nuggets.py

import math

n = 1 # potential number of nuggets to be bought
bestSoFar = [] #  that keeps track of largest number of McNuggets that cannot be bought in exact quantity
packages = [6,9,20]   # list that contains package sizes


count = 0 # of times 'n' test has returned True
count_limit = 6 # limit to n, n+1,...,n+5 theorem, if 6 consecutive numbers are True then all after are True. 

def check_if_purchasable(potential, package_list):
    for a in range(math.ceil(potential/package_list[0])): # test all size '6' package purchase amounts up to multiplers resulting in greater than test number nugget amounts, min 1
        for b in range(math.ceil(potential/package_list[1])): # test all size '9' package purchase amounts up to multiplers resulting in greater than test number nugget amounts, min 1
            for c in range(math.ceil(potential/package_list[2])): # test all size '20' package purchase amounts up to multiplers resulting in greater than test number nugget amounts, min 1.
                if ((package_list[0]*a)+(package_list[1]*b)+(package_list[2]*c) == potential): # check if test amounts equal the goal amount
                    return True # that goal has been reached
    return False # that goal has not been reached

# nugget_problem
while count < count_limit: # check if count has reached limit for n, n+1,...,n+5 theorem.
    if check_if_purchasable(n, packages): # if goal was reached
        count += 1 # add to count for n, n+1,...,n+5 theorem, if 6 consecutive numbers are True then all after are True. 
    else: # if goal was not reached
        bestSoFar.append(n) # save test as non purchasable amount of nuggets
        count = 0 # reset count
    n += 1 # set next number to test
print ("Largest number of McNuggets that cannot be bought in exact quantity: " + str(bestSoFar[-1]))