my solution for 40 cups and 9 oranges problem.

cups.py

#!/usr/bin/python3.2
from itertools import combinations
"""
You have 40 bowls, all placed in a line at exact intervals of 1 meter. You also have 9 oranges. You wish to place all the oranges in the bowls, no more than one orange in each bowl, so that there are no three oranges A, B, and C such that the distance between A and B is equal to the distance between B and C. How many ways can you arrange the oranges in the bowls?.
(http://www.bittorrent.com/company/about/developer_challenge)
"""
def find_count(orange_count=9,cup_count=40,start_point=0,l=[]):
    """
    orange_count: how many oranges should be placed in cups. for our question it is 9.
    cup_count: how many cups should be used
    rest of the arguments are used in recursive calls.you don't need to give them to the method

    start_point: from which cup we should start. default is zero
    l: holds cup numbers that we have oranges inside
    """
    if len(l)==orange_count:
        # we have enugh of oranges. stop recursive calls
        result=1
        #print(l)
    else:
        result = 0
        for i in range(start_point,cup_count):
            is_valid = True
            # Choose ABC cups as C is being current current bowl
            # And AB is being every combination of current stack of bowls
            tuples = combinations(l,2)
            for t in tuples:
                if t[1]-t[0] == i - t[1]:
                    is_valid = False
                    break
            # Check if current bowl is a valid one
            if is_valid:
                # There is no such ABC as B-A == C-B
                # We can now add another orange to stack
                result += find_count(orange_count,cup_count,i+1,l+[i])
    return result

if __name__ == '__main__':
    import sys
    print('total =',find_count(int(sys.argv[1]),int(sys.argv[2]),0,[]))