An XY-Chain is created by following a chain of cells with exactly two candidates. Going from one cell to the next in the chain requires that the 2 connected cells must share a group and a candidate. The chain ends when the last cell shares a candidate with the first cell AND is in the same group as the first cell OR or their peers share at least 6 cells.
If the start and end of the chain are in the same group and share a candidate, then one of the 2 cells must take the value of that candidate. Therefore the intersection of their peers cannot hold that candidate, and therefore can be removed.
XY-Chain for digit 7 with start and end cells in row 1.
That means that candidates 7 can be removed from row 1 if they are not in the chain.
XY-Chain for digit 9 with start and end cell in column 5.
That means that candidates 9 can be removed from column 5 if they are not in the chain.
XY-Chain for digit 9 with start and end cells in box 2.
That means that candidates 9 can be removed from box 2 if they are not in the chain.
XY-Chain for digit 9 with start and end cells having at least 6 overlapping peers.
That means that candidates 9 can be removed from the intersection of the peers of the start and end cells, cell [1,9].
This algorithm is currently not easy to do without paper and pencil. You can take a picture of the puzzle and print it, then follow the instructions below.
If you tap on the following links on an iOS device which has the Sudoku Tutor app installed, it will launch the app and open the practice puzzle. Tap hint once the puzzle is open to see the strategy in action.Sample Puzzle 1 Sample Puzzle 2 Sample Puzzle 3 Sample Puzzle 4