A banana plantation is located next to a desert. The plantation owner has 3000 bananas that he wants to transport to the market by camel, across a 1000 kilometer stretch of desert. The owner has only one camel, which carries a maximum of 1000 bananas at any moment in time, and the camel eats one banana every kilometer it travels.
What is the largest number of bananas that can be delivered at the market?
Hint: You can cache bananas in the desert.
1a. Load the camel with 1000 bananas, travel 200 km, cache 600 bananas (keeping 200 bananas on the camel for feed) and return.
1b. Repeat with the second 1000 bananas.
1c. Load the camel with the final 1000 bananas and travel 200 km to the cache.
At this point the camel is 200 km into the desert, with 2000 bananas.
2a. Load the camel with 1000 bananas, travel 333 1/3 km, cache 333 1/3 bananas (keeping 333 1/3 bananas on the camel) and return to the cache.
2b. Load the camel with the final 1000 bananas and travel 333 1/3 km to the second cache.
At this point the camel is 200+333 1/3 km into the desert, with 1000 bananas remaining.
3a. Load the camel with all 1000 bananas, travel the remaining (1000 - 533 1/3) = 467 2/3 km; there are 1000 - 467 2/3 = 533 1/3 bananas remaining.