# 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).
# (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.

# [1] What is the maximum product for collection of 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 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.

# Given a permutation of numbers 1 to n, what's the minimum number of swaps one can use to get to the identity permutation.
# Given a permutation p what's the minimum k so that p^k(i) = i for all i in {1..n}.
# (romanian ioi selection 98, topcoder 2004) Find a permutation p of n elements which maximizes k so that p^k(i) = i for all i in {1..n}.

# [1] There are 6 people at a party. Two people can be either friends or enemies. Prove that there is at least a group of three mutual friends or a group of three mutual enemies.
# (acm.sgu.ru) How many n beads black white circular necklaces are there? (babb is the same with bbab because the first necklace can be rotated to align with the second one)

# [1] 6 people are at a party. Each two persons can be either friends or enemies. Prove that there is at least a group of three mutual friends or a group of three mutual enemies.
# (acm.sgu.ru) How many length n black/white circular necklaces are there? (babb is the same with bbab because the first necklace can be rotated to align with the second one)

Some math books useful for programming competition entusiasts:
[1] Ioan Tomescu "Probleme de combinatorica si teoria grafurilor"
Every year during my highschool there was at least one problem in the national olympiad or in the ioi team selection tests from this book.