A ship's carpenter had to turn a 9×16 plank into a 12-inch square, in two pieces
A ship's carpenter needed to plug a hole exactly 12 inches square, and the only wood to hand was a plank 9 inches by 16 inches, the same area, since 9×16 = 144 = 12². Cut it into only two pieces that fit together to form the square exactly, with no waste and no overlap. How?
Reveal the answer
Cut a staircase of 3 equal steps diagonally across the plank, then slide the smaller piece up and over by one step: the two pieces lock together into a perfect 12×12 square. The step-cut works in two pieces only when a rectangle's sides are consecutive square numbers, here 9 = 3² and 16 = 4², so the staircase has 3 steps and the resulting square is 3×4 = 12 on a side. Henry Dudeney published this as 'The Carpenter's Puzzle' in his 1926 collection, 'Modern Puzzles.'
— Henry Ernest Dudeney, Modern Puzzles — 1926, puzzle no. 115
Go deeper: get the book →