combinations.py

# Determine whether, in any state, the expected chosen prize is greater than the maximum prize
from itertools import combinations
from math import log, exp

cases = {1,10,100,1000}
maxprize = 200

s = set.union(*[set(combinations(cases, i)) for i in range(1, len(cases)+1)])
ss = sorted(s)

def pretty(set):
    for combo in sorted(set):
        print(', '.join(map(str, combo)))

ours = lambda c: float(sum(c)) / len(c)**2
his = lambda c: exp(sum(map(log, c)) / len(c))
comp = lambda c: max(ours(c), his(c)) > maxprize

def f(c, n=None):
    if n is None:
        n = len(c)
    if his(c) > ours(c):
        return any(acceptable(x) for x in combinations(c, n-1))
    else:
        return ours(