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Author Topic: Re: I wanna present a puzzle too DISCUSSION THREAD -- SPOILER ALERT  (Read 1771 times)

ivan

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Re: I wanna present a puzzle too DISCUSSION THREAD -- SPOILER ALERT
« on: February 02, 2011, 05:34:55 PM »
If you haven't cracked Jaepheth's puzzle yet, and still plan on trying, then don't read beyond this post.






















Ok, then.
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ivan

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Re: I wanna present a puzzle too DISCUSSION THREAD -- SPOILER ALERT
« Reply #1 on: February 02, 2011, 05:35:12 PM »
Quote from: Jaepheth on February 01, 2011, 12:51:59 AM
Ok, since this is a pretty difficult problem I'll give you all a Big Hint

Hint, shmint. What are you trying to pull here? The dudes pay the same price every week, so over time they get the same deal. Anyone can see that!

Here, I will prove it:

Week 1: Price $5 per kilo. Adam buys 1 kilo for $5, Bob buys .2 kilos for $1
Week 2: Price $4 per kilo. Adam buys 1 kilo for $4, Bob buys .25 kilos for $1.
Week 3: Price $8 per kilo. Adam buys 1 kilo for $8, Bob buys .125 kilos for $1.
Week 4: Price $2 per kilo. Adam buys 1 kilo for $2, Bob buys .5 kilos for $1.

Total: Adam bought 4 kilos for $19. Bob bought 1.075 kilos for $4.

In aggregate, Adam paid $4.75 per kilo, and Bob paid exactly the same, $3.72 per kilo.

Oh shit.

Common sense didn't work out so well.

Another thing common sense tells me is that one method of buying should be advantageous when prices are rising, and a disadvantageous when prices are falling. But that also appears to be false.

So, about that Schwarz Inequality... how does it work?
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"I TYPE 120 WORDS PER MINUTE, BUT IT'S IN MY OWN LANGUAGE!"  -Detta

xolik: WHERE IS OBAMA'S GIFT CERTIFICATE?
Demosthenes: Is that from the gifters movement?

Detta: Crappy old shorts and a tank top.  This is how I dress for work. Because my job is to get puked on.
Demosthenes: So is mine.  I work in IT.

bananaskittles: The world is 4chan and God is a troll.

Jaepheth

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Re: Re: I wanna present a puzzle too DISCUSSION THREAD -- SPOILER ALERT
« Reply #2 on: February 09, 2011, 02:59:14 AM »
Strictly speaking, the Cauchy-Schwarz inequality isn't absolutely necessary to solve the problem. Perhaps I just felt like being mean.

But what if there were two n dimensional vectors, the lengths of which described Adam and Bob's respective averages?
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Banshee

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Re: I wanna present a puzzle too DISCUSSION THREAD -- SPOILER ALERT
« Reply #3 on: February 09, 2011, 08:11:07 AM »
Now you're just trying to act like a stupid-face smarty pants.  :slap
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ivan

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Re: I wanna present a puzzle too DISCUSSION THREAD -- SPOILER ALERT
« Reply #4 on: February 09, 2011, 10:41:31 AM »
Quote from: Banshee on February 09, 2011, 08:11:07 AM
Now you're just trying to act like a stupid-face smarty pants.  :slap

^
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"I TYPE 120 WORDS PER MINUTE, BUT IT'S IN MY OWN LANGUAGE!"  -Detta

xolik: WHERE IS OBAMA'S GIFT CERTIFICATE?
Demosthenes: Is that from the gifters movement?

Detta: Crappy old shorts and a tank top.  This is how I dress for work. Because my job is to get puked on.
Demosthenes: So is mine.  I work in IT.

bananaskittles: The world is 4chan and God is a troll.

ivan

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Re: I wanna present a puzzle too DISCUSSION THREAD -- SPOILER ALERT
« Reply #5 on: February 09, 2011, 10:42:36 AM »
I gotta say I'm impressed, however.
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"I TYPE 120 WORDS PER MINUTE, BUT IT'S IN MY OWN LANGUAGE!"  -Detta

xolik: WHERE IS OBAMA'S GIFT CERTIFICATE?
Demosthenes: Is that from the gifters movement?

Detta: Crappy old shorts and a tank top.  This is how I dress for work. Because my job is to get puked on.
Demosthenes: So is mine.  I work in IT.

bananaskittles: The world is 4chan and God is a troll.

Jaepheth

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Re: Re: I wanna present a puzzle too DISCUSSION THREAD -- SPOILER ALERT
« Reply #6 on: February 09, 2011, 08:15:47 PM »
Ok, Here's another tidbit

When I said I was being mean. That was a clue
« Last Edit: February 09, 2011, 09:27:29 PM by Jaepheth »
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Banshee

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Re: Re: I wanna present a puzzle too DISCUSSION THREAD -- SPOILER ALERT
« Reply #7 on: February 09, 2011, 08:52:48 PM »
Quote from: Jaepheth on February 09, 2011, 08:15:47 PM
Ok, Here's another tidbit

When I said I was being mean. That was a [http://en.wikipedia.org/wiki/Mean]clue[/url]

What is this I don't even
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Jaepheth

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Re: Re: I wanna present a puzzle too DISCUSSION THREAD -- SPOILER ALERT
« Reply #8 on: February 15, 2011, 10:00:12 PM »
Ok, THIS is the crux of the proof. Now you just have to algebra the numbers to show who is paying what mean.
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Demosthenes

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Re: I wanna present a puzzle too DISCUSSION THREAD -- SPOILER ALERT
« Reply #9 on: February 15, 2011, 10:15:47 PM »
Hey... I knew this was familiar.  There was a Jensen's Inequality problem that had to do with something like this, years and years ago when I was still in school.
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