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July 24, 2025, 06:01:22 am
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Author Topic: Apples  (Read 12591 times)  Share 

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kamil9876

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Apples
« on: July 01, 2009, 12:36:36 am »
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Long story - short:
  • There are 3000 apples at town A
  • A truckie wants to deliver apples from town A to B
  • |AB|=1000km
  • Max Capacity of truck is 1000apples
  • Every 1km truckie eats one apple


1.) What is the maximum number of apples he can deliver to B?
2.) What's the minimum value of apples that he should start of with (rather than 3000) at A so that he can deliver 1000 apples to B?

EDIT:

Lol ok, maybe I should add that he can drop off his load somewhere and leave it there without the apples rotting or being burgled :)
« Last Edit: July 01, 2009, 12:41:09 am by kamil9876 »
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Over9000

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Re: Apples
« Reply #1 on: July 01, 2009, 12:38:52 am »
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Quote from: kamil9876 on July 01, 2009, 12:36:36 am
Long story - short:
  • There are 3000 apples at town A
  • A truckie wants to deliver apples from town A to B
  • |AB|=1000km
  • Max Capacity of truck is 1000apples
  • Every 1km truckie eats one apple


1.) What is the maximum number of apples he can deliver to B?
2.) What's the minimum value of apples that he should start of with (rather than 3000) at A so that he can deliver 1000 apples to B?
1.)0, 2.) impossible?
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kamil9876

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Re: Apples
« Reply #2 on: July 01, 2009, 12:40:22 am »
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Lol ok, maybe I should add that he can drop off his load somewhere and leave it there without the apples rotting or being burgled :)
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Over9000

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Re: Apples
« Reply #3 on: July 01, 2009, 12:42:11 am »
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Quote from: kamil9876 on July 01, 2009, 12:40:22 am
Lol ok, maybe I should add that he can drop off his load somewhere and leave it there without the apples rotting or being burgled :)
Oh
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Mao

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Re: Apples
« Reply #4 on: July 01, 2009, 12:55:07 am »
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Kinda guessing:

1) 500

2) 4000

^^ I have a feeling that is very very wrong though
« Last Edit: July 01, 2009, 12:58:04 am by Mao »
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kamil9876

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Re: Apples
« Reply #5 on: July 01, 2009, 01:09:11 am »
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What strategy did you use in 2? I think it can show why (1) is wrong :)
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/0

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Re: Apples
« Reply #6 on: July 01, 2009, 01:41:04 am »
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for a) I can get 400 at most
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TrueTears

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Re: Apples
« Reply #7 on: July 01, 2009, 01:42:04 am »
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I got >450 at least l0l
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kamil9876

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Re: Apples
« Reply #8 on: July 01, 2009, 11:14:43 pm »
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Just to keep people motivated, I would like to inform you that no one's answer to (1) is correct. I know that for sure as I know how to deliver more apples. I'm 99% sure Mao's answer to b is correct, I suspected it is 4000 myself based on heurestical reasoning so I strongly encourage proofs for this part as well :)
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shinny

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Re: Apples
« Reply #9 on: July 02, 2009, 01:23:43 am »
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I've gotten 668 for 1, unless I'm misunderstanding the rules. This figure could increase marginally if I started working with theoretical recurring numbers, but I'm just sticking with integers for both the kilometers and apples for now.

EDIT: Scrap that, I think I just beat it =\ Gimme a sec.

EDIT 2: OK whoops errors. I've gotten 666 as my best. Yesno?
« Last Edit: July 02, 2009, 01:44:45 am by shinny »
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kamil9876

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Re: Apples
« Reply #10 on: July 02, 2009, 01:42:03 am »
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Unfortunately I'm still in the lead. But good to see progress being made. Maybe from now on we should post strategies along with the numbers just so to see how the ideas improve :)
Basically, we're getting pretty close to my number, but I don't know how close we're getting in terms of ideas which is what I'm more interested in hehe
« Last Edit: July 02, 2009, 01:43:40 am by kamil9876 »
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Re: Apples
« Reply #11 on: July 02, 2009, 01:52:10 am »
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Hmm, probably a fault in my initial assumption then. Basically, I think 666 is the best you can get assuming you use one drop-off point. The table should hopefully make things more clear.
A667B
300000
20003330
10006660
09990
00666
Note: sorry I suck at formatting in bbcode D:
Basically, what I'm doing is grabbing 1k of apples, shipping them to the point whilst eating 1 per km, then driving back to A and not eating any apples because he has none on him atm (this is legit right?). You'll see that using 666 as the drop-off yields the same result, basically because these two numbers surround 666.6 recurring, the ideal number to ensure that you have 1000 apples at the drop off point. There's a bit more explanation to why I aimed to get 1000 apples at the drop off point (might be obvious to some of you), but it's redundant anyway if you've beaten 666 kamil =\. Mind sharing what you've got atm?

EDIT: Also works for 333.3 recurring, i.e. 334 and 333. Relies on the same principle really, but using these two numbers leaves 2k at the drop off, which ultimately gives the same answer I got above.
« Last Edit: July 02, 2009, 02:12:27 am by shinny »
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kamil9876

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Re: Apples
« Reply #12 on: July 02, 2009, 02:05:47 am »
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Yes sorry I forgot to add that if there are no apples in the truck he can drive without eating (I read this problem like four years ago and I was just reminded that it had the word "temptation" in it so that explains that). I didn't see the solution to it though because it was on some Math Genius's blog and there were no solutions lol and I don't think the page is around anymore, and so my answer is not 100% certain but I have heuristically convinced myself that it is.

So far I have 750. I worked that out by working it out for 2000 (since 2000=1000+1000 so only 2 journeys required which is simpler) and then extending that by figuring out what to do with the extra 1000.

Oh and Q2 I just made up myself last night so I am even less certain of that haha. Let's just treat it as a "research question" haha.
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Re: Apples
« Reply #13 on: July 02, 2009, 02:09:16 am »
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Quote from: kamil9876 on July 02, 2009, 02:05:47 am
Yes sorry I forgot to add that if there are no apples in the truck he can drive without eating (I read this problem like four years ago and I was just reminded that it had the word "temptation" in it so that explains that). I didn't see the solution to it though because it was on some Math Genius's blog and there were no solutions lol and I don't think the page is around anymore, and so my answer is not 100% certain but I have heuristically convinced myself that it is.

So far I have 750. I worked that out by working it out for 2000 (since 2000=1000+1000 so only 2 journeys required which is simpler) and then extending that by figuring out what to do with the extra 1000.

Oh and Q2 I just made up myself last night so I am even less certain of that haha. Let's just treat it as a "research question" haha.

No revealing the magician's secret? ]: Stayed awake just to find out LOL I'll come back tmrw night then.
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kamil9876

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Re: Apples
« Reply #14 on: July 02, 2009, 02:12:27 am »
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Hahaha I'm staying up for /0. He's been at it for over 2hours now on "who's online" :P He shows promise :D
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