Brain Teasers
Quarter Lineup
120 quarters are lined up on a table. Every second coin is replaced with a dime. Then, every third coin is replaced with a nickel. Finally, every fourth coin is replaced with a penny.
How much are the coins remaining on the table worth?
How much are the coins remaining on the table worth?
Hint
Consider the value of twelve coins after the replacements.Answer
The value of the remaining coins is $13.80.Since the least common multiple of 2, 3, and 4 is 12, the value of each consecutive set of 12 coins will have the same value as the other sets after the replacements.
Here is a diagram of the replacements for 12 coins:
QQQQQQQQQQQQ
QDQDQDQDQDQD
QDNDQNQDNDQN
QDNPQNQPNDQP
4 quarters = $1
2 dimes = $.20
3 nickels = $.15
3 pennies = $.03
12 coins = $1.38
120 coins = $13.80
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