Problem Set 2 #1

# Variable definitions:
#	a = # of 6 McNugget packages
#	b = # of 9 McNugget packages
#	c = # of 20 McNugget packages
#	n = test # of McNuggets to be purchased
#	successful_n = a list of all the "n" values that can be purchased
#	bestSoFar = the highest number that cannot be purchased

#Initialize variables
successful_n = [0]
bestSoFar = 0
n = 1
a = 0

#Start loops to test all possible combinations of a, b and c
#Store successful 'n's in successful_n and failed numbers in bestSoFar
while successful_n[-1] - bestSoFar < 6:
	while a <= n/6:
		b = 0
		while b <= n/9:
			c = 0
			while c <= n/20:
				result = 6*a + 9*b + 20*c
				if result == n:
					if successful_n.count(n) == 0:
						successful_n.append(n)
				c = c + 1
			b = b + 1
		a = a + 1
	if successful_n.count(n) == 0:
		bestSoFar = n
	n = n + 1
	a = 0

##print successful_n	#used in testing phase
##print bestSoFar	#used in testing phase
print """
Given package sizes of 6, 9 and 20, the largest quantity of McNuggets
that cannot be purchased in an exact quantity is:
"""
print bestSoFar