# Math puzzle: Farmer delivery problem

You can get an ice cream from me if you get this right...

A farmer has 3000 melon to deliver to the market which is 1000m away from where he is now. His donkey can only carry 1000 melons at a time and will eat 1 melon per meter. You are not allowed to drop the melon on the road and pick up later. What is the maximum number of melons the farmer can deliver to the market? The min is 500.

This is supposed to be a pre-calculus question. I am appalled when I couldn't solve it at all after so many years of formal Math education. Just walking back and forth to carry the other 2000s, the farmer will never reach the marketplace.. since he is not allowed to drop some melons on the roads for later pick-up.... Because of this, I can't even write a deterministic program to calculate the maximal subarray or as a series... (some sequence of numbers)

Anyone has any idea how to get this started? Is this even computable..?

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The min is actually zero :) –  process91 Jun 12 '12 at 2:32
Are these numbers correct? –  user17794 Jun 12 '12 at 2:34
@TimDuff They can't be, right? I'm seeing that the donkey can take 1000 melons, eat all of them by the time it gets to the market, and then presumably die of hunger if it tries to get back. Maybe the maximum is 3000 - the farmer just takes as many as he can carry over and over, and the donkey is a red herring. –  process91 Jun 12 '12 at 2:35
@JohnWong The answer to a similar riddle is here: edurite.com/kbase/answer-to-4th-grade-math-problem. This one does not stipulate that you cannot drop the melons, however, and clearly the same strategy will not apply to your question. There is a loose upper bound of 3000 - miles walked, so 2000 melons, however my contention is that the upper bound equals the lower bound, which is zero. –  process91 Jun 12 '12 at 2:50
Without the "not allowed to drop the melon" provision, this is usually posed as "cross the desert" or "the jeep problem", and many discussions can be found by searching those terms. With that provision, it's hard to see how you can get anywhere. –  Gerry Myerson Jun 12 '12 at 3:17