The Cashier's Problem Puzzle - Solution

The Puzzle:

The Cashier's Problem
An old man goes to a bank with a check of $200 and asks the cashier "Give me some one-dollar bills, ten times as many twos and the balance in fives!".

What will the cashier do?

Our Solution:

The smallest amount of one-dollar and two-dollar bills the cashier may give to the old man is 1x1+10x2=21.

He must give the old man a multiple of 21 i.e. 21 or 42 or 63 or 84 or 105 or 126 or 147 or 168 or 187; without exceeding 200. Out of all these numbers only 105 can be added to a multiple of 5 to sum up to make 200 altogether.

So he must give the balance of 95 in five-dollar bills.

Therefore, the cashier must give 5 one-dollar bills, 50 two-dollar bills and 19 five-dollar bills.

Puzzle Author: Loyd, Sam

See this puzzle without solution
Discuss this puzzle at the Math is Fun Forum