The Mango Tree with Seven Gates
RAY: 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: 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.
[ Car Talk Puzzler ]