## Falling Apples (Solution)

I think the answer is 833.

Assuming I’m right, the main insight is that you want the truck as full of apples as possible at all times. No matter how many apples are in the truck, one will fall out per mile, so by having as many apples in the truck as possible you have the best ratio of apples moved to apples wasted.

The way I thought about it was that the truck would always move all the apples one mile at a time.

To start, we have 3000 apples at mile 0. The truck would then take 3 trips from mile 0 -> 1 and it would drops 3 apples doing so.

Now we have 997 apples all at mile 1. The truck again takes 3 trips from mile 1 -> 2 and drops another 3 apples.

Carry this on until you’ve moved all the apples to mile 333. How many apples will you have left? Each mile takes 3 trips, so you’ve dropped 999 apples and you have 2001 left, but consider yourself as having only 2000 apples because that extra apple is no use.

For the next 500 miles, you only need 2 trips per mile and therefore you only drop 2 apples per mile. Now you’re at mile 833 and you’ve dropped an additional 1000 apples, leaving 1000 apples remaining (all at mile 833).

From there, you just pack up a full truck and make a run for it. 167 miles left, which means you drop 167 apples and are left with 833 apples by the time you reach Town B.