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Intriguing Logic Puzzle
Greg
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Post Posted: Sat Oct 07, 2006 4:05 pm
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I blundered across an intriguing scientific allegory somewhere out there. I can't find it now, but it went something like this.

If you were fill a small glass with salt water right up to its rim, and then drop an Alka Seltzer tablet into the glass, you'd get a bit of mess on your kitchen counter. From that, we can conclude that Alka Seltzer tablets cause vessels of salt water to increase in volume and overlfow.

So, what would happen if you were to toss an Alka Seltzer tablet into the Atlantic Ocean? Would it make a difference if you used a really powerful slingshot to throw the Alka Seltzer tablet way out? What if everybody in the world tossed an Alka Seltzer tablet into the ocean? (That would be about 6 billion Alka Seltzer tablets.)

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Greg
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Ghostman
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Post Posted: Sat Oct 07, 2006 4:44 pm
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Well, the quocient of the mass of a glass of water and the mass of an Alka Seltser is way much bigger than that of 6 billion Alka Seltzer and all the water in the world. So I'm guessing we would not drawn.

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David D.
miros1
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Post Posted: Sat Oct 07, 2006 6:35 pm
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After you give the answer to this one, I'll supply a mathematical one...

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Greg
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Post Posted: Sat Oct 07, 2006 7:54 pm
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The point of the first exercise is as David surmised: Although a scientific phenomenon can have a dramatic effect on a small scale, extrapolating it to the the large scale more often than not doesn't make sense.

Even something as dramatic as six billion repetitions of the small-scale event adds up to no measurable effect on the large scale.

In other words, the vast oceans of Mother Earth really wouldn't give a flip if the entire population of the planet were to venture to their coasts for a happy Fizzies party.

It's really a lesson in humility: We vain humans think we are powerful, but all our works are as nothing compared to the forces of nature.

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miros1
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Post Posted: Sun Oct 08, 2006 9:00 am
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Ok, here's the mathematical one...

Setup: If the Earth were a perfect sphere (which it's not), and you wrapped a string around the equator...

then added 6 inches to the string and evenly distributed it around the globe...

Could an ant walk under the string?

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Rose/Miros
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Ghostman
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Post Posted: Sun Oct 08, 2006 9:41 am
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yes

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David D.
Greg
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Post Posted: Tue Oct 10, 2006 9:40 am
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miros1 wrote:
Ok, here's the mathematical one...

Setup: If the Earth were a perfect sphere (which it's not), and you wrapped a string around the equator...

then added 6 inches to the string and evenly distributed it around the globe...

Could an ant walk under the string?


I remember when Dr. Green posed that question in Physics 101. The way he phrased it was to ask if you would be able to get under the rope, which invoked the answer: It depends on how skinny you are!

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miros1
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Post Posted: Tue Oct 10, 2006 9:44 am
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I assume he added more than 6 inches to the string... no normal human is gonna fit through an inch of clearance!

I heard it from Dr. Reed in Abstract Algebra. She said it caused her to not believe in pi for several years. Yes, she used the word 'believe' and she has since departed this mortal coil, so I can't ask her why.

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Rose/Miros
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Greg
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Post Posted: Wed Oct 11, 2006 3:59 pm
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Oops. Yeah, he said six feet.

Innocent bystanders might want to know that the formula for the circumference of a circle is:
    c = 2 * PI * r

    where c is the cumference and r is the radius


Hint: To answer these questions, you do not need to know either the radius or the circumference of the Earth.

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Intriguing Logic Puzzle
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