# (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).

# (agora scholarships [4], 'infoarena':problema/drepte2) 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.

# ([4], agora scholarships 2001, 'infoarena':problema/drepte2) 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 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.

# ([1], romanian national olympiad, 10th grade, 2000) How many ways can you tile a 3xn rectangle with dominoes.

# (romanian IOI selection, 1999)
==code(c) |

                   print ‘*’
==
How many stars will be printed for a given n and k.

# ( [1], '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.

# ( [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

# (county level olympiad, 1994 [1]) How many correct bracket sequences of length 2n are there.

# ( [1], county level olympiad, 1994) How many correct bracket sequences of length 2n are there.

# (10th grade math course) How many paths are there on a grid from 1,1 to n, m if at each step you can either increase your x coordinate or increase your y coordinate.
# Given a permutation of numbers 1 to n, what's the minimum number of swaps one can use to get to the identity permutation.
# ('infoarena':problema/perm2) 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, 'infoarena':problema/perm5) Find a permutation p of n elements which maximizes k so that p^k(i) = i for all i in {1..n}.

# (romanian ioi selection 99, topcoder 2004, 'infoarena':problema/perm5) Find a permutation p of n elements which maximizes k so that p^k(i) = i for all i in {1..n}.

# [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)