University of South Carolina High School Math Contest/1993 Exam/Problem 20
Problem
Let be the 63 nonempty subsets of
. For each of these sets
, let
denote the product of all the elements in
. Then what is the value of
?
![$\mathrm{(A) \ }5003 \qquad \mathrm{(B) \ }5012 \qquad \mathrm{(C) \ }5039 \qquad \mathrm{(D) \ }5057 \qquad \mathrm{(E) \ }5093$](http://latex.artofproblemsolving.com/4/b/b/4bb3af1414663cc5a3d37b49c5ccc4c0bb56273b.png)
Solution
We have (The
since we have one less set). This is
.
If you don't understand what the above means, just think about the simplifying of the brackets. Open the brackets and you should notice why it is correct.