In article <see-5B769E.email@example.com>, Barb Knox <firstname.lastname@example.org> wrote:
> In article <email@example.com>, > Stone Bacchus <firstname.lastname@example.org> 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 > > <email@example.com> 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).
> 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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