2010 AIME I Problems/Problem 10
Problem
Let be the number of ways to write
in the form
, where the
's are integers, and
. An example of such a representation is
. Find
.
Solution
If we choose and
such that
there is a unique choice of
and
that makes the equality hold. So
is just the number of combinations of
and
we can pick. If
or
we can let
be anything from
to
. If
then
or
. Thus
.
See Also
2010 AIME I (Problems • Answer Key • Resources) | ||
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Followed by Problem 11 | |
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