Discuss the solutions in the comment section.
# (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 staircase if at each step you can climb one or two levels.

# 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).

# ([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 = 3 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.
# ([1], romanian national olympiad, 10th grade, 2000) How many ways can you tile a 3xn rectangle with dominoes.
# (romanian IOI selection, 1999)

# (acm.sgu.ru) Count the number of circular black/white necklaces of length n. (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 enthusiasts:

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.
[2] Ioan Cuculescu "Olimpiadele Internationale de Matematica ale Elevilor"

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