Problem:
Several students are competing in a series of three races. A student earns points for winning a race, point.s for finishing second and point for finishing third. There are no ties. What is the smallest number of points that a student must earn in the three races to be guaranteed of earning more points than any other student?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
If one student earns points, no other student can earn more than points.
If one student earns points, no other student can earn more than points.
However, if one student earns or points, some other student can earn or points.
Thus points is the smallest number of points a student must earn to be guaranteed of earning more points than any other student.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions