Problem:
A game uses a deck of different cards, where is an integer and . The number of possible sets of cards that can be drawn from the deck is times the number of possible sets of cards that can be drawn. Find .
Solution:
The conditions of the problem imply that , so . . Then !, so . Thus is a solution, and because is increasing for , conclude that is the only solution for .
The problems on this page are the property of the MAA's American Mathematics Competitions