ps2ex1-4

# equation: 6a + 9b + 12c

# Equation is defined as the following:
# x(a) + y(b) + z(c) = n
# the goal is to determine what values of (a, b, c) are possible for given (x, y, z)
def isComboPossible(n, x, y, z):
    for a in range(0, (n / x) + 1 ):
        for b in range (0, (n / y) + 1):
            for c in range (0, (n / z) + 1):
                #print 'a: ', a ,' b: ', b ,' c: ', c
                if((x * a) + (y * b) + (z * c)) == n:
                    return (a, b, c)

    return False

# theorem: if it is possible to buy a, a+1...a+5 nuggets then it is possible to buy all
# combinations > a
#
# problem, given that the theorem is true find the highest possible combination that is NOT
# possible
def findHighestImpossibleCombo(x, y, z):
    currentHighest = 0       # stores failures as we come across them
    possibleCount = 0        # keeps track of how many tests are positive in a row
    comboNumberTest = 6;     # start at the lowest possible combo of nuggets which is 6
    while possibleCount < 6:
        if isComboPossible(comboNumberTest, x, y, z) == False:
            currentHighest = comboNumberTest
            possibleCount = 0
        else:
            possibleCount = possibleCount + 1

        comboNumberTest = comboNumberTest + 1

    return currentHighest


#number = int(raw_input("How Many?\n"))
packageSizes = (6, 9, 20)

#print 'PS2q1 TEST +++++++++++++++++++++++++++++++++\n\n\n'
#chickenNuggetTest = isComboPossible(number, *packageSizes)
#if chickenNuggetTest == False:
#   print '\nnot possible'
#else:
#   print '\n6: ', chickenNuggetTest[0], '\n9: ', chickenNuggetTest[1], '\n20: ', chickenNuggetTest[2]

#print '\n\n PSq4 TEST  +++++++++++++++++++++++++++++++++++++\n\n\n'

print 'The Highest possible combination using ', packageSizes[0] ,', ', packageSizes[1] ,',', packageSizes[2] ,' is ', findHighestImpossibleCombo(*packageSizes)