Chicken McNugget quantity test

#Program to see what is the largest number that can not be derived from when ordering Chicken McNuggets in
#6pc, 9pc, 20pc sizes. This checks every possible case and develops a list of possible combinations
#then examines what numbers are not on that list to find the largest number you can't buy.

#James Tuvell
#Feb-1-12


bestSoFar = 0
packages = (6,9,20)
endtest = 150


listcombos = []

#checkChicken
#input numb is the number to be checked
#a,b,c are the 3 possible piece counts a=6pc b=9pc c=20pc
#output None
#checks weather a combination is possible.
def checkChicken (numb,a,b,c):

    combine=(packages[0]*a)+(packages[1]*b)+(packages[2]*c)
    if combine == numb:
        print (numb, "is a combination of ", a, b, c, " times ", packages[0], packages[1], packages[2])
        if numb not in listcombos:
            listcombos.append(numb)
    return

#main routine
#Not much here. I chose a nested while loop and reduced the number of iterations by
#dividing the test size by the piece count giving the maximum number of pieces that
#could be giving in that size. This reduces the load considerably.
i = 1
while i <= endtest:
    a = 0
    while a <= endtest/packages[0]:
        b = 0
        while b <= endtest/packages[1]:
            c=0
            while c <= endtest/packages[2]:
                checkChicken(i,a,b,c)
                c=c+1
            b=b+1
        a=a+1
    i=i+1

print ("finished")
print ("The list of possibilities up to ",i-1, "that can be bought are ", listcombos)

#this is the section that checks for missing number on the sucess list. That will show
#which ones were failures and what is the largest of them.
for q in range (1, endtest):
    if q not in listcombos:
        bestSoFar=q
        print (bestSoFar, "is not in the list")

print "The highest number you can not make with 6pc 9pc and 20pc mcnuggets is:",bestSoFar