## Camel and banana problem

For fans of all other kinds of logic puzzles

### Camel and banana problem

A person has 3000 bananas and a camel. The person wants to sell maximum number of bananas to the market, which is 1000 KMs away, using only the camel as a mode of transportation. The camel cannot carry more than 1000 bananas at a time and eats a banana every km it travels. Find the maximum number of bananas that can be sold.
rjamil

Posts: 604
Joined: 15 October 2014
Location: Karachi, Pakistan

### Re: Camel and banana problem

The potential of being a trick question is considered. There are also ways of getting bananas to destination "Out of the box" and have also been considered

In the very basic way, however, I managed to get 500 bananas & camel to destination assuming a path free from bandits & hungry animals

Tarek

tarek

Posts: 3748
Joined: 05 January 2006

### Re: Camel and banana problem

tarek wrote:I managed to get 500 bananas & camel to destination

You have 6.25% less bananas sold.
rjamil

Posts: 604
Joined: 15 October 2014
Location: Karachi, Pakistan

### Re: Camel and banana problem

Ahh. I was close!!!

Good brain work

tarek

tarek

Posts: 3748
Joined: 05 January 2006

### Re: Camel and banana problem

See <Jeep In the Desert Problem>

There are various complications that can be added. The worst is the flight commander on a remote island with 5 spotter aircraft and unlimited supply of fuel. If the aircraft have a range of x miles, can land, refuel and take off again instantly, and can refuel each other in mid air, what is the furthest distance away from the island he can send a plane and retrieve it (and all the others) safely.

It's years since I tackled that one, but I could only solve it by testing cases. I might have the answer somewhere, but don't hold your breath.

David PB
David P Bird
2010 Supporter

Posts: 1043
Joined: 16 September 2008
Location: Middle England

### Re: Camel and banana problem

Hi David P Bird,

The answer to this puzzle is as follows:

First, the camel carry 1000 bananas to a distance of 200 km. 200 bananas eaten by camel and 200 more need to return back to origin. 600 surplus unload at that point.

Similarly, in second trip, 200 eaten, 200 need for return trip and another 600 unload at same point. Now total 1200 bananas at that point and 800 eaten.

In third trip, camel carry remaining 1000 bananas, travel 200 km and eat 200 bananas.

Load 200 out of 1200 bananas and travel further 333 1/3 km, eat 333 1/3 bananas, need another 333 1/3 bananas for return to previous point and drop 333 1/3 bananas at new point.

Load remaining 1000 bananas, travel 333 1/3 km towards next point and eat 333 1/3 bananas.

Now, 200 + 333 1/3 = 533 1/3 km covered, 666 2/3 bananas loaded and 333 1/3 bananas at new point, total 1000 bananas and 1000 - 533 1/3 = 466 2/3 km away from market.

Load 333 1/3 bananas. At market, total 466 2/3 more bananas eaten by camel and 1000 - 466 2/3 = 533 1/3 bananas sold.
rjamil

Posts: 604
Joined: 15 October 2014
Location: Karachi, Pakistan