Solution for the 9 digit problem posed at -> http://csokavar.hu/blog/2010/04/problem-of-the-week-9-digit-problem/

nine_digit.py

checkers = [
    lambda nums: False,
    lambda nums: True,
    lambda nums: nums[-1] % 2 == 0,
    lambda nums: sum(nums) % 3 == 0,
    lambda nums: (10 * nums[-2] + nums[-1]) % 4 == 0,
    lambda nums: nums[-1] in [0, 5],
    lambda nums: sum(nums) % 3 == 0 and nums[-1] % 2 == 0,
    lambda nums: sum([10 ** i * nums[-(i + 1)] for i in xrange(len(nums))]) % 7 == 0,
    lambda nums: sum([10 ** i * nums[-(i + 1)] for i in xrange(3)]) % 8 == 0,
    lambda nums: sum(nums) % 9 == 0
]

digits = set(xrange(1, 10))

def convert(num_list):
    return sum(map(lambda x: 10 ** (x[0] - 1) * x[1], zip(xrange(9, 0, -1), num_list)))

def check(num):
    for i in xrange(9, 0, -1):
        if num % i != 0:
            return False
        num /= 10
    return True

if __name__ == "__main__":
    curr = [[]]
    for i in xrange(1, 10):
        next = []
        for c in curr:
            for j in digits - set(c):
                n = c[::]
                n.append(j)
                if checkers[i](n):
                    next.append(n)
        curr = next
    converted = map(convert, curr)
    if not all(map(check, converted)):
        print "Some numbers don't satisfy the criteria"
        exit(-1)
    print "There are %s such numbers" % len(curr)
    print "The numbers are the following: "
    for c in converted:
        print c