Date: Sat, 25 Jan 1997 15:26:09 -0600 (CST)
Name: Emily
Level: Middle

Question:
There is a donkey who carries carrots. A farmer has 3,000 carrots to carry to the market. The market is 1,000 miles away. The donkey can only carry 1,000 carrots at a time and he eats 1 carrot every mile that he walks but this is only when he is carrying carrots. How many carrots can the farmer get to market by having the donkey carrying them?

P.S. The answer is not 0

P.P.P.S. I need to know how to get this answer.

Hi Emily

This is an interesting problem. I am sure that I don't know the best strategy but I can show you an idea that will get quite a few carrots to market.

Load up the donkey with 1,000 carrots and go one third of the way to market. Drop off the carrots that you have left (two-thirds of 1,000 carrots) and return to the start to get another load of 1,000 carrots. This time when you get to the one third mark pick up half of the carrots you dropped (that is one third of 1,000 carrots) and continue to the two-thirds mark. Drop off the carrots you have (two-thirds of 1,000 carrots) and return to the start. Load up the remaining 1,000 carrots, at the one third mark pick up the remaining carrots there and continue to the two-thirds mark. Now you are two-thirds of the way to market and have four-thirds of 1,000 carrots.

Now load up half of the remaining carrots, go one-sixth of a mile and drop off the carrots left (that is 2/3 - 1/6=3/6=1/2 of 1000 carrots). Go back to the two-thirds mark, pick up the remaining carrots procede to the point where you left the 500 carrots. Pick them up and procede to market with five-sixths of 1,000 carrots.

I am sure that you can do better! Let me know what you get.

Cheers
Penny

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