2002 AIME I Problems/Problem 14
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
Let the sum of the integers in be
, and let the size of
be
. We are given that
and
are integers. Thus
is a multiple of
. Now
, Template:Incomplete
See also
2002 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
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