By drawing a triangle on a sphere, the surface is divided into smaller areas. How many areas that are not further subdivided can you get? For this puzzle, each side of the triangle must be part of a great circle of the sphere and span less than 360 degrees of the sphere.
If that is too easy: How many areas can you get by drawing two triangles on a sphere? Can you prove that your solution is optimal?
I (think I) have solved these, but I haven't proved that the two triangle solution is optimal. I posted this problem to rec.puzzles on the 2nd of january 2002.
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