Problem:
Which of the following numbers is a perfect square?
Answer Choices:
A. 214!15!​
B. 215!16!​
C. 216!17!​
D. 217!18!​
E. 218!19!​
Solution:
Note that 2n!(n+1)!​=(n!)2⋅2n+1​, which is a perfect square if and only if 2n+1​ is a perfect square. Only choice D​ satisfies this condition.
The problems on this page are the property of the MAA's American Mathematics Competitions