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X - Wings

Warning! The X - 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 X - Wings pattern is a candidate elimination technique, meaning that it eliminates possible values from cells. The X - Wings technique states that if a digit can only occur in two places in two rows, both instances sharing the same column, then all other instances of that candidate can be eliminated from other positions on the two columns. The same argument applies if a digit can only occur on two rows in two columns. An example of this pattern is shown here:

The cells highlighted in orange form an X-wing, allowing "3" to be eliminated from the cells highlighted in red. The reason for this is that, the digit "3" can only occur in the same two columns on rows 3 and 8 (the orange cells). On each row, one of the cells must contain a "3", and they cannot share a column. So if the cell marked A contains a "3", then the cell D must contain one. If, on the other hand, the cell marked B contains a "3", then the cell C must contain one. In both of these cases, there cannot be a "3" in any of the cells marked in red.

Another example is shown here:

In this case, the digit "4" can be eliminated from both the cells highlighted in red, because the orange cells form an X-wing in "4"s. The X-wing technique is a special case of the Single Colouring technique, which is discussed later. Although it is rare to find a puzzle which requires an X-wing, they are often easy to spot, and therefore can be useful in both easy and advanced puzzles.

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