Difference between revisions of "2001 AIME I Problems/Problem 10"
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== Problem == | == Problem == | ||
| + | Let <math>S</math> be the set of points whose coordinates <math>x,</math> <math>y,</math> and <math>z</math> are integers that satisfy <math>0\le x\le2,</math> <math>0\le y\le3,</math> and <math>0\le z\le4.</math> Two distinct points are randomly chosen from <math>S.</math> The probability that the midpoint of the segment they determine also belongs to <math>S</math> is <math>m/n,</math> where <math>m</math> and <math>n</math> are relatively prime positive integers. Find <math>m + n.</math> | ||
== Solution == | == Solution == | ||
{{solution}} | {{solution}} | ||
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== See also == | == See also == | ||
| − | + | {{AIME box|year=2001|n=I|num-b=9|num-a=11}} | |
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Revision as of 23:24, 19 November 2007
Problem
Let 
be the set of points whose coordinates 
and 
are integers that satisfy 
and 
Two distinct points are randomly chosen from 
The probability that the midpoint of the segment they determine also belongs to is 
where 
and 
are relatively prime positive integers. Find 
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See also
| 2001 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 9 |
Followed by Problem 11 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
