## Gem 17: The Bank Teller's Predicament Puzzle

The Bank Teller's Predicament PuzzleIt was a strange lapse on the part of the bank teller. Evidently he

misread the check, for he handed out the amount of the dollars

in cents, and the amount of the cents in dollars. When the error

was pointed out to him he became flustered, made an absurd

arithmetical mistake, and handed out a dollar, a dime, and a cent

more. But the customer declared that he was still short of his due.

The teller pulled himself together, doubled the total amount he

had already given to the customer, and so precisely settled the

transaction to the latter’s satisfaction.

What was the amount of the check? Note: Here we must solve an equation where we require positive

integer solutions. This requirement places the problem in a large

and famous Class of problems known as Diophantine equations

named for third century Greek mathematician Diophantus. The

concept of zero was not invented yet in the third century.

Click here to see Moshe Shweiger's solution...

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