Math Playground
Activities

Counting Coins

Sort, stack, total — coins are arithmetic you can stack.

Sort coins by value. Stack them. Count by tens, by fives. Total your handful. Money is arithmetic you can hold.

Try this
67
fewest US coins = greedy: quarters, then dimes, nickels, pennies = 2×25¢ + 1×10¢ + 1×5¢ + 2×1¢ (6 coins)

The biggest-coin-first trick

To make an amount with the fewest US coins, keep taking the largest coin that still fits: quarters, then dimes, then nickels, then pennies. That 'greedy' rule happens to give the true minimum for US coins — drag the slider and count.

Your turn

What's the fewest US coins that make 41¢?

Watch out

Greedy is not always optimal for every coin system. With a hypothetical 1-, 3-, 4-cent set, making 6¢ greedily gives 4+1+1 (3 coins) but 3+3 is just 2. US coins are designed so greedy always wins.

Try it

3 quarters, 4 dimes, 7 nickels, 12 pennies

75 + 40 + 35 + 12 = $1.62.

Always count the biggest coins first. Easier on the brain — and that's how cashiers do it.