History of MacMahon Squares

Percy Alexander MacMahon (1854–1929)

Major Percy Alexander MacMahon was a British mathematician and military officer known for his extensive work in combinatorics, partition theory, and recreational mathematics. He served in the Royal Artillery before dedicating his career to mathematics.

The 1921 Discovery

In 1921, MacMahon published his work on coloured square tiles in his book "New Mathematical Pastimes". He explored all possible ways to colour the four triangular regions of a square using 3 colours, discovering that exactly 24 unique tiles could be created.

The Puzzle Challenge

MacMahon proved that these 24 tiles can be arranged into a 6×4 rectangle where all internal adjacent edges match in colour. He further showed that the border of the rectangle could be made a single uniform colour — adding an extra layer of challenge to an already formidable puzzle.

Legacy

Over a century later, MacMahon's puzzle continues to fascinate mathematicians and puzzle enthusiasts. Its blend of combinatorial complexity and spatial reasoning makes it a timeless challenge — one that feels like a perfect fusion of Sudoku and a Rubik's Cube.