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Dotty Right Triangle (Posted on 2005-06-09) Difficulty: 3 of 5

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)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re(2): SolutionRichard2005-06-14 22:05:26
re(2): Half solution -- the second halfBractals2005-06-09 21:17:31
re: SolutionCharlie2005-06-09 20:06:46
Solutionre: Half solution -- the second halfCharlie2005-06-09 19:36:35
SolutionHalf solutionBractals2005-06-09 18:43:12
SolutionSolutionJer2005-06-09 17:42:57
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