Question

I can get PS2 working, but solution is clumsy. Any suggestions on improvements?
The snippet:
int(math.ceil(target*1.0/pack2))+1
tries to find the max number of times we can include a package of size pack2, without exceeding the target.

packages = (6,9,20)
pack1 = packages[0]
pack2 = packages[1]
pack3 = packages[2]
inattain = []
consec_attain = 0
for target in range(1,200):
attain = False
for ii in range(0,int(math.ceil(target*1.0/pack1))+1):
for jj in range(0,int(math.ceil(target*1.0/pack2))+1):
for kk in range(0,int(math.ceil(target*1.0/pack3))+1):

Answer 1

if pack1*ii+pack2*jj+pack3*kk == target: #We can get it
attain = True
#End exhaustive search
if not attain:
inattain.append(target)
consec_attain = 0
else:
consec_attain += 1
if consec_attain == min(packages):
break
#End outer for
print "Given package sizes, largest number that cannot be bought is: ", inattain.pop()

Answer 2

To find the max number of times you can include pack2 in target, you can just use:
target/pack2

I attached my ps2a.py for reference if you're interested.