Sudoku Solving Techniques

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Y-Wing Chains Strategy

Y-Wing Chains Strategy

Y-Wings have a ‘hinge’ and two pincers. The pincers allow us to target certain cells but the hinge is not involved in the elimination. It only holds the pincers together in a vice of logic. There is no reason why the hinge has to be a single cell. An odd number of identical pairs linked together will also work. In fact a Y-Wing is just a Y-Wing Chain of length 1.

Here is an excellent example (with all solutions bar 8 removed for clarity). The pincers are in the dark shade and the hinge chain is in the light shade.

Fig. 22.1

In a normal Y-Wing we’d expect a chain like this:
                        1/8 -> 1/3 -> 3/8
In a chain we’re extending the hinge, so the above example is:
                        1/8 -> 1/3 -> 1/3 -> 1/3 -> 3/8
Which ever end is 8 the chain will solve to either
                        8 -> 1 -> 3 -> 1 -> 3
            or            1 <- 3 <- 1 <- 3 <- 8

There are two cells at A3 and B7 which can be seen by the pincers B2 and A8, so they can have their 8’s removed.

Here is a more sophisticated example: Ignore the circled cells for now. The pincers are the dark shaded cells. Our 5 to be eliminated is at B6.

Naked Pairs
Fig. 22.2

Y-Wing Chain Exercise

The above example has two cells marked with a circle. They are pincer parts of two other Y-Wing Chains. Find these two other Y-Wing Chains and the candidates that are eliminated. No additional candidate elimination is necessary from this point to identify the solutions.

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