XY-Cycle

An XY-Cycle or XY-Ring is a Continuous Nice Loop limited to cells with only 2 candidates each. These do not need to be candidates for the same 2 digits as in Remote Pairs, but 2 adjacent cells in the loop must share one of the candidates for the loop to be correct.

The cycles are similar to XY-Chains.

rncx(a,b) - rncy(b,c) - rmcy(c,d) - rmcx(d,a) - rncx

In Nice Loop notation, this would be:

-[rncx]-b-[rncy]-c-[rmcy]-d-[rmcx]-a

This XY-Cycle eliminates the following candidates:

1. All other candidates for digit b in row n
2. All other candidates for digit c in column y
3. All other candidates for digit d in row m
4. All other candidates for digit a in column x

The XY-Cycle does not need to have an even number of cells, as long as the last cell can see the first and shares a candidate with it.