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Don't drink and run (Posted on 2006-04-03) Difficulty: 2 of 5
A man runs n times round a circular track with radius t miles.
He drinks s quarts of beer for every mile that he runs.
Prove that he will only need one quart!

See The Solution Submitted by Jer    
Rating: 3.0000 (2 votes)

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Solution Measure for measure | Comment 3 of 5 |

Lets begin with 1 quart = 1 quart.

The equation for the area of a circle, c, is c = 2πr2,
thus r = √(c/2π).  We can, therefore, restate the equation as:
1 quart = 1 qua(√c/2π)t

On the complex plane, , if we appy the Guinness factor to the circle, we get a hyperbolic curve. We can then apply the Coor's Corollary and divide the first coefficient to the hypertangent, n, and substitute this in the equation for a.  We now have:
1 quart = 1 qu n (√(c/2π)t

Now taking the Heineken derivative for ∆q/t and multiplying by the Pilsner constant (ps) we rewrite the equation:
1 quart = (√(c/2π))2)u)/(1/8π(ps))

Simplifying we get:
1 quart = 4 (c)(u)(ps)

And we know 4 (c)(u)(ps) = 2 pi(n)(t)(s)

Edited on April 4, 2006, 4:23 am
  Posted by Dej Mar on 2006-04-04 00:25:30

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