Difference between revisions of "2011 AIME I Problems/Problem 10"

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The probability of this happening is obviously lesser than <math>\frac{1}{2}</math>, but <math>\frac{93}{125}>\frac{1}{2}</math>.  Thus there is no such possible n-gon?
 
The probability of this happening is obviously lesser than <math>\frac{1}{2}</math>, but <math>\frac{93}{125}>\frac{1}{2}</math>.  Thus there is no such possible n-gon?
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== See also ==
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{{AIME box|year=2011|n=I|num-b=8|num-a=10}}

Revision as of 07:58, 29 March 2011

Problem

The probability that a set of three distinct vertices chosen at random from among the vertices of a regular n-gon determine an obtuse triangle is $\frac{93}{125}$ . Find the sum of all possible values of $n$.

Solution

This is not complete and may not be correct. triangle is obtuse $\Longleftrightarrow$ there exists $\frac{n}{2}$ consecutive points that are not chosen. (i.e. all 3 points of the triangle are on the same half of the n-gon.

The probability of this happening is obviously lesser than $\frac{1}{2}$, but $\frac{93}{125}>\frac{1}{2}$. Thus there is no such possible n-gon?

See also

2011 AIME I (ProblemsAnswer KeyResources)
Preceded by
Problem 8
Followed by
Problem 10
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
All AIME Problems and Solutions