Problem:
How many triangles with positive area have all their vertices at points in the coordinate plane, where and are integers between and , inclusive?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
There are ways to choose three vertices, but in some cases they will fall on a line. There are that fall on a horizontal line, another that fall on a vertical line, that fall on a line with slope , another that fall on a line with slope , and each that fall on lines with slopes , and . Therefore the answer is .
The problems on this page are the property of the MAA's American Mathematics Competitions