[Guest]

Hello everyone,

I amnew to this forum. I saw this puzzle on internet. I liked it.

The distance between the towns A and B is 1000 miles. There is 3000 apples in A, and the apples have to be delivered to B. The available car can take 1000 apples at most. The car driver has developed an addiction to apples: when he has apples aboard he eats 1 apple with each mile made. Figure out the strategy that yields the largest amount of apples to be delivered to B.

Generalize the strategy for an arbitrary amount of apples.

The site did not give a solution. I have one but not sure if it is the best one. I will post my solution soon.

Imran

[Guest]

find a new driver!!

[Guest]

ya, here is what I did.

Distance (from A) Original Apples Apples Eaten Remaining
---------------------------------------------------------------------------------
0 3000 0 3000
334 1200 1998
833 998 1000
1000 167 833

I STILL DONT GET IT!!!!!!!

[Guest]

Allow me...

I think the 1200 is a typo. It should be 1002.

The idea is to drive only as far as you need to go to lose a total of 1000 apples per checkpoint since that is the maximum number of apples you can fit:

Load up with 1000 apples.

Drive 334 miles (a third of the way), eat 334 apples.

Drop of your 666 remaining apples.

Go back and load up with another 1000 apples.

Drive 334 miles, eat 334 apples.

Drop of your 666 remaining apples.

Go back and load up with another 1000 apples.

Drive 334 miles, eat 334 apples.

You have now eaten 1002 apples and have a total of 666*3=1998 apples at 334 miles.

Now load up with 999 apples.

Drive another 499 miles to mile 833, eat 499 apples.

Drop of your 500 remaining apples.

Go back and load up with another 999 apples.

Drive 499 miles, eat 499 apples.

You have now eaten 1002+998 = 2000 apples and have a total of 1000 apples at 833 miles.

Load up with your last 1000 apples.

Drive the last 167 miles to mile 1000, eat 167 apples.

You have now arrived having eaten 2000+167 apples and have a total of 833 left.

Edited June 4, 2008 by MAD