battleclams1.py

from collections import Counter
from itertools import combinations

types = [1,2,3,4]

# creatures have 2 of the 4 types
# so there are c(4,2) = 6 creatures
creatures = list(combinations(types, 2))

# there are four creatures in each ocean
sets = list(combinations(creatures, 4))

# there are three ocean levels
choices = list(combinations(sets, 3))

# we want to find the set of creatures in each ocean
# that has the same number of types in each set

def equal_subtypes(t):
    (s1, s2, s3) = t
    c1 = Counter([f for p in s1 for f in p])
    c2 = Counter([f for p in s2 for f in p])
    c3 = Counter([f for p in s3 for f in p])
    return c1 == c2 and c2 == c3

solutions = filter(equal_subtypes, choices)

for l in solutions:
    for c in l:
        print(c)