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How to prove that the only figure of which 3 copies can be used to tile a rectangle is a rectangle?

Is it possible to cut a rectangle into 5 equal (modulo rotations/reflections) non-rectangular pieces, which type of pieces?

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In the situation of using 3 copies, is it possible to simply define the rectangle as the following: All touching/adjacent sides of the combined rectangle must have a summed interior angle of either 90 (the corners of the larger rectangle), 180 (along the outside edge of the larger rectangle), or 360 (a point inside the larger rectangle). From this, can we deduce that the only shape that can accomplish this can ONLY have right angles, and thus must be a rectangle? – Nicolas Villanueva Jul 7 '11 at 12:44
By "rectangle", are you insisting non-square? Is the answer known in the case of a square? – Aubrey da Cunha Jul 8 '11 at 19:04
up vote 5 down vote accepted

There is a lot of information about this problem at

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Perhaps the person who voted this down could come up with a better answer? – Gerry Myerson Jul 8 '11 at 1:42
They probably did it just to annoy you. But seriously, forks... (+.8) for the link and (+.2) to offset the down-vote – The Chaz 2.0 Jul 8 '11 at 16:52

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