The new play needed a raised platform in the middle of the stage. The director gave the carpenter two numbers and nothing else. The platform had to cover forty square metres of floor, because that was how much space the dancers needed. And it had to have a border of twenty-six metres of wooden edging, because that was exactly how much edging was left in the store.
"Give me the length and the width," the carpenter said. The director did not know them. She only knew the two numbers she had been given.
The carpenter sat down with a pencil. Twenty-six metres of edging went all the way round, so one length plus one width came to thirteen metres — half of the border. And length times width came to forty. He needed two numbers that added to thirteen and multiplied to forty.
He wrote the pairs in order, the way he always did. One and forty: too far apart. Two and twenty: still too far. Four and ten: their sum was fourteen, very close. Five and eight: their sum was thirteen. That was it.
He cut the platform five metres by eight metres. When the edging went on, the last piece ran out at the corner where he had started, with nothing to spare.
The director was amazed. The carpenter was not. "You did not give me a puzzle," he said. "You gave me a sum and a product. There is only one pair that fits, and it takes four lines to find."