Problem:
At a competition with players, the number of players given elite status is equal to
Suppose that 19 players are given elite status. What is the sum of the two smallest possible values of ?
Note: is the greatest integer less than or equal to .
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The given conditions imply that and . Because is a positive integer, so is ; thus for some integer . It follows that and the two smallest values of are and , whose sum is .
Note: This formula for the number of elite status players provides a method used to determine the number of first-round byes in a single-elimination tournament.
The problems on this page are the property of the MAA's American Mathematics Competitions