Difference between revisions of "2011 AIME I Problems/Problem 10"
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== Solution == | == Solution == | ||
| + | This is not complete and may not be correct. | ||
| + | triangle is obtuse <math>\Longleftrightarrow</math> there exists <math>\frac{n}{2}</math> 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 <math>\frac{1}{2}</math>, but <math>\frac{93}{125}>\frac{1}{2}</math>. Thus there is no such possible n-gon? | ||
Revision as of 06:57, 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 
. Find the sum of all possible values of 
.
Solution
This is not complete and may not be correct.
triangle is obtuse 
there exists 
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 
, but 
. Thus there is no such possible n-gon?
