Difference between revisions of "1991 AIME Problems/Problem 13"

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== Solution ==
 
== Solution ==
{{solution}}
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Let <math>r</math> and <math>b</math> denote the number of red and blue socks, respectively. Also, let <math>t=r+b</math>.
  
 
== See also ==
 
== See also ==
 
{{AIME box|year=1991|num-b=12|num-a=14}}
 
{{AIME box|year=1991|num-b=12|num-a=14}}

Revision as of 17:51, 18 April 2007

Problem

A drawer contains a mixture of red socks and blue socks, at most 1991 in all. It so happens that, when two socks are selected randomly without replacement, there is a probability of exactly $\displaystyle \frac{1}{2}$ that both are red or both are blue. What is the largest possible number of red socks in the drawer that is consistent with this data?

Solution

Let $r$ and $b$ denote the number of red and blue socks, respectively. Also, let $t=r+b$.

See also

1991 AIME (ProblemsAnswer KeyResources)
Preceded by
Problem 12
Followed by
Problem 14
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
All AIME Problems and Solutions
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