[NatureNS] Christmas brain teazer

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From: c.majka@ns.sympatico.ca
Date: Wed, 20 Dec 2006 17:51:10 -0400
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Hi Dave,

Nice riddle: made me scratch my head for a few minutes, However, as  
Paul points out (a - b - c) = 0 and dividing by 0 (at the last step)  
allows one to prove whatever one wishes. ;->

Cheers,

Chris

On 20-Dec-06, at 9:17 AM, David & Alison Webster wrote:

> Dear All,     Dec 20, 2006
>    I recently came across an old article about Raymond Smullyan, a
> highschool dropout who e.g. satisfied the course requirements for a  
> PhD
> in Math and Philosophy by teaching the required courses. He also  
> created
> many logic puzzles. One thing leads to another, so I blew the dust off
> of an old copy of Martin Gardner's 1959 Mathematical Puzzles and
> Diversions.
>
>    One of his fallacies follows. I hope you have not seen this  
> previously.
> Proof that unequal numbers are equal
>
>    Given two numbers a & b such that b is smaller than a by an amount
> c; thus
>
> a = b + c
>
> prove that a = b
>
> multiply both sides by (a - b) to obtain--
>
> a^2 - ab = ab +ac - b^2  - bc
>
> subtract ac from both sides to obtain
>
> a^2 - ab - ac = ab - b^2  - bc
>
> Factor :
> a ( a - b -c) = b ( a - b -c)
>
> Divide both sides by ( a - b - c) to obtain
>
> a = b
>
> QED
>
>    "The road to correct conclusions is full of pitfalls" (DHW, Dec  
> 20, 2006).
>
> Merry Christmas, Dave Webster, Kentville
>
>

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