Camel and Bananas - One puzzle a day - Puzzle Buddies

Puzzle:

A banana plantation is located next to a desert. The plantation owner has 3000 bananas which he wants to transport to the market by camel. The market is located 1000 kilometre away from the plantation with desert in between. The owner has only one camel, which carries a maximum of 1000 bananas at any moment in time. The camel eats one banana every kilometre it travels.

What is the largest number of bananas that can be delivered at the market?

Answer:

The camel needs to make more than one trip to deliver all bananas to the market. No doubt he needs to make at least one stop in between otherwise he can never have enough bananas left for the comeback journey. And this point needs to be less than 500 if he wants any bananas to be left when he reaches the market. Let’s say it’s A.

Plantation======A=====================Market

The trick is to make sure that the camel always travels with his full capacity of bananas. This is true initially as there are total 3000 bananas and the camel carries 1000 bananas at a time. So, he will make 3 trips with 1000 bananas to point A. To make sure he carried his full capacity after point A, we should have a multiple of 1000 bananas left when all bananas are at point A. This number can thus be 2000 at best. So he is eating 1000 bananas from the plantation to point A, making 5 trips in between. So, he eats 200 bananas in 1 trip. Point A is 200 km from the plantation.

Again we need a stopping point in between A and the plantation where there will be 1000 bananas left after 3 trips. So the camel eats 333 1/3 bananas in each trip, point B being 333 1/3 km away from A.

Plantation======A=========B===========Market

In the end, the camel needs to make only 1 trip from B to the market which is 466 2/3 km away, leaving 533 1/3 bananas at the market.

Winner: Ashish and Prabharan