Feb 12, 2001
RAY: This Puzzler came from Kevin Tobin, back in December of '88.
TOM: He was a high school student at the time. Now he's incarcerated.
RAY: Kevin says he got this puzzle from a guy in India. Here it is: A maharaja owned a mango tree that had very sweet, abundant fruit. People would come from miles around to pick the fruit. So the maharaja decided to protect the tree by erecting a series of seven concentric fences around it.
Each fence had a gate with a guard. To get to the tree a person would have had to pass through seven gates and pass seven guards.
One day, a man approached the guard at the first gate and said, "If you let me pass, when I come back I'll bring you some mangoes. I will give you half of the mangoes I have, but you must give me one back." For example, if he brings back 10 mangoes, he'll give five to the guard and the guard will give one back. The guard let the man in through the gate, and the man proceeded to make the same deal with the other six guards.
The question is: How many mangoes did the man have to get to pass back through the seven gates, giving half to each guard and the guard giving one back?
TOM: And we struggled with this. We started with infinity, and we started working backwards. Two?
RAY: Yeah, yeah.
TOM: The question is: What if it were only six guards? No, that's next week!
RAY: That's next week!
TOM: But this was quite clever. So who's our winner?
RAY: The winner is T. J. Hahn from Oak Park, Illinois.