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CEMC Gauss (Grade 8), 2011

Combinatorics Difficulty 3.0 AMC 10/12 Find the answer Canada

A collection of coins includes only pennies ( $1\text{¢}$ ), nickels ( $5\text{¢}$ ), dimes ( $10\text{¢}$ ) and quarters ( $25\text{¢}$ ). Using the coins in this collection, it is possible to create any amount of money less than one dollar ( $100\text{¢}$ ). What is the smallest possible number of coins in the collection?

(A) $10$ (B) $7$ (C) $11$ (D) $13$ (E) $12$

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