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The Banana Eating Camel

Page history last edited by mwclarkson 9 years, 7 months ago

A mathematical puzzle that takes a bit of thought.

 

Puzzle

I have 3000 bananas to take to market, and 1 camel. The market is 1000km away. The camel can carry up to 1000 bananas at a time but eats 1 banana for every km it walks.

 

How many bananas can I get to market?

 

Answer

 

533 1/3 bananas.

 

The camel could carry 1000 bananas for 500km, then turn around and eat the 500 remaining bananas on the return journey.

Or, it could travel x km. to point A, drop off all but x bananas and head back (leaving 1000 - 2x bananas at point A).

This could be repeated 3 times, meaning the 3000 bananas is not 3000 - 5x (the last journey is only one way). Ideally this would leave us with 2000 bananas as this gives us 2 full loads for the next leg.

 

The camel would take the next load of 1000 bananas and drop them off at point B (y km. away) leaving us with 1000 - 2y bananas. But with 2000 bananas the camel would do this twice, leaving us with 2000 - 3y bananas (again, the last trip is one way).

 

Hopefully we now have 1000 bananas for the final leg - one way.

 

So, from leg 1. 3000 - 5x = 2000. This means 5x = 1000, or x = 200km.

 

From leg 2, 2000 - 3y = 1000. This means 3y = 1000 or y = 333.3km.

 

That means we must have 466.6km to go.

 

If we load the camel up with the remaining 1000 bananas then 466 2/3 will be eaten, leaving us with 533 1/3 bananas left.

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