# The Mango Gates – Puzzler

From Car Talk:

RAY: This Puzzler came from Kevin Tobin. A maharajah 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?

Similar to Gone Fishin’ puzzler.

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### 2 Responses to The Mango Gates – Puzzler

1. Seen as a first order discrete system with an integer steady state the answer is somewhat surprising, but I got the answer before the analysis.

2. Joshua says:

To me, this puzzler seems under specified.

Also, if the intended answer is what I think it is, then what motivation would the guards have to let the man through? If you think their prior verbal commitment to the agreement is sufficient, what about their prior verbal commitment to the maharajah?
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