## Chain requirements

Advanced methods and approaches for solving Sudoku puzzles

### Chain requirements

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"?
caraemily

Posts: 2
Joined: 11 March 2008

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

Pat

Posts: 3879
Joined: 18 July 2005

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".
ronk
2012 Supporter

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Joined: 02 November 2005
Location: Southeastern USA

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 --

Pat

Posts: 3879
Joined: 18 July 2005

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?

Steve
Steve R

Posts: 74
Joined: 03 April 2006

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 ?
eleven

Posts: 2241
Joined: 10 February 2008

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?
ronk
2012 Supporter

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Location: Southeastern USA

In general, t ≠ x.

Steve
Steve R

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Joined: 03 April 2006