1. How many diagonals does a convex 12-gon have?
2. Divide a square into rectangles using segments of lines so that no two rectangles together would form a bigger rectangle.
3. How many 6-digit numbers such that all their digits are odd are there?
4. Suppose you have a square with side of length 1. Is it possible to place inside it a number of disjoint circles the sum of radii of which is more than 100?
5. Serge had 7 potatoes, Paul had 5 and Nick none. They boiled all 12 and shared equally. Nick gave 12 cents to Serge and Paul as his share. How should Serge and Paul divide this amount?
