Question

cookies are sold singly or packages of 6 or 18. with this packaging, how many ways can you buy 36 cookies?
Help Please!

Answer 1

time to count

Answer 2

ok can't count properly, lets try again
one package has 18, how many ways?
18, 18
18, 6, 6, 6
18, 6, 6, ones
18, 6, ones
18, ones

Answer 3

i count 5 if one package has 18 cookies
now suppose there no package has 18 cookies

then there are either
6 packages of 6 or
5 packages of 6 or
4 packages of 6 or
3 packages of 6 or
2 packages of 6 or
1 package of 6 or
no packages of 6

Answer 4

which gives me 7 if no packages of 18, and 5 if there is a package of 18
for a total of 12

now there may be some slicker way to do this, but i don't know it and in any case it is nice to have a problem you can solve by counting