The item I had just bought cost 29 cents. I gave the cashier a dollar bill, and she gave me two quarters, two dimes, and a penny in change. She could just as well have given me seven dimes and a penny or some other combination of coins adding up to 71 cents, but there’s no way she could have made change with fewer than five coins.
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Most businesses in the United States make change using just four different types of coins: 1 cent (penny), 5 cents (nickel), 10 cents (dime), and 25 cents (quarter). This distribution of coinage suggests an interesting question: Is it the most efficient way to make change? In other words, is this the optimal choice of coin values for minimizing the number of coins required to handle typical transactions?