Problem short lists are often used in math camps to cover some subject by going through a bunch of tricks. I've thought of doing the same for programming contests. My first list is related to combinatorics.

Short lists are often used in math camps to cover some subject by going through a bunch of problems. I've thought of doing the same for programming contests. My first list is related to combinatorics.

1. (olimpiada online 2001) Given n points on a circle. Join all possible n(n-1)/2 cords. What’s the maximum number of triangles one can see. Example: With n = 4 there are 8 triangles (4 with 3 of the 4 circle points and 4 with 2 circle points and 1 the intersection of the diagonal).
2. (agora scholarships) What is the maximum number of regions the plane can be split into by n lines. (Same problem for n circles, n planes, n spheres) Example: For n = 4 we can get 7 regions.