MacMahon’s Squares

This puzzle was invented by the combinatorialist P.A. MacMahon in 1921. He was thinking about a square that has been divided into four triangular regions by diagonals. He wondered how many different ways there are to colour the various regions, using three colours. He discovered that if rotations and reflections are regarded as the same colouring, there are exactly 24 possibilities. Find them all.

Now, a 6 x 4 rectangle contains 24 1 x 1 squares. Can you fit the 24 squares together to make such a rectangle, so that adjacent regions have the same colour, and the entire perimeter of the rectangle has the same colour?

(Thanks to Prof. Ian Stewart for putting this in his cabinet and I pulled it out of it !! :-))

Nalin Pithwa

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