2010 AMC 10B Problem 3

Problem 3 of 25EasierCombinatorics

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?

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Solution

To maximize the number of socks, we want to grab as many single socks as possible before getting a pair. There are

4

colors, which means that we can draw one sock of each color before drawing a pair. This means that it takes at least

4 + 1 = 5

socks to be drawn before a pair is guaranteed. Thus, C is the correct answer.

Tagged: pigeonhole principle