2009 AIME I Problems/Problem 14
Problem
For , define
, where
. If
and
, find the minimum possible value for
.
Solution
Because the order of the s doesn't matter, we simply need to find the number of
s
s
s and
s that minimize
. So let
and
represent the number of
s,
s,
s, and
s respectively. Then we can write three equations based on these variables. Since there are a total of
s, we know that
. We also know that
and
.
See also
2009 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
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All AIME Problems and Solutions |