2016 AMC 10A Problems/Problem 20
For some particular value of , when
is expanded and like terms are combined, the resulting expression contains exactly
terms that include all four variables
and
, each to some positive power. What is
?
Solution
All the desired terms are in the form , where
(the
part is necessary to make stars and bars work better.)
Since
,
,
, and
must be at least
, let
,
,
, and
, so
. Now, we use stars and bars to see that there are
solutions to this equation. We have
, so
.