2010 AMC 10B Problem 3

Question

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?

3

4

5

8

9

Use the worst case before a pair appears

You can draw one sock of each of the four colors first

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.

Problem 3 in other years