Difference between revisions of "2010 AMC 10B Problems/Problem 3"
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| + | == 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? | ||
| + | |||
| + | <math> | ||
| + | \mathrm{(A)}\ 3 | ||
| + | \qquad | ||
| + | \mathrm{(B)}\ 4 | ||
| + | \qquad | ||
| + | \mathrm{(C)}\ 5 | ||
| + | \qquad | ||
| + | \mathrm{(D)}\ 8 | ||
| + | \qquad | ||
| + | \mathrm{(E)}\ 9 | ||
| + | </math> | ||
| + | |||
| + | == Solution == | ||
After you draw <math>4</math> socks, you can have one of each color, so (according to the pigeonhole principle), if you pull <math>\boxed{\mathrm{(C)} 5}</math> then you will be guaranteed a matching pair. | After you draw <math>4</math> socks, you can have one of each color, so (according to the pigeonhole principle), if you pull <math>\boxed{\mathrm{(C)} 5}</math> then you will be guaranteed a matching pair. | ||
Revision as of 19:09, 22 January 2011
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?
Solution
After you draw 
socks, you can have one of each color, so (according to the pigeonhole principle), if you pull 
then you will be guaranteed a matching pair.
