Difference between revisions of "2010 AMC 10B Problems/Problem 3"

m (see also, box)
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<math>
 
<math>
\mathrm{(A)}\ 3
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\textbf{(A)}\ 3
 
\qquad
 
\qquad
\mathrm{(B)}\ 4
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\textbf{(B)}\ 4
 
\qquad
 
\qquad
\mathrm{(C)}\ 5
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\textbf{(C)}\ 5
 
\qquad
 
\qquad
\mathrm{(D)}\ 8
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\textbf{(D)}\ 8
 
\qquad
 
\qquad
\mathrm{(E)}\ 9
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\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.
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==See Also==
 +
{{AMC10 box|year=2010|ab=B|num-b=2|num-a=4}}

Revision as of 23:51, 25 November 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?

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

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.

See Also

2010 AMC 10B (ProblemsAnswer KeyResources)
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