An old beggar collects cigarette ends from ashtrays and pavements and uses the tobacco to roll her own cigarettes. She has this practice down to a fine art, knowing that seven cigarettes ends will make one cigarette. Since she has collected 49 ends, how many cigarettes can she make from these?

The key insight is that cigarettes made from ends also produce new ends. 49 ends make 7 cigarettes initially. After smoking these 7 cigarettes, you get 7 more ends, which makes 1 additional cigarette. Total = 7 + 1 = 8. After smoking that final cigarette, you get 1 end, but need 7 to make another, so you stop. The recursive nature gives 8 total.