#Nathan Fox
#Homework 18
#I give permission for this file to be posted online

##Problem 1
#Generate all depth-up-to-n Conway games
#using Sage
optionRemember = dict()
optionRemember[0] = frozenset((frozenset([]),frozenset([])))
def conwayGames(n):
    if n in optionRemember:
        return optionRemember[n]
    pset = powerset(conwayGames(n-1))
    ret = set([])
    for g in pset:
        for h in pset:
            ret.add((g,h))
    ret = frozenset(ret)
    optionRemember[n] = ret
    return ret