Difference between revisions of "2010 AMC 10B Problems/Problem 3"
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| − | 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{\ | + | == 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> | ||
| + | \textbf{(A)}\ 3 | ||
| + | \qquad | ||
| + | \textbf{(B)}\ 4 | ||
| + | \qquad | ||
| + | \textbf{(C)}\ 5 | ||
| + | \qquad | ||
| + | \textbf{(D)}\ 8 | ||
| + | \qquad | ||
| + | \textbf{(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{\textbf{(C)}\ 5}</math> then you will be guaranteed a matching pair. | ||
| + | |||
| + | ==Video Solution== | ||
| + | https://youtu.be/wAnVjpaNFIA | ||
| + | |||
| + | -Education, the Study of Everything | ||
| + | |||
| + | ==Video Solution== | ||
| + | https://youtu.be/uAc9VHtRRPg?t=130 | ||
| + | |||
| + | ~IceMatrix | ||
| + | |||
| + | ==See Also== | ||
| + | {{AMC10 box|year=2010|ab=B|num-b=2|num-a=4}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 15:59, 1 August 2022
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.
Video Solution
-Education, the Study of Everything
Video Solution
https://youtu.be/uAc9VHtRRPg?t=130
~IceMatrix
See Also
| 2010 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 2 |
Followed by Problem 4 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
