# ([1]) What is the maximum product for collection of natural numbers that sum up to n.
# ([1], romanian national olympiad, 10th grade, 2000) How many ways can you tile a 3xn rectangle with dominoes.
# (romanian IOI selection, 1999)

<pre>
  for i1 = 1,n\\newline

<tex>
  for i1 = 1,n\newline

      for i2 = i1,n\newline
          for i3 = i2,n\newline
               …\newline
               for ik = ik - 1,n\newline
                   print ‘*’\newline

</pre>

</tex>

How many stars will be printed for a given n and k.
# ([5], 'acm.sgu.ru':http://acm.sgu.ru/problem.php?contest=0&problem=222) How many ways can k rooks be placed on a nxn chessboard so that they don’t attack each other.
# (romanian county olympiad, 11th grade 2000 [1], 'acm.sgu.ru':http://acm.sgu.ru/problem.php?contest=0&problem=356) How many permutations of length n have no fixed points. A fixed point in a permutation p is p(i) = i