Belt Loop - Futility Closet

Belt Loop

belt loop puzzle

A puzzle by Harry Langman:

A thin belt is stretched around three pulleys, each of which is 2 feet in diameter. The distances between the centers of the pulleys are 6 feet, 9 feet, and 13 feet. How long is the belt?

	Select Click for Answer
This has a surprisingly neat solution. The belt can be divided into straight and curved sections. The lengths of the straight sections are the same as the distances between the centers of the pulleys, and the curved sections total one complete circumference. So the total length is 6 + 9 + 13 + 6.2832 = 34.2832 feet. From Scripta Mathematica, March 1949.

December 23, 2012February 8, 2013 | Puzzles