How do you make up 55 cents Without one being a 5c coin?

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The answer will depend on the country in question. In Europe, for example, you can use 20 + 20 + 10 + 2 + 2 + 1.
A half dollar and a nickel. One of them isn't a nickel, the other one is.
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Is it possible to make 55 cents using two coins without using nickels?

The answer to the question as written is no. The smallest numberwould be 4 coins: 1 quarter, 4 dimes However the question isn't correctly written. It's a actually brainteaser
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How to make 55 cents with 12 coins?

You will make 55 cents with 12 coins by using 5 pennies, 3 dimes,and 4 nickels.5 pennies, 3 dimes, and 4 nickels will make 55 cents with 12 coins.