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 perplexus dot info

 Dotty Right Triangle (Posted on 2005-06-09)

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?

 See The Solution Submitted by Richard Rating: 4.5000 (2 votes)

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 re: Solution | Comment 4 of 6 |
(In reply to Solution by Jer)

The formula

.5(x-1)(y-1)

for x=1, y=1, results in zero, not even counting the 1 for all the vertices together.

 Posted by Charlie on 2005-06-09 20:06:46

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