Is it possible to select 100 points on a circle so that there are exactly 1000 right triangles with the vertices at selected points?
Sergey Dvoryaninov
The only time three points on a circle form a right-angled triangle is when two of them form a diameter (which is the hypotenuse). Since there are 100 points, one diameter will form 98 right angled triangles. Hence the number of triangles formed from n diameters is 98n. However 1000 is not divisible by 98, so it is impossible to form exactly 1000 right angled triangles with 100 points.