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.
Feel free to discuss the solutions in the comment section.

# How many different strings of length 9 are there which contain 3 'a's, 3 'b's and 3 'c's.
# (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).
# (agora scholarships [4]) 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.