Best Answer plasmid, 23 June 2013 - 04:10 PM

Spoiler for Let's work backwards

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Up until he gets the 3000 apples to his destination, he will have to transport more than 3000 apples through any point "A" along the way and will need to make at least four trips carrying apples from point A to his final destination. In order to move a bunch of apples from point A to his destination if he brings them in four hauls, he would essentially be eating 4 apples per mile from point A to the destination. If point A is 250 miles from his destination, then to bring four hauls of apples from point A to the destination he would eat 1000 apples, and therefore would have to start at point A with 4000 apples. At any point farther away from his destination than that, he would have to have more than 4000 apples and therefore need to bring them forward in at least five hauls.

The pattern of how this progresses should now be obvious.

If we allow him to slice the apples that he's going to eat along the way and eat fractions of apples for fractions of miles, then going backwards from his destination, we would have:

Destination - 3000 apples

Point A - 4000 apples - 250 miles from destination

Point B - 5000 apples - 200 miles from point A and 450 miles from destination

Point C - 6000 apples - 166 2/3 miles from point B and 616 2/3 miles from destination

Point D - 7000 apples - 142 6/7 miles from point C and 759 11/21 miles from destination

Point E - 8000 apples - 125 miles from point D and 884 11/21 miles from destination

Point F - 9000 apples - 111 1/9 miles from point E and 995 40/63 miles from destination

To get from the start to point F which is 4 23/63 miles away in 10 trips, eating 10 apples per mile, he would consume 43 41/63 apples along the way. So he would have to start with 9043 41/63 apples.

That raises the question of whether his supplier is frugal enough to want to cut an apple into 63 pieces and try to sell the remaining 22 slivers of apple. If he were, I doubt he'd want to hire someone who'll eat twice as many apples as he delivers.

The pattern of how this progresses should now be obvious.

If we allow him to slice the apples that he's going to eat along the way and eat fractions of apples for fractions of miles, then going backwards from his destination, we would have:

Destination - 3000 apples

Point A - 4000 apples - 250 miles from destination

Point B - 5000 apples - 200 miles from point A and 450 miles from destination

Point C - 6000 apples - 166 2/3 miles from point B and 616 2/3 miles from destination

Point D - 7000 apples - 142 6/7 miles from point C and 759 11/21 miles from destination

Point E - 8000 apples - 125 miles from point D and 884 11/21 miles from destination

Point F - 9000 apples - 111 1/9 miles from point E and 995 40/63 miles from destination

To get from the start to point F which is 4 23/63 miles away in 10 trips, eating 10 apples per mile, he would consume 43 41/63 apples along the way. So he would have to start with 9043 41/63 apples.

That raises the question of whether his supplier is frugal enough to want to cut an apple into 63 pieces and try to sell the remaining 22 slivers of apple. If he were, I doubt he'd want to hire someone who'll eat twice as many apples as he delivers.