A "dot" (commonly also called a "lattice point") is a point with integer coordinates.

In the plane, what is the total number of dots inside or on the boundary of the triangle with vertices (0,0), (x,0), (x,y) where x and y are positive integers?

In the event that it is not utterly obvious from the form of your answer that a whole number is being specified, give an independent argument to show this.

What total do you get if you count the three vertex dots together as just half a dot and any other boundary dots as half a dot each?

You are correct that Jer's answer to the last part is incorrect, but your answer to the last part is also incorrect. You misread the last sentence -- the three vertices are to be counted together as 1/2, not 1.

Posted by Richard on 2005-06-14 22:05:26