The Mango Gates

Feb 13, 2016

RAY: This Puzzler came from Kevin Tobin.

A maharaja owned a mango tree that had very sweet, abundant fruit. People would come from miles around to pick the fruit. So the maharajah 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?


RAY: Of course, you can't cut any mangoes in half...that would be 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! So who's our winner?

TOM: Congratulations to Nancy Mullins from Haddonfield, New Jersey!

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