2. Equal partition: Given a set A of 40 real numbers, find out if there is any way to split A in two sets such that the sums of their elements are equal. (O(2^n))
3. Minimal vertex cover: Given a graph of n nodes (n <= 30), find out a set with the smallest number of vertices such that each edge in the  graph has at least one node inside the set. (O(3^n/2))
4. Square: You're given an array L which represents the sizes of n planks. You have to answer if there's any way to form a square using the planks without breaking them of overlapping them. (complexity O(4^n/2))

5. 8 puzzle: Solve 8 puzzle in at most 40 moves.

5. 8 puzzle: Solve 8 puzzle. (Each position is solvable in at most 31 moves.)

6. Pancake puzzle: sort pancakes in optimal number of moves.
Try the to solve these problems in the comment section.