
Naked XY Chains 

A Naked XYChain is a series of cells that contain only 2 candidates each in a chain pattern, each cell sharing a unit with the cell behind and ahead of it with a different candidate. If the remaining candidates in the first and last cells are the same, then any candidate in the puzzle that shares a unit with both of those can be eliminated.
Consider the example on this page. We'll consider the first cell in the chain to be the one that contains a 7 and an 8. The 8 shares a unit with the 5,8 cell, then the 5 of that cell shares a unit with the 5,9 cell, then the 9 of that cell shares a unit with the 7,9 cell. The remaining candidate in the first and last cells are both 7's. Since the 7 highlighted in green shares a unit with both these 7's, it can be eliminated.
Consider the following logic. The first cell must be either a 7 or an 8. If it is a seven then the green 7 gets eliminated. If instead it is an 8, the second cell is a 5, the third cell is a 9, and the last cell is a 7, which also causes the 7 in green to be eliminated.
Naked XY Chains can be very long in puzzles that have a lot of cells with only two candidates. To augment the program's execution speed, and since naked XYChains can be engulfed in higher solving methods, Sudoku Snake stops searching once a Naked XYChain is more than 7 cells long.
Note that Naked XYChains differ from Hidden XYChains in that it is the leftover candidates in the first and last cell cause the elimination, while in Hidden XYChains it's the connecting candidates that do.
Sudoku Snake gives Naked XYChains a skill value of 900.






