XY-Chain
The XY-Chain technique is an extension of the
XY-Wing technique where a chain of cells is formed. Each link in the chain is a pair of cells in the same unit that have two candidates each and share a common candidate. If you form a chain of links, and the unused candidates at the endpoints of the chain are the same, you can remove that candidate from the intersection of the endpoints.
Consider the sudoku below.
We can create our first link with
the cells r1c2 and r1c7 sharing the common candidate 2.
A second link can be built using
the cells r1c7 and r3c9 sharing the common candidate 5.
A third link can be built using
the cells r3c9 and r8c9 sharing the common candidate 6.
Finally, a fourth link can be built using
the cells r8c9 and r8c5 sharing the common candidate 8.
The two endpoints both have the same unlinked candidate 1, so one of the cells
must contain the digit 1. Therefore, we can remove the candidate 1 from
the intersection of the endpoints.
Note: The intersection of two cells is defined as all cells that share a unit with both cells.
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Last Updated: 11/24/2020 12:00:33 AM CST