Camels and Apples .................

[Gizmonster]

You have 3,000 apples and a camel which can carry at most, 1,000 apples at a time.
The camel eats an apple before moving a unit.
You want to transport the apples 1,000 units.

Note: you can move back and forth, dropping apples along the way and picking them up on your way back (just remember though, that you can never carry more than 1000 apples at a time).
..... and note that moving backwards a unit, still requires the camel to eat an apple.

So, for example, you could pick up 1000 apples, move ..... say 300 units, drop 400 apples and then just have enough apples to get you back to the start to pick up some of the remaining 2000 apples.

So:
What is the maximum number of uneaten apples that you can move 1,000 units?

[factor-fiction]

533⅓ apples?

Since there are 3000 apples and the camel can carry at most 1000 apples, at least five trips are needed to carry away all apples from the plantation (three trips away from the plantation and two return trips):

First, the camel takes 1000 apples to point A. There it drops 600 apples and returns with 200 apples. Then the camel takes again 1000 apples to point A. Again, it drops 600 apples and returns with 200 apples. After this, the camel takes the last 1000 apples from the plantation to point A.

From point A, it leaves with 1000 apples to point B. In point B, it drops 333⅓ apples and returns with 333 ⅓ apples. Then it takes the second load of 1000 apples from point A to point B. Finally, it carries the 1000 apples from point B to the market, where it arrives with 533 ⅓ apples.

[Gizmonster]

At last - I was thinking no-one was gonna get it ......

The trick is working out that every unit travelled will cost you 5 apples initially, 'cos as Factor30 pointed out, you've gotta go there, back, there, back and there (5 trips).

This is only until you get down to 2000 apples - now every unit travelled will only cost 3 apples - only takes 3 trips for 2000 apples (there, back and there).
At 5 units per apple, you can see that you need to drop off the apples at the 200 unit mark - so that you end up with exactly 2000 apples at the 200 unit mark.
When you're down to 2000 apples you need to work out where you need to drop the apples to end up with 1000 apples left.
Factor30 has assumed we're allowing fractions (which is ok as I never said otherwise).
The next drop is a further 333 1/3 units along (at the 533 1/3 unit mark) - where you'll end up with 1000 apples and 466 2/3 units to travel.
Travel to the end and you end up with 533 1/3 apples as Factor30 correctly stated.

[factor-fiction]

Just me and you on this one, Gizmonster.