A

missing dollar problem

Three people have dined at a restaurant and received a total bill for \$30. They agree to split the amount equally and pay \$10 each. The waiter hands the bill and the \$30 to the manager, who realizes there's been a mistake and the correct charge should be only \$25. He gives the waiter five \$1 bills to return to the customers, with the restaurant's apologies. However, the waiter is dishonest. He pockets \$2, and gives back only \$3 to the customers. So, each of the three customers has paid \$9 and the waiter has stolen \$2 making a total of \$29. But the original bill was for \$30. Where has the missing dollar gone? (See solution below.)

A version of this problem first appeared in R. M. Abraham's Diversions and Pastimes in 1933.1 See also nine rooms paradox.

Solution

There is no missing dollar (of course!). Adding \$27 and \$2 (to get \$29) is a bogus operation. They paid \$27, \$2 went to the dishonest waiter, and \$25 went to the restaurant. You have to subtract \$27 minus \$2 to get \$25. There never was a \$29; it's a phony calculation designed to confuse the unwary.

Reference

1. Abraham, R. M. Diversions and Pastimes. London: Constable & Co., 1933. Reprinted , 1964.