## 25 Cent Coin Combinations

**Math Teaser**

How any combinations of US coins are there that add up to 25 cents?

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There are 12 possible coin combinations of the penny, nickel, dime, and quarter that add up to 25 cents. These coin combinations are easier to count if you realize that you will not be able to use the penny in any combination that is not a factor of 5. This is because there is no other way to get the value of the next smallest coin, the nickel.

p = penny, n = nickel, d = dime, q = quarter

1. 25p

2. 20p + 1n

3. 15p + 2n

4. 10p + 3n

5. 5p + 4n

6. 1d + 15p

7. 1d + 10p + 1n

8. 1d + 5p + 2n

9. 1d + 3n

10. 2d + 5p

11. 2d + 1n

12. 1q

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