Chain requirements

Advanced methods and approaches for solving Sudoku puzzles

Chain requirements

Postby caraemily » Tue Mar 11, 2008 9:17 pm

Can the two ends of an XY chain inhabit the same box and validly eliminate one or more candidates in that box?

A post on this forum from 2005 stated that an XY chain "has more than four cells" - should this be corrected to "four or more cells"?
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Postby Pat » Wed Mar 12, 2008 11:08 am

caraemily wrote:A post on this forum from 2005 stated that an XY chain "has more than four cells"
-- should this be corrected to "four or more cells"?



3-or-more cells --

SuDoPedia wrote:The shortest XY-Chain is an XY-Wing with only 3 cells

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Postby ronk » Wed Mar 12, 2008 11:40 am

Pat wrote:
SuDoPedia wrote:The shortest XY-Chain is an XY-Wing with only 3 cells


For many people, the length is the "loop length" which includes the elimination cell of a discontinuous "nice loop".
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Postby Pat » Sun Mar 16, 2008 1:56 pm

ronk wrote:For many people, the length is the "loop length" which includes the elimination cell of a discontinuous "nice loop"


thanks, ronk, you are absolutely right,
and 4 cells should be considered the minimum size
    ( obvious, but i mention this since ronk and i so rarely agree on anything )

caraemily wrote:Can the two ends of an XY chain inhabit the same box and validly eliminate one or more candidates in that box?


meanwhile, caraemily has moved this question to a separate Topic --
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Postby Steve R » Sun Mar 16, 2008 6:34 pm

So a sequence of three cells with candidates x, y z and t

(xy) – (yz) - (zt)

is not a chain.

Does it have a name?

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Postby eleven » Mon Mar 17, 2008 4:35 pm

ronk wrote:For many people, the length is the "loop length" which includes the elimination cell of a discontinuous "nice loop".
This is odd for me. An xy-chain (or wing) can eliminate up to 4 candidates. Then such an xy-wing would be a xy-chain of length 7 ?
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Postby ronk » Mon Mar 17, 2008 5:06 pm

eleven wrote:
ronk wrote:For many people, the length is the "loop length" which includes the elimination cell of a discontinuous "nice loop".
This is odd for me. An xy-chain (or wing) can eliminate up to 4 candidates. Then such an xy-wing would be a xy-chain of length 7 ?

For loop length, either count multiple eliminations as one, or count the number of links (inferences). Hmm, maybe the origin is the number of links.

Code: Select all
 .  xz .  | *  xy *
 *  *  *  | yz .  .
 .  .  .  | .  .  .

[r1c46,r2c123] -z- r1c2 -x- r1c5 -y- r2c4 -z- [r1c46,r2c123], implies r1c46<>z, r2c123<>z

There is a potential for five eliminations, but chain_length = 3 and loop_length = 4.

Steve R wrote:So ... (xy) – (yz) - (zt)

is not a chain.

Does t = x?
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Postby Steve R » Mon Mar 17, 2008 5:30 pm

In general, t ≠ x.

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