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 == | ||
| + | {{AIME box|year=2011|n=I|num-b=8|num-a=10}} | ||
Revision as of 06:58, 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 
. 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?
See also
| 2011 AIME I (Problems • Answer Key • Resources) | ||
| 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 | ||
