A Problem on Hinged Dissections with Colours

Abstract.

We examine the following problem. Given a square C we want a hinged dissection of C into congruent squares and a colouring of the edges of these smaller squares with k colours such that we can transform the original square into another with its perimeter coloured with colour i, for all i in We have the restriction that the moves have to be realizable in the plane, so when swinging the pieces no overlappings are allowed. We show a solution for k colours that uses p ² pieces, with p an even number and at least this by using a necklace made of the p ² pieces and an ingenious way to wrap it into a square.