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The Cashier's Problem Puzzle - Solution
The Puzzle:
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.
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