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. 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?
4. Present 12 as a sum of positive integers such that their product is maximal.
5. If you multiply all integers from 1 to 100 (1 and 100 included), you will get a large number ending in a lot of zeros. Exactly how many zeros will be at the end of this number?
6. Paint a plane with nine colors so that any two points at the distance of 1 from each other would be of different colors.
7. Place 7 points on the plane so that among any three of them at least two are at the distance of 1 from each other.
