Soda can contest problem The store's rule is that you can use 3 empty cans to exchange for 1 can of soda. Alex's class has 17 students and each bought a can of soda at the beginning of the party. At most, how many more cans of soda can Alex's class get by exchanging?
First of all, I'm not sure I understood the question correctly. I thought that all it's really asking for is how many full cans of soda you can get from 17 empty ones, so basically just 17/3 which is 5 remainder 2, so 5 soda cans.
I don't think it's that easy, so I probably interpreted it wrongly.

If I start with 5 cans, I can get 2 free ones.
First, I take 3 of my 5 empty cans and exchange them for 1. I then take that new can and drink the soda, and use it along with the remaining 2 cans to get another free one.
How does that extend to starting with 17?
