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Difference between revisions of "2010 AMC 10B Problems/Problem 3"
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<math>
 
<math>
−
\mathrm{(A)}\ 3
+
\textbf{(A)}\ 3
 
\qquad
 
\qquad
−
\mathrm{(B)}\ 4
+
\textbf{(B)}\ 4
 
\qquad
 
\qquad
−
\mathrm{(C)}\ 5
+
\textbf{(C)}\ 5
 
\qquad
 
\qquad
−
\mathrm{(D)}\ 8
+
\textbf{(D)}\ 8
 
\qquad
 
\qquad
−
\mathrm{(E)}\ 9
+
\textbf{(E)}\ 9
 
</math>
 
</math>
  
 
== Solution ==
 
== 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{\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 16:59, 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?

$\textbf{(A)}\ 3 \qquad \textbf{(B)}\ 4 \qquad \textbf{(C)}\ 5 \qquad \textbf{(D)}\ 8 \qquad \textbf{(E)}\ 9$

Solution

After you draw $4$ socks, you can have one of each color, so (according to the pigeonhole principle), if you pull $\boxed{\textbf{(C)}\ 5}$ 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

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

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