RAY: OK, here's last week's Puzzler. This was a mathematical Puzzler from India. It seems there was a mango tree owned by a certain maharajah that had very sweet and very abundant fruit. Everyone would come from miles around to pick the fruit, so in order to protect the tree the owner erected a series of seven fences around the tree. Concentric, circular fences. Each fence had a gate with a guard. So to get to the tree, a person had to pass through seven gates guarded by seven guards. Practically impossible. One day a man approaches the guard at the outermost gate and says, "If you let me pass through, when I come back I will give you half the mangoes I have. But then you must give me one back." The guard agrees and lets the man go through the gate.
The man proceeds to make the same deal with the other six guards, eventually reaching the mango tree, where a helicopter comes down and helps him steal 150,000 mangoes. No, no, not really.
The question is: How many mangoes did the man have to collect to pass back through the seven gates, giving half of his stash to each guard, and the guard giving one back? Of course, you can't cut any mangoes in half...that would be cheating...so the challenge here is to find the number that, when you divide it by two, gives you an odd number, because if you give the guard half of that amount and you will wind up with an odd number, when he gives you one back you'll have an even number. Then you want to divide that number by two again and wind up again with an odd number, so when he gives you one back you'll have an even number. Because we all know that odd numbers are not divisible by two, and you can't do it unless the number is two.
TOM: Wow.
RAY: Yeah.
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, and for having the answer picked at random from among the bushels of correct answers that we got this week, T. J.'s going to get a $25 gift certificate to the Shameless Commerce Division, which is at the Car Talk section of cars.com. You go to cars.com, you click on Car Talk, and you go the store and get a $25 gift certificate. You look at all the things you can buy, you find nothing that you want, and you throw the thing away. That's it. Why not?
TOM: It was succinct, if nothing else. Anyway, we'll have a new Puzzler in the third half of today's show. This is your chance to win, folks, so stay tuned for that. In the meantime, if you have a question about your car or anything else, the number is 888-CAR-TALK. That's 888-227-8255.
[ Car Talk Puzzler ]
