3. What is the maximum product you can obtain from a set of positive natural numbers that sum up to n.
4. (romanian national olympiad, 10th grade 2000) How many ways can you tile a 3xn rectangle with dominoes.
5.

[code]

==code(c) |

  for i1 = 1 to n
    for i2 = i1 to n
      for i3 = i2 to n
        …
         for ik = ik - 1 to  n
             print ‘*’

[/code]

==

How many stars will be printed for a given n and k.
6. How many ways can k rooks on a nxn chessboard so they don’t attack eachother.
7. How many permutations of length n have no fixed points. A fixed point for a permutation p is p(i) = i