enumerate.py

import collections

unique = collections.defaultdict(list)

def simulate(sample, B, N, C, K):
    global unique

    if len(sample) == B:
        counts = [0] * N
        for s in sample: counts[s] += 1

        success = filter(lambda h: h >= C, counts)
        success = len(success) >= K

        if success:

            h = map(str, counts)
            h = ''.join(h)

            unique[h].append(''.join(map(str, sample)))

            return 1
        else:
            return 0

    ret = 0
    for i in xrange(N):
        sample.append(i)
        ret += simulate(sample, B, N, C, K)
        sample.pop()

    return ret

B = 6
N = 3
C = 2
K = 2
sample = []

print 'Total possibilities: ', N**B
print 'Number that have at least C copies of K elements: ', simulate(sample, B, N, C, K)
print 'Core problem solutions: ', len(unique.keys())
print 'Bounds warning: ', B - C*K > C

for k in sorted(unique.keys()):
    print '+'.join(k), '=', B, len(unique[k]), 'combinations.'