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.

Polyominoes Polyiamonds
Pentominoes One-sided hexiamonds
One-sided pentominoes Heptiamonds
Hexominoes Enneiamonds
One-sided Hexominoes  

 

Polycubes Polyaboloes
  Pentaboloes
  One-sided Pentaboloes
   

 

Polyares  
Tetrares  
One-sided triares  

 

Other Polyforms
Domsliced Pentominoes One-sided strip hexominoes
One-sided domsliced tetrominoes One-sided tridominoes
One-sided 2-4 cellominoes Domsliced 3-ominoes