"I'm fed up with this old tiled floor," said Prunella.
"I like it," said Dillwyn. "I like squares. And not only is each tile one foot square, but the whole floor is square—11 by 11 feet."
"Tiles are cold in winter. The cat doesn't like walking on them."
Dillwyn said nothing. They both knew that the cat came first.
"Let's get carpet," said Prunella. "We can lay it over the tiles."
"Can we afford that with the credit crunch?" asked Dillwyn.
"There's a sale on at the Cheapo Carpet Cash 'n' Carry."
When Prunella came back, Dillwyn was bemused to see her hauling five rolls of carpet from the boot of the car.
"Ends of rolls," Prunella said. "A bargain. I think they'll fit."
"You mean you didn't check?" said Dillwyn, annoyed.
"I didn't have time," said Prunella. "But the total area of all five pieces of carpet put together is 121 square feet, like the floor."
"It's not that simple," said Dillwyn. "Even with the same area, the shapes might not fit into a square without overlapping."
When Dillwyn tried to cover the floor, he found that all five pieces of carpet were rectangles, measuring a whole number of feet on both sides. Interestingly, all of the numbers from one to ten occurred once as a side of one of the rectangles. And, much to his surprise, the pieces of carpet fitted exactly over the tiles, without overlapping or needing to be cut further.
What was the arrangement of the pieces of carpet?
Prospect invites you to solve the puzzle and send us the solution. Correct answers will be entered into a draw. The winner will receive 100 Essential Things You Didn't Know You Didn't Know by John D Barrow (Bodley Head, £10). This book aims to explain life's perplexing questions by simple mathematics.
Send answers by post or to answer@prospect-magazine.co.uk by 5th December. The winner will be announced in our January issue.
