Y-Wing

This is an excellent method for eliminating possible solutions. The method looks like X-wing, but has only three corners instead of four.


The Theory :

the theory of Y-wing


A, B and C stands for possible solutions in the coloured cells as indicated in the figure here on the left.


The three corners of the Y-wing are marked (AB), (BC) and (AC).


The cell (AB) id the key to the solutions. If the solution of this cell is (A) then, (C) will occur in the lower left corner. If the solution of the cell(AB) is (B), then the (C) will occur in the upper right cell.


Whatever happens in cell (AB), there can never be a (C) in the lower right corner. This means that the (C) can be eliminated from the lower right corner.

More Theory :

more theory about Y-wing


In this example more numbers can be eliminated then just the corners of a rectangle.


The cell (BC) can see the cell (AB), because both of them occur in the same box. The cell (AB) can see the cell (AC), because both of them are on the same row.


If there is a number (A) in cell (AB), then the solution of cell (AC) is (C). If the solution of cell (AB) is (B) then the solution of cell (BC) is (C). This means that whatever the solution of cell (AB) might be, all the numbers (C) can be eliminated

Example 1 :

first example about Y-wing


In this example the number (AB) can be found in cell B!. The number (8) is linked to cell C2 en the number 3 is linked to cell B9.


The cell (BC) can see the cell (AB), because both of them occur in the same box. The cell (AB) can see the cell (AC), because both of them are on the same row.


The cells C2 and B1 have the number (4) in common. This means that the number (4) in the cells C2 or B1 shall occur, so that there can not be any (4) in cell C8. This will eliminate the (4) in cell C8.

Example 2 :

second example about Y-wing


The cells B1 and A7 are linked with cell B9 (AB from the theory section).


The cell B1 and A7(BC) can see the cell (AB), because both of them occur in the same box. The cell (AB) can see the cell (AC), because both of them are on the same row.


The cells C2 and B1 have the number (8) in common. The (8) will occur in cell C2 or B1. This means that there can not be a number (8) in the cells A2 and A3. So the number (8) can be eliminated from these cells.