A camel must travel 1000 miles across a desert to the nearest city. She has 3000 bananas but can only carry 1000 at a time. For every mile she walks, she needs to eat a banana. What is the maximum number of bananas she can transport to the city?
Let's begin by imagining how the camel might get the bananas across the desert. If she starts off with 1000 bananas and carries them 1000 miles, she won't be able to return for the rest of them because she won't have any bananas to fuel her trip back. She won't have any bananas to give to her friends either, because she will have eaten them all during the journey. This suggests that the camel needs to cache piles of bananas at certain points in the desert so she can actually move some of them instead of using them all for fuel.
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