Y-Wing
Although Y-Wing and X-Wing have similar names, the methods are different. X-Wing extends to SwordFish and JellyFish, while
Y-Wing brings a nice set of other rules which we will examine in later articles.
Structurally, Y-Wing is comprised of 3 cells, all of which have exactly two candidates.
One of the cells is called a hinge and suppose the two candidates in the hinge are X and Y. The hinge sees the other two cells,
which will contain a new candidate Z and exactly one of X and Y. In other words, the non-hinge cells will have candidates XZ
and YZ respectively. Once we have this structure of cells, we can eliminate candidates Z from other cells.
Y-Wing Setup
Let us first clearly illustrate this structure and see how the eliminations occur. The hinge cell is C6 and the non-hinge
cells are A4 and C3. With the notation above - X=5, Y=2 and Z=7. Now, let us see why we can eliminate the
candidate 7 from A2 and A3.
If C6 has a value of 2, then C3 is a 7 and there can be no other sevens in the left square.
If C6 has a value of 5, then A4 has a value of 7 and there can be no sevens in row A.
We can now specify the elimination rule of Y-Wing. The Z candidate can be eliminated from all cells which are
seen by both non-hinge cells.
Let us consider a couple of boards which make use of the Y-Wing method.
Y-Wing - Example 1
In the first example , the hinge cell is D3 and the Z candidate is 6, which is present in the non-hinge cells I3 and D6. Placing either 5 or 9 in the hinge cell forces one of the non-hinge cells to become 6 and so we can eliminate the highlighted candidate in I6.
Y-Wing - Example 2
The second example shows that we can have significantly more eliminations, depending on the positions of the hinge cells. The setup is the same. The hinge cell is C9 and the Z candidate is present in both B8 and G9. On this board, there are more cells with candidate 6, which are seen by both non-hinge cells, which leads to more eliminations. The eliminated candidates are highlighted in red.
Another method which we will examine later is XY-Chains. The reason for mentioning it here is that a Y-Wing can be represented as an XY-Chain, where both Z candidates in the non-hinge cells are the beginning and end of the chain.
