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?

$3$

$4$

$5$

$8$

$9$

Answer: C

Concepts:pigeonhole principle

Difficulty rating: 720

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.

2010 AMC 10B Problem 3

Answer: C

Difficulty rating: 720

Solution:

Problem 3 in Other Years