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2010 AMC 10B Problems/Problem 3

Revision as of 19:09, 22 January 2011 by R31415 (talk | contribs)

Problem

A drawer contains red, green, blue, and white socks with at least 2 of each color. What is the minimum number of socks that must be pulled from the drawer to guarantee a matching pair?

$\mathrm{(A)}\ 3 \qquad \mathrm{(B)}\ 4 \qquad \mathrm{(C)}\ 5 \qquad \mathrm{(D)}\ 8 \qquad \mathrm{(E)}\ 9$

Solution

After you draw $4$ socks, you can have one of each color, so (according to the pigeonhole principle), if you pull $\boxed{\mathrm{(C)} 5}$ then you will be guaranteed a matching pair.

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