# Forbidden Double X-wing

by Marijn van Bijlert
(Oosterbeek, Netherlands)

When you see in two 3*3 squares a pattern that looks almost a double X-wing, you are certain a double X-wing there is forbidden because then there would not be a single solution to the puzzle.

See diagram.
Three squares of the rectangle have only a and b as possible solutions, the fourth one has a, b and c (c may have multiple values)

Suppose you can prove c is not a solution and you remove it. In that case you have a double X-wing (or 4 naked pairs in a rectangle). This is forbidden in this case as there will be no way to say which cells will be a and which b, so the puzzle has at least two solutions.
This means the solution must be c, so a and b may be removed from that square.

This trick does not work when the four cells are in four different 3*3 blocks, as a solution then can be inserted from another cell in a 3*3 block. The black a says the red ab of that block must be b.

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Note: The pattern on the left is similar to the Gordonian Rectangle. I wrote an article about it on this page: http://www.sudokuessentials.com/brain-teaser.html.

Thanks Marijn for the excellent submission.

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