Problem 184

Triangles containing the origin.

Consider the set `I _{r}` of points (

For a radius of 2, `I`_{2} contains the nine points
(0,0), (1,0), (1,1), (0,1), (-1,1), (-1,0), (-1,-1), (0,-1) and (1,-1).
There are eight triangles having all three vertices in `I`_{2} which contain the origin in the interior. Two of them are shown below, the others are obtained from these by rotation.

For a radius of 3, there are 360 triangles containing the origin in the interior and having all vertices in `I`_{3} and for `I`_{5} the number is 10600.

How many triangles are there containing the origin in the interior and having all three vertices in `I`_{105}?

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These problems are part of
Project Euler
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