XY-Chain

The XY-Chain technique uses a chain of cells that have exactly two candidates. In the sudoku diagram below, the XY string is made up of R1C1, R8C1, R8C6 and R2C6 cells. If the R1C1 cell is set to 6, then the R8C1 cell will be set to 1, the R8C6 cell will be set to 7 and the R2C6 cell will be set to 9. On the other hand, if the R2C6 cell is set to 7, then the R8C6 cell will be set to 1, and the R8C1 cell will be set to 6 and the R1C1 cell will be set 9. Therefore, it follows that either the R1C1 cell or the R2C6 cell will have the digit 9. Thus, from the cells that simultaneously "see" the R1C1 and R2C6 cells we can remove the digit 9, i.e. from the R1C4 and R2C2 cells. Thanks to this elimination, only the digit 7 can be placed in the R1C4 cell.