Quote from zedDoubleNaught:
Don't mean to argue, but ... it appears you're making an assumption, not stated in the initial question, that somehow Dow Jones is aware that 7 cigarette butts would magically turn into a full cigarette. Further, you are assuming that Dow Jones can in fact collect up to 7 butts, in addition to keeping the butts from the magic cigarettes as he goes. In the scenario laid out, Mr Jones would probably smoke the butts as he found them to avoid the risk that someone would steal his collection or injure him in the process of stealing his collection.
I can understand "8" as the target answer, but I think the real-world answer would be around 39 butts (assuming he tosses the butts where the tobacco is completely gone, and these are around 15% of total butts).