A carpenter needs a square piece of wood measuring 30 inches by 30 inches. Unfortunately the only suitable piece in his workshop is a rectangle 25 inches by 36 inches.
How does he saw the wood into two pieces, such that the two pieces can be glued together to make the square he wants?
Alex Bellos, author of the puzzle book “Can You Solve My Problems,” wrote this satisfying math puzzle.
The kicker here is that you can only cut the rectangle of wood into two pieces, not more.
Here is his answer and explanation:
The cut you need to make is not a straight one, because you need to take from one side to add to the other in an uneven way.
And then once you’ve cut the pieces, you flip one of them over in order to assemble the square: