Solving Techniques 13
XY-Chains

As shown below, there is a chain from the red cell’s [12] going to [23] [34] [14].

If [R3C2] is [1], the result is as follows.

If [R3C2] is [2], the result is as follows.

In either solution, 1 would not be in the overlapping area X.

This situation is known as an XY-chain.

XY-Chains 2

This is another pattern. As seen below, [23], [34], [14] is linked to the red cell [12].

If [R2C3] is [1], the result is as follows.

If [R2C3] is [2], the result is as follows.

In either position of 1, 1 can’t be entered in the overlapping area X.

These are rarely seen in actual problems. However, when you are solving a very advanced problem and get stuck, it is a good technique to remember.

We made a slightly different pattern. As shown below, the red [12] is linked to [23][34][34][45][15].

If [R2C3] is [1], the result is as follows.

If [R2C3] is [2], the result is as follows.

In either position of 1, there can’t be 1’s in the overlapping area X.