puzzle games

XY-Wings

<< The Swordfish technique <<


The XY-Wing technique


The XY-Wing or Y-Wing technique sounds similar but is different. It is based on a kind of forcing chain consisting of two links for candidates.

Let’s have a look on an example.
Here the marked cells are involved and assuming to enter a number will force the next to decide for a number too. We start assuming that cell 1,2 will get value 6. That would force cell 1,8 to take number 9 (because it then cant take 6). That again would force cell 2,9 to take value 5 (because it then cant take 9). Finally that would mean for our target cell 2,1 that it can not take 5 (because it is on the same row).

Ok, when going back to start we could also assume that cell 1,2 takes 5 (instead of 6). Ether way that would also force cell 2,1 to not take 5.


sudoku XY-wing

In conclusion we see it doesn’t matter whether cell 1,2 takes 5 or 6. Ether way cell 2,1 cant take 5 and we can:

- remove candidate 5 from cell 2,1


>> The XY-Chain technique >>

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