2019 Mock AMC 10B Problems/Problem 16
Revision as of 14:50, 5 November 2023 by Excruciating (talk | contribs) (Created page with "Solution by excruciating: For each of <math>a,b,c,d,e,f,g</math>, they all need to be at least <math>1</math>, so we have: <math>7 +a+b+c+d+e+f+g\leq n,</math> or <math>a+b+c+...")
Solution by excruciating:
For each of , they all need to be at least
, so we have:
or
without the "
need to be
restriction." So now it's stars and bars:
which simplifies to
which we can write as
.
Expanding, we get .
Because we only have terms,
is to be around
the highest divisor. Thus, we must have
as a divisor too.
is one too. We have left is
and
, to make
terms, so we have
, and
. Thus we have: $$ (Error compiling LaTeX. Unknown error_msg)(n-1)(n-2)(n-3)(n-4)(n-5)(n-6) =
$