Y-Wing

From PuzzleWiki

Jump to: navigation, search

A Y-wing is an advanced technique in Sudoku. A Y-wing arises when there are three connected cells which can only contain the values AB, BC, and AC respectively and allows for the elimination of A from any cells that "see" both the AB and AC cells. The AB and AC cells must be connected in different "directions" to the BC cell, such as one in the same row, and the other in the same column (or also variations with the same region).

The Y-wing elimination arises due to the communication between the connected cells. If the AB cell is an A, then any cell that "sees" the AB cell cannot be A. If the AB cell is a B, then the connectivity forces the BC cell to be a C, which means the AC cell must be an A, so any cell that "sees" AC cannot be A. Since one of these two conditions must be true, the elimination of A from all cells that "see" both AB and AC in the same row/column/region is allowed.


In the following example of a Y-wing, from Just One Cell Sudoku, three cells with values 48, 47, and 78 are shaded, forming a Y-wing that allows an elimination of an 8 (in red) in a cell that sees both the 48 and 78 cells. As a result of this Y-wing elimination, there is now a Hidden Single 8 in the upper-right most cell as it is the only position left for an 8 in this region.

Personal tools