In article <firstname.lastname@example.org>, Stone Bacchus <email@example.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 > <firstname.lastname@example.org> 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.
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).
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. So, dividing the 2000 GBs by 4 stocking loads (2 roundtrips and twice the load for the final one-way trip) gives 500 GBs to stock per trip.
The donkey can carry 1000 GBs total, leaving 500 for donkey food on each roundtrip. The donkey uses half of this for each leg of a roundtrip, or 250 GBs. Thus depot Y can be 250 miles from the origin.
Except, you run out of GBs. 250 GBs * 5 legs = 1250 GBs, but there are only 1000 GBs left behind. So, the maximum donkey fuel per leg is only 1000 / 5 = 200 GBs. Thus depot Y can only be 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. 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 diabetic donkey.
 Exercise: why twice?
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