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Assuming only the use of currently produced US Coins, there are 9 combinations: 21 pennies 16 pennies, 1 nickel 11 pennies, 2 nickels 11 pennies, 1 dime 6 pennies, 3 nickels 6 pennies, 1 nickel, 1 dime 1 penny, 4 nickels 1 penny, 2 nickels, 1 dime 1 penny, 2 dimes If you allowed the use of obsolete denominations (half cents, 2 cent pieces and 3 cent pieces) the number would be higher, and if you further differentiated between different coins of the same denomination (e.g., large cents vs small cents, three cent silver vs 3 cent nickels, half dimes vs nickels, etc.) the number would be higher still.

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