Math Forum Discussions

Barb Knox

Posts: 578
Registered: 12/6/04

Re: Interesting trivia - anybody has a different answer than I keep getting - zero
Posted: Nov 29, 2012 10:39 AM

Plain Text

In article <see-5B769E.20491929112012@news.eternal-september.org>,
Barb Knox <see@sig.below> wrote:

> In article <kpkab8tdbc77kkrg9mjeahi0hkrsb8rml3@4ax.com>,
> Stone Bacchus <x@x.com> wrote:
>
> > Thanks Jussi, yours and Mike's answer have me thinking on those lines.
> > Thanks for your input. They will help for a nice evening of more
> > analysis on those lines. appreciated.
> >
> > s
> >
> > On 27 Nov 2012 23:21:37 +0200, Jussi Piitulainen
> > <jpiitula@ling.helsinki.fi> wrote:
> >
> > >Stone Bacchus writes:
> > >
> > >> My daughter and I were solving a math trivia and I could not come up
> > >> with any answer other than zero. Would be interesting to see if
> > >> somebody has a different opinion. The problem follows:
> > >>
> > >> You are at the start of a 1000 mile road with 3000 gummybears and a
> > >> donkey. At the end of the road is a supermarket. You want to find
> > >> the greatest number of gummy bears you can sell. Unfortunately, your
> > >> donkey has a disease and can only carry 1000 gummybears at 1 time.
> > >> Also, the donkey must eat 1 gummybear per mile.
> > >>
> > >> - You can drop off gummybears anywhere on the road
> > >> - You can't carry gummybears while walking
> > >> - No loopholes
> > >>
> > >> Again, this was a math trivia question and I could not ask anybody for
> > >> clarification about what some the caveats meant or what the "no
> > >> loopholes" meant, therefore I got zero.
> > >
> > >Take 900 bears on the donkey, walk it 300 miles and back, leaving 300
> > >bears at that milepost. The donkey will have eaten 600 bears. You and
> > >the donkey and 2100 bears are standing where you started.
> > >
> > >Take 1000 bears, walk the 300 miles. The donkey will have eaten
> > >another 300 bears and has room for the pile of 300 bears that are
> > >waiting there. (Take them.)
> > >
> > >The donkey is again carrying 1000 bears. Walk the remaining 700 miles.
> > >You will have taken 300 bears to the market (and left 1100 behind).
> > >
> > >Therefore, the answer is at least 300. Probably more, of course.

> Using a depot:
>
> 1. Stock up the depot: Load 1000 GBs; walk 333 1/3 miles;
> leave 333 1/3 GBs at the depot; walk back 333 1/3 miles.
> 2. Final leg: Load 1000 GBs; walk 333 1/3 miles; load the 333 1/3 GBs
> from the depot.
>
> You have now effectively moved the origin for your final leg (with 1000
> GBs) ahead 333 1/3 miles. Walk the remaining 667 2/3 miles to the
> market. You have 333 1/3 GBs remaining on the donkey, and can sell 333
> of them (and maybe also the partly chewed 1/3 one if someone is desperate).
>
> Note that you have used only 2000 of the original 3000 GBs, having left
> 1000 GBs behind at the origin. Instead of wasting them, you can use
> them to push your depot (call it Z) forward some amount by using
> another, previous depot (call it Y).

[Error corrected:]

> Y will need to have 2000 GBs, in order to be the new origin for stocking
> depot Z. You can not stock Y in 1.5 roundtrips like depot Z, since the
> donkey cannot carry enough. With < 1000 GBs moveable per trip, you need
> at least 2.5 roundtrips. Coincidentally, those 3 trips can carry 3000 GBs total
> (3 donkey loads), which is exactly the number of GBs you have to start with
> (ah, if only real life were as tidy as maths problems). So, for the 5 legs of the
> 2.5 roundtrips you will use 1000 GBs for donkey fuel (3000 to start with - 2000 placed
> at Y), so each leg uses 200 GBs. Thus depot Y is 200 miles from the origin.
>
> So depot Z will be 200 miles closer to the market, so you will have 200
> more GBs remaining from the 1000 you start out with on the final leg
> from Y to the market. So the total remaining at the market will be
> 333 1/3 + 200 = 533 1/3 GBs.
>
>
> > >(I don't see how to get the donkey back, though.)
>
> Hopefully there is some suitable long-distance donkey food available at
> the market which is much cheaper per mile than GBs, and which the donkey
> can carry 1000 miles' worth. And besides, if you only feed the donkey
> GBs it is sure to get diabetes and other health problems.
>
> Alternatively, sell the pre-diabetic donkey.

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