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Y - Wings

Warning! The Y - Wings technique is an advanced technique, meaning that it is only used when you ask Puzzle Tiger for a "Very Hard" puzzle. As such you will almost certainly never come across a published puzzle in a newspaper or magazine which requires this or any of the more advanced techniques. If, however, you're interested in really stretching yourself, read on...

The Y - Wings pattern is a candidate elimination technique, meaning that it eliminates possible values from cells. It is also (for reasons unclear to me) often called the XY - Wing. To find a Y-wing, you need to find three simple pairs (cells which can contain only two candidates), where one of the cells shares a group with both of the others. The cell which shares groups with both the other cells is called the "pivot", and the other cells are called the "wings". In general if the pivot contains the candidates {A, B}, and the wings each contain {B, C} and {A, C}, then any cell which can "see" (shares a group with) both the wings cannot be a C. Here is an example:

In this example, the cells highlighted in orange form a Y-wing pattern, allowing "3" to be eliminated from the cell in red. The pivot can be a 6 or an 8, and the wings can be {3, 6} and {3, 8} respectively. To see how this works, consider what would happen if the pivot were a "6". The orange cell to the right of it would then have to be a "3". If, however, the pivot were an "8", then the orange cell below it would be a "3". This means that whatever value the pivot takes, the cell in red cannot be a "3", so we can eliminate that candidate.

In many cases, you will find that an elimination you can make with a Y-wing can also be made with an Aligned Pair, but there are instances (such as the example above) where this is not true.

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