Can YOU figure this out?
Lei Li
Here is a problem I encountered yesterday, and just cannot figure it
out. The main story is:
There are 3,000 bananas that need to be transported over a 1,000 mile
wide desert. There is 1 camel that can carry as much as 1,000 bananas
at 1 time. The camel also eats 1 banana per mile. What is the maximum
number of bananas that can be carried over the desert?
Here a some rules involved:
You cannot feed the camel lots of bananas at one time and have it go for
a long distance. You can, though, drop bananas as you go.
The Maximum I've reached is 500, but I hear the answer is higher than
that.
Good Luck!!
Robert Hill
In article <33fb0a43....@news.demon.co.uk>, J...@opticon.demon.co.uk (John Goodwin) writes:
> On 20 Aug 1997 13:39:45 +0200, Andreas Weingessel
> <Andreas.W...@ci.tuwien.ac.at> wrote:
>
> >Lei Li <psych...@juno.com> writes:
> >
> >>
> >> Here is a problem I encountered yesterday, and just cannot figure it
> >> out. The main story is:
> >>
> >> There are 3,000 bananas that need to be transported over a 1,000 mile
> >> wide desert. There is 1 camel that can carry as much as 1,000 bananas
> >> at 1 time. The camel also eats 1 banana per mile. What is the maximum
> >> number of bananas that can be carried over the desert?
> >>
> >> Here a some rules involved:
> >>
> >> You cannot feed the camel lots of bananas at one time and have it go for
> >> a long distance
>
>
> > You can, though, drop bananas as you go.
> >>
> >> The Maximum I've reached is 500, but I hear the answer is higher than
> >> that.
> >>
> >> Good Luck!!
> >>
> >
> >
> >Take 1000 bananas and transport them for 200 miles. After 200 miles
> >you have 800 left (200 were eaten by the camel), drop 600 and with the
> >other 200 go back to the start. Transport the next 1000 bananas in the
> >same way, then go back again and take the last 1000 bananas. Transport
> >them also to mile 200 where you arrive with 800 bananas. Now, you have
> >2000 bananas (600+600+800) left at mile 200. Take 1000 bananas and
> >transport them for another 334 miles. At mile 534 your camel carries
> >666 bananas, drop 332 bananas and use the other 334 bananas to go back
> >to mile 200. Take the 1000 bananas left at mile 200, transport them to
> >mile 534. At mile 534 you have 666 bananas on your camel plus 332 you
> >dropped before, that gives 998 bananas. With these bananas you travel
> >the remaining 466 miles and you arrive with 998-466=532 bananas.
>
> Barely worth the effort is it?
Super-efficient compared with the mass you need to launch from the
Earth to get a man to the Moon and back.
--
Robert Hill
University Computing Service, Leeds University, England
"Though all my wares be trash, the heart is true."
- John Dowland, Fine Knacks for Ladies (1600)
Andreas Weingessel
Lei Li <psych...@juno.com> writes:
>
> Here is a problem I encountered yesterday, and just cannot figure it
> out. The main story is:
>
> There are 3,000 bananas that need to be transported over a 1,000 mile
> wide desert. There is 1 camel that can carry as much as 1,000 bananas
> at 1 time. The camel also eats 1 banana per mile. What is the maximum
> number of bananas that can be carried over the desert?
>
> Here a some rules involved:
>
> You cannot feed the camel lots of bananas at one time and have it go for
> a long distance. You can, though, drop bananas as you go.
>
> The Maximum I've reached is 500, but I hear the answer is higher than
> that.
>
> Good Luck!!
>
I reach 532:
Take 1000 bananas and transport them for 200 miles. After 200 miles
you have 800 left (200 were eaten by the camel), drop 600 and with the
other 200 go back to the start. Transport the next 1000 bananas in the
same way, then go back again and take the last 1000 bananas. Transport
them also to mile 200 where you arrive with 800 bananas. Now, you have
2000 bananas (600+600+800) left at mile 200. Take 1000 bananas and
transport them for another 334 miles. At mile 534 your camel carries
666 bananas, drop 332 bananas and use the other 334 bananas to go back
to mile 200. Take the 1000 bananas left at mile 200, transport them to
mile 534. At mile 534 you have 666 bananas on your camel plus 332 you
dropped before, that gives 998 bananas. With these bananas you travel
the remaining 466 miles and you arrive with 998-466=532 bananas.
Andreas
Terry Moore
> On 20 Aug 1997 13:39:45 +0200, Andreas Weingessel
> <Andreas.W...@ci.tuwien.ac.at> wrote:
>
> >Lei Li <psych...@juno.com> writes:
> >
> >>
> >> Here is a problem I encountered yesterday, and just cannot figure it
> >> out. The main story is:
> >>
> >> There are 3,000 bananas that need to be transported over a 1,000 mile
> >> wide desert. There is 1 camel that can carry as much as 1,000 bananas
> >> at 1 time. The camel also eats 1 banana per mile. What is the maximum
> >> number of bananas that can be carried over the desert?
> >I reach 532:
> >
> >Take 1000 bananas and transport them for 200 miles. After 200 miles
> >you have 800 left (200 were eaten by the camel), drop 600 and with the
[...]
> >the remaining 466 miles and you arrive with 998-466=532 bananas.
>
> Barely worth the effort is it?
The next question is "How are you going to shift next year's
crop?" Not by the same camel.
--
Terry Moore, Statistics Department, Massey University, New Zealand.
Theorems! I need theorems. Give me the theorems and I shall find the
proofs easily enough. Bernard Riemann
Robert Israel
In article <tq7k9hh...@elrond.ci.tuwien.ac.at>, Andreas Weingessel <Andreas.W...@ci.tuwien.ac.at> writes:
|> Lei Li <psych...@juno.com> writes:
|> > There are 3,000 bananas that need to be transported over a 1,000 mile
|> > wide desert. There is 1 camel that can carry as much as 1,000 bananas
|> > at 1 time. The camel also eats 1 banana per mile. What is the maximum
|> > number of bananas that can be carried over the desert?
|> I reach 532:
|> Take 1000 bananas and transport them for 200 miles. After 200 miles
|> you have 800 left (200 were eaten by the camel), drop 600 and with the
|> other 200 go back to the start. Transport the next 1000 bananas in the
|> same way, then go back again and take the last 1000 bananas. Transport
|> them also to mile 200 where you arrive with 800 bananas. Now, you have
|> 2000 bananas (600+600+800) left at mile 200. Take 1000 bananas and
|> transport them for another 334 miles. At mile 534 your camel carries
|> 666 bananas, drop 332 bananas and use the other 334 bananas to go back
|> to mile 200. Take the 1000 bananas left at mile 200, transport them to
|> mile 534. At mile 534 you have 666 bananas on your camel plus 332 you
|> dropped before, that gives 998 bananas. With these bananas you travel
|> the remaining 466 miles and you arrive with 998-466=532 bananas.
Almost right. You can reach 533. Instead of transporting bananas 334 miles
from mile 200, transport them 333 miles, drop 334 and use the remaining 333
to go back. When you get to mile 533 the second time you have 1001 bananas.
Throw away one, travel the remaining 467 miles and arrive with 533 bananas.
Robert Israel isr...@math.ubc.ca
Department of Mathematics (604) 822-3629
University of British Columbia fax 822-6074
Vancouver, BC, Canada V6T 1Y4
-Mammel,L.H.
In article <5ti675$2c8$2...@nntp.ucs.ubc.ca>,
Robert Israel <isr...@math.ubc.ca> wrote:
>
>Almost right. You can reach 533. Instead of transporting bananas 334 miles
>from mile 200, transport them 333 miles, drop 334 and use the remaining 333
>to go back. When you get to mile 533 the second time you have 1001 bananas.
>Throw away one, travel the remaining 467 miles and arrive with 533 bananas.
>
How about going to mile 533 1/3 ? The three trips will cost
exactly 1000 bananas and you'll have 1000 banana's with
466 2/3 miles to go ( and a freshly fed camel. ) You'll
feed it the 466th banana with 2/3 of a mile to go and arrive
with 534 bananas and 1/3 of a mile to spare.
For that matter, starting from 533 really only requires
466 bananas since you arrive just as the camel is due
for one, and I guess it will just stop or die or something.
In fact, any way station between 533 and 533 1/2 will
get you there with 534 bananas. Using 533 1/4, you get
the maximum of 1/2 mile to spare before the camel would
need another banana.
Lew Mammel, Jr.
Tom Hofmann
> >> There are 3,000 bananas that need to be transported over a 1,000 mile
> >> wide desert. There is 1 camel that can carry as much as 1,000 bananas
> >> at 1 time. The camel also eats 1 banana per mile. What is the maximum
> >> number of bananas that can be carried over the desert?
> >I reach 532:
> >
> >Take 1000 bananas and transport them for 200 miles. After 200 miles
> >you have 800 left (200 were eaten by the camel), drop 600 and with the
> >other 200 go back to the start. Transport the next 1000 bananas in the
> >same way, then go back again and take the last 1000 bananas. Transport
> >them also to mile 200 where you arrive with 800 bananas. Now, you have
> >2000 bananas (600+600+800) left at mile 200. Take 1000 bananas and
> >transport them for another 334 miles. At mile 534 your camel carries
> >666 bananas, drop 332 bananas and use the other 334 bananas to go back
> >to mile 200. Take the 1000 bananas left at mile 200, transport them to
> >mile 534. At mile 534 you have 666 bananas on your camel plus 332 you
> >dropped before, that gives 998 bananas. With these bananas you travel
> >the remaining 466 miles and you arrive with 998-466=532 bananas.
You waste one banana! From mile 200, transport 1000 bananas for 333
miles
only. At mile 533 you arrive with 667 bananas, drop 334 and use the
other
333 bananas to go back to mile 200. Take the 1000 bananas left at mile
200,
transport them to mile 533. At mile 533 you have 667 bananas on your
camel
plus 334 you dropped before, that gives 1001 bananas. Now leave one
banana
in the desert (generosity pays). With the other 1000 bananas you travel
the
remaining 467 miles, and you arrive with 1000-467=533 bananas.
Tom Hofmann
wt...@chbs.ciba.com
Joe McCauley
I claim it's possible to get 601 bananas 200 miles into the desert on the
first trip out. My reasoning is as follows:
If you assume that the camel eats his banana at the beginning of each
mile, then at the start you put 1000 bananas on his back, grab one more
from the remaining 2000 and feed it to him. You will then need to feed
him only 199 more bananas for the remainder of the 200 mile journey, so
you can drop 601 bananas and have 200 left for the return trip.
If you assume he eats the banana at the end of each mile, then you will
be feeding him the 200th banana just as you arrive at the 200 mile mark,
where you can drop 601 bananas and bring back 199. You will feed him
the last banana with 1 mile to go, then a mile later, you reach the pile
of 2000 and feed him one of those.
I'll let someone else figure out how many (if any) extra bananas this is
good for over the whole journey.
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William L. Bahn
But if you switch feeding times, you force the camel to go 2 miles between
bananas at one point. If you feed him a banana 1 mile before you get to the
200 mile mark the camel then goes the remaining mile without a banana. If
you then delay feeding him until a mile into the return journey, the camel
has now gone two miles without a banana. I don't think there is anyway to
avoid feeding the camel one banana at each intermediate stop.
Joe McCauley <jmc...@iatcmail.ed.ray.com> wrote in article
<8726072...@dejanews.com>...