|
|
|
Naked XY Chains |
| |
A Naked XY-Chain 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 XY-Chains can be engulfed in higher solving methods, Sudoku Snake stops searching once a Naked XY-Chain is more than 7 cells long.
Note that Naked XY-Chains differ from Hidden XY-Chains in that it is the left-over candidates in the first and last cell cause the elimination, while in Hidden XY-Chains it's the connecting candidates that do.
Sudoku Snake gives Naked XY-Chains a skill value of 900.
|
|
|
|
|
|
|
|
