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Another spin on a classic: Transporting Apples


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

Spoiler for Let's work backwards
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#11 DeGe

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Posted 10 July 2013 - 08:34 PM

 

The problem statement says

  • "His truck can only hold 1000 apples."

​the update says that the store is 1000 miles away

 

If the driver starts with a full load [1000 apples] and drives 1000 miles, he will have 0 apples left upon arrival.

 

Thus, unless he can ferry apples to some point(s) in between and then move these forward, there is no way to every deliver even 1 apple.

 

If we assume that there is a point halfway [500 miles] then he could do the following:

  • leave the warehouse with 1000 apples
  • drive 500 miles [now has 500 apples]
  • leave the apples at the halfway point [now has 500 apples]
  • drive back to the ware house
  • leave the warehouse with 1000 apples
  • drive 500 miles [now has 500 apples]
  • Picks up 500 the apples at the halfway point [now has 1000 apples in the truck and 0 apples at the halfway point]]
  • Drives the remaining 500 miles to the store and delivers 500 apples

Thus for 2 trips[500 and 1000 miles one way (3000 miles total round trip)] 500 apples can be delivered

 

to deliver 3000 apples would require:

  • an interim storage area at 500 miles
  • 6 "short" round trips between the warehouse and the interim storage area [1000 miles R/T each]
  • 6 "long" round trips from the warehouse [stopping at the interim storage area to reload] to the store [2000 miles R/T each]

Notes:

  • you can break this up many ways
  • it is not clear what the optimal interim storage area distance [from the ware house] is [and if more than 1 helps]

 

Yes, but for returning also he would need to eat apples

So, if he goes 500KM, he would eat 500 while going and 500 while coming back.

Spoiler for Max apples i got so far


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#12 BMAD

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Posted 10 July 2013 - 08:46 PM

 

 

The problem statement says

  • "His truck can only hold 1000 apples."

​the update says that the store is 1000 miles away

 

If the driver starts with a full load [1000 apples] and drives 1000 miles, he will have 0 apples left upon arrival.

 

Thus, unless he can ferry apples to some point(s) in between and then move these forward, there is no way to every deliver even 1 apple.

 

If we assume that there is a point halfway [500 miles] then he could do the following:

  • leave the warehouse with 1000 apples
  • drive 500 miles [now has 500 apples]
  • leave the apples at the halfway point [now has 500 apples]
  • drive back to the ware house
  • leave the warehouse with 1000 apples
  • drive 500 miles [now has 500 apples]
  • Picks up 500 the apples at the halfway point [now has 1000 apples in the truck and 0 apples at the halfway point]]
  • Drives the remaining 500 miles to the store and delivers 500 apples

Thus for 2 trips[500 and 1000 miles one way (3000 miles total round trip)] 500 apples can be delivered

 

to deliver 3000 apples would require:

  • an interim storage area at 500 miles
  • 6 "short" round trips between the warehouse and the interim storage area [1000 miles R/T each]
  • 6 "long" round trips from the warehouse [stopping at the interim storage area to reload] to the store [2000 miles R/T each]

Notes:

  • you can break this up many ways
  • it is not clear what the optimal interim storage area distance [from the ware house] is [and if more than 1 helps]

 

Yes, but for returning also he would need to eat apples

So, if he goes 500KM, he would eat 500 while going and 500 while coming back.

Spoiler for Max apples i got so far

 

very very close.  consider the fact that the store he delivers to accepts and sells parts of apples to :)


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#13 plasmid

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Posted 11 July 2013 - 04:04 AM

Wait, does the driver have to have apples in his truck and be eating them in order to drive?

If so, then I'll have to change my answer in post 6. I was thinking that he only ate apples if there were any in his truck, but he could drive without eating apples if he wasn't carrying any.


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#14 BMAD

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Posted 13 July 2013 - 12:46 AM

Wait, does the driver have to have apples in his truck and be eating them in order to drive?

If so, then I'll have to change my answer in post 6. I was thinking that he only ate apples if there were any in his truck, but he could drive without eating apples if he wasn't carrying any.

very good point plasmid, the way i wrote the op is that he only eats apples if he has them so i made a mistake when i made my previous post.  now the other answer is close if he was eating to drive.


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#15 DeGe

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Posted 16 July 2013 - 10:34 AM

very very close.  consider the fact that the store he delivers to accepts and sells parts of apples to :)

selling an apple that is 2/3rd eaten would be difficult :excl:

But if you insist, add 1/3 to my previous answer


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#16 BMAD

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Posted 16 July 2013 - 12:05 PM

 

very very close.  consider the fact that the store he delivers to accepts and sells parts of apples to :)

selling an apple that is 2/3rd eaten would be difficult :excl:

But if you insist, add 1/3 to my previous answer

 

that bellies the assumption that he must have apples to drive.  which is not the case.  he only eats apples while driving if they are available.

 

ps. you are also answering a different question.


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#17 DeGe

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Posted 16 July 2013 - 01:16 PM

 

that bellies the assumption that he must have apples to drive.  which is not the case.  he only eats apples while driving if they are available.

 

ps. you are also answering a different question.

If he eats apples only if they are available, it is much simpler then

Spoiler for Driving on an empty stomach

 

Although a better way could be for the driver to drive an empty truck to the local store and explain the problem. Let the local store send a non-apple-eating driver with the truck who makes 3 trips delivering all the 3000 apples.


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#18 Rainman

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Posted 19 July 2013 - 07:59 AM

Spoiler for

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#19 BMAD

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Posted 19 July 2013 - 02:31 PM

Spoiler for

Plasmid's answer is more efficient in terms of the amount of apples to be used.


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#20 Rainman

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Posted 20 July 2013 - 12:08 AM

Actually we have the same amount of apples used, but he was more efficient in terms of answering first :P
Spoiler for

Edited by Rainman, 20 July 2013 - 12:09 AM.

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