**Similar Hole Problems**

In 1974 Jean Meeus proposed the problem 'to construct an area containing an interior hole of the same shape' for sets of polyominoes and polyiamonds. If the total area of the set of pieces is A then we require to find integers x, y and n such that A = n(x²-y²) in which case we have a pattern of area nx² with a similar hole of area ny². It is also possible to look for multiple congruent figures with similar holes.

The links below lead to various sections of the site where solutions to this problem may be found.

PolyominoesPolyiamondsPentominoes One-sided hexiamonds One-sided pentominoes Heptiamonds Hexominoes Enneiamonds One-sided Hexominoes

PolycubesPolyaboloesPentaboloes One-sided Pentaboloes

PolyaresTetrares One-sided triares

Other PolyformsDomsliced Pentominoes One-sided strip hexominoes One-sided domsliced tetrominoes One-sided tridominoes One-sided 2-4 cellominoes Domsliced 3½-ominoes