Sudoku Tutorial
XY Chains

The rules in any chain are:
  1. The chain must begin and end with strong links.
  2. There cannot be any two consecutive weak links anywhere in the chain.
  3. There must be an odd number of links in the chain.
(Remember that two candidates in a bivalue cell are always strongly linked)

In an XY Chain, all involved cells are bivalue cells.  Links in the chain must alternate between link INSIDE a cell (always strong) to a link between two related cells (weakly or strongly linked).   Every other link must be inside a bivalue cell. The links between cells can be either weak or strong but since every other link in the chain is inside a bivalue cell, there will not be any consecutive weak links in the chain.  Also since the chain alternates between bivalue cells and links between cells, there will always be an odd number of links in the chain.

In this example, the chain begins and ends with a 7.  This means at least one of the 7's (shown in blue) must exist.  (It is possible that both end of the chain are 7's since the ends cannot see each other).   7's can be eliminated from any cell that can see both end of the chain (r4c6 in this example).
XY_chain.jpg Chain starts with 7

1).  (r3c6)              7- 3    (strong link)
2).  (r3c6 to r3c2)  3 - 3   (weak link)
3).  (r3c2)              3 - 1    (strong link)
4).  (r3c2 to r8c2)  1 -1    (strong link)
5.)  (r8c2)               1 - 3   (strong link)
6).  (r8c2 to (r8c7)  3 - 3  (strong link)
7.)   (r8c7)               3 - 9   (strong link)
8).  (r8c7 to (r6c7)  9 - 9   (strong link)
9.). (r6c7)                 9 - 4  (strong link)
10). (r6c7 to r5c8)     4 - 4 (weak link)
11). (r5c8)                 4 - 7 (strong link)
12). (r5c8 to r5c2)    7 - 7 (weak link)
13). (r5c2)                 7 - 9 (strong link)
14). (r5c2 to r4c2)     9 - 9 (strong link)
15). (r4c2)                  9 - 7 (strong link)
Chain ends with 7

7 removed from r4c6)

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