Difference between revisions of "2002 AIME I Problems/Problem 14"
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== Problem == | == Problem == | ||
| + | A set <math>\mathcal{S}</math> of distinct positive integers has the following property: for every integer <math>x</math> in <math>\mathcal{S},</math> the arithmetic mean of the set of values obtained by deleting <math>x</math> from <math>\mathcal{S}</math> is an integer. Given that 1 belongs to <math>\mathcal{S}</math> and that 2002 is the largest element of <math>\mathcal{S},</math> what is the greatet number of elements that <math>\mathcal{S}</math> can have? | ||
== Solution == | == Solution == | ||
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== See also == | == See also == | ||
| − | + | {{AIME box|year=2002|n=I|num-b=13|num-a=15}} | |
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Revision as of 15:15, 25 November 2007
Problem
A set 
of distinct positive integers has the following property: for every integer 
in 
the arithmetic mean of the set of values obtained by deleting from is an integer. Given that 1 belongs to and that 2002 is the largest element of what is the greatet number of elements that can have?
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See also
| 2002 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 13 |
Followed by Problem 15 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
