2010 AMC 10B Problems/Problem 3: Difference between revisions
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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 | ||
These problems are copyrighted © by the Mathematical Association of America. 
