How many coins equal one dollar?


Quick Answer

There are 293 different coin combinations that equal one American dollar, according to Frank Morgan of the Mathematical Association of America. A list of all 293 ways are listed at the bottom of Morgan's page, as he credits Raymond Hettinger for making a list of all possibilities. The most coins that make $1 is 100 pennies, while the fewest is a $1 coin.

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Full Answer

Several combinations include two half-dollars, four quarters, 10 dimes and 20 nickels. A combination using all five coins includes one half-dollar, one quarter, one dime, two nickels and five pennies. All five types of coins can also make $1 with one half-dollar, one quarter, one dime, one nickel and 10 pennies. These are the only two ways to make change for $1 using five different coins, according to Morgan's list.

There are two ways to make $1 using only two types of coins with 19 pieces, either with 10 pennies and nine dime or 18 nickels and one dime. Math instructor Jim Wilson of the University of Georgia explains a question regarding how many ways can 19 coins equal $1. There are three ways using three coins to make change for $1 with 19 coins, and four ways using four coins. It is impossible to make change for $1 using all five types of coins to equal 19 coins total.

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