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WXYZ Wings |
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A WXYZ-Wing is like an XY-Wing and an XYZ-Wing, except it is a group of four cells, one sharing a unit with the other three. The first cell in a WXYZ-Wing has three or four candidates while the other three, called the wings, have two each. Each of the wings must share one candidate with the first cell, (that's part of sharing a unit) but each wing must share a different value. If the second candidates in the wings are all the same, and are also the same as the left-over candidate of the first cell if the first cell has four candidates, then if any fifth cell shares that candidate and a unit with all the others, that candidate can be eliminated.
Consider the example on this page. The highlighted cell with 5, 8 and 9 as candidates is the first cell, and the other three are the wings. One wing shares the 5 with the first cell, another shares the 8 and the last shares the 9. That leaves a 1 in each wing, which all three share a unit with the 1 highlighted in green. Whether the first cell is a 5, 8 or 9, any way we go, the 1 in green can be eliminated. If the first cell also contained the candidate 1, the same elimination could still be made.
In theory, the Wings techniques could be extended to 4+ wings, but due to the rarity of this occurrence, it is not included in the Sudoku Snake rating system or hint generator.
Sudoku Snake gives WXYZ-Wings a skill value of 350.
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