Maths Toys

Dudeney's Dissection

Henry Ernest Dudeney (1857-1930) was one of the greatest 19th century puzzlers, and in 1902 he posed a problem in his column in the newspaper The Weekly Dispatch.

The problem was 'starting with an equilateral triangle, what is the minimum number of pieces you can cut the triangle into, so that the pieces can be rearranged into a square?'

Many readers wrote in, giving a solution that involved 5 pieces. However one person, a Mr C McElroy of Manchester, sent in a solution involving only 4 pieces. Interestingly, it appears that there is some doubt as to whether Henry Dudeney actually knew of the 4 piece solution at the time he wrote his original newspaper column! He subsequently included this problem in a book published in 1907 called The Canterbury Puzzles, where he called it the haberdasher's problem. However it is more commonly known as Dudeney's Dissection.

We are very proud to be able to offer this beautiful physical version of Dudeney's Dissection, where the 4 pieces are hinged, so that you can transform one shape into the other. Created specially for us by a local engineering company, the 4 pieces are made on a CNC mill from solid aluminium, which is subsequently anodized. The equilateral triangle has sides of length 15cm, while the square has sides of length 10cm. It is 9mm thick, and weighs about 250g.