# (10th grade math course) How many different strings of length 9 are there which contain 3 'a's, 3 'b's and 3 'c's.
# How many ways are there to climb a n level stair if at each step you can climb one or two levels.

# (olimpiada online 2001) Given n points on a circle. Draw all possible n(n-1)/2 chords. What’s the maximum number of triangles one can see. Example: With n = 4 there are 8 triangles (4 with 3 of the 4 circle points and 4 with 2 circle points and 1 the intersection of the diagonal).

# (olimpiada online 2001) Given n points on a circle. Join all possible n(n-1)/2 cords. What’s the maximum number of triangles one can see. Example: With n = 4 there are 8 triangles (4 with 3 of the 4 circle points and 4 with 2 circle points and 1 the intersection of the diagonal).

# (agora scholarships [4]) What is the maximum number of regions the plane can be split into by n lines. (Same problem for n circles, n planes, n spheres) Example: For n = 4 we can get 7 regions.
# [1] What is the maximum product for set natural numbers that sum up to n.
# (romanian national olympiad, 10th grade, 2000 [1]) How many ways can you tile a 3xn rectangle with dominoes.
# (romanian IOI selection, 1999)

==code(c) |

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

==

How many stars will be printed for a given n and k.
# [1] 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]) How many permutations of length n have no fixed points. A fixed point in a permutation p is p(i) = i