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Two puzzles, same analysis

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#1 bonanova



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Posted 02 March 2013 - 10:40 AM

This is not a puzzle but an observation of something that to me was surprising.


Two unrelated puzzles - the oldie with a twist and the weight-loss problem, succumb to identical analyses.

Both present an equation that does not have an analytical solution for a crucial angle, let's call it x.

The equation that presents itself is this:


tan(x) = x + k


where k is some constant, and x is expressed in radians.

You can't get a general solution x = x(k), but you can solve the equation iteratively for x for any particular value of k.

When that is done, the the desired answer turns out to be


cos(x) = answer.


I wonder whether there is a prototypical problem for which this is the best analysis?


Did this post turn out to be a puzzle after all?

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Vidi vici veni.



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Posted 02 March 2013 - 11:16 PM

Spoiler for I am not sure if i understand the question but

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