to EITHER r7c2 or or r9c2 in clm 2. Ungood and illegal.

I am pretty sure that you can't eliminate 2 from r9c3 at this point (at least not with an XY-Chain). You can eliminate 2 from r8c1, although with a very long chain:
Code: Select all
[r2c1]-6-[r2c3]-9-[r2c7]-4-[r5c7]-1-[r5c8]-4-[r9c8]-9-[r9c2]-3-[r9c3]=>[r8c1]<>2, [r1c3]<>2
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Postby ArkieTech » Sat Feb 23, 2008 7:54 pm

How about an xy-wing?
Code: Select all
.---------------.---------------.---------------.
| 4    37   23  | 9    6    8   |*12   17   5   |
| 26   8    69  | 7    1    5   | 9-4  3   *24  |
| 1    79   5   | 2    4    3   | 6    79   8   |
:---------------+---------------+---------------:
| 9    2    4   | 1    7    6   | 8    5    3   |
| 7    6    8   | 5    3    2   |*14   14   9   |
| 3    5    1   | 4    8    9   | 7    2    6   |
:---------------+---------------+---------------:
| 5    49   7   | 8    29   1   | 3    6    24  |
| 26   1    69  | 3    29   4   | 5    8    7   |
| 8    349  23  | 6    5    7   | 249  49   1   |
'---------------'---------------'---------------'


dan
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Postby Carcul » Sat Feb 23, 2008 8:31 pm

Stumble wrote:Here’s the BrainBasher 2-22-08SuperHard original


I would be a good practice to post the original puzzle as given.
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Postby daj95376 » Sat Feb 23, 2008 9:31 pm

Carcul wrote:I would be a good practice to post the original puzzle as given.

If I'm not mistaken, stumble posted the original puzzle as a PM.

stumble wrote:Here’s the BrainBasher 2-22-08SuperHard original
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Postby daj95376 » Sat Feb 23, 2008 9:39 pm

ArkieTech wrote:How about an xy-wing?

Dan, an XY-Wing is just a short XY-Chain. So you provided stumble with an alternate XY-Chain.

hobiwan, nice catch on the second elimination. I missed it while reviewing stumble's XY-Chain.
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Re: something I just noticed with XYChains

Postby stumble » Sat Feb 23, 2008 9:42 pm

hobiwan wrote:It is correct, but with that chain you can also eliminate 4 from r7c9, which solves the puzzle.

ARGHHHHH!!! I never can learn to look for that.
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Postby stumble » Sat Feb 23, 2008 9:45 pm

ArkieTech wrote:How about an xy-wing?
Code: Select all
.---------------.---------------.---------------.
| 4    37   23  | 9    6    8   |*12   17   5   |
| 26   8    69  | 7    1    5   | 9-4  3   *24  |
| 1    79   5   | 2    4    3   | 6    79   8   |
:---------------+---------------+---------------:
| 9    2    4   | 1    7    6   | 8    5    3   |
| 7    6    8   | 5    3    2   |*14   14   9   |
| 3    5    1   | 4    8    9   | 7    2    6   |
:---------------+---------------+---------------:
| 5    49   7   | 8    29   1   | 3    6    24  |
| 26   1    69  | 3    29   4   | 5    8    7   |
| 8    349  23  | 6    5    7   | 249  49   1   |
'---------------'---------------'---------------'


dan

I never can see those XYWings, thanks.
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Posts: 52
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