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Johnders
 Expert Boarder
Posts: 86 
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Hi,
This is probably a well known puzzle, i think i've seen it before, but forgot the solution. Can you cover an M (as in a 4x4 grid with the top quarter triangle cut out) with 4 congruent shapes?
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Johnders
Expert Boarder
Posts: 86
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I've seen a reference to this in an old puzzle book. The Henry Dudeney states that it is impossible to dissect the mitre (his term for the square with a quarter triangle removed) into four congruent pieces. It is possible to cover the mitre with four congruent shapes if you allow bits to stick out and/or overlap. It's trivial to produce a covering where the overhangs and overlaps are large, but it is possible to make them close to zero.
Spoiler...
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. . / / / / A / B / +
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