# The riddle of the 4 trolls

Started Aug 18, 2009 | Discussions thread
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 Re: A NEW problem with NO KNOWN solution, yet... REVISED In reply to Sunshine_boy, Sep 1, 2009

My initial reaction is it's impossible as stated to provide one single answer since there are multiple answers within a range.

For example, a variation of the problem is to find only integer solutions. Another is to find only the smallest integer solution.

That implies there are non-integer solutions as well, which to my point implies it's unsolvable as stated here (not a criticism at all btw...just explaining my initial take before reading the info in the link).

One can easily prove there is a range of values for 'x', the width of the base, by taking to pencils of unequal length, fixing the intersection at a given height, then sliding the (rotating really) one of the pencils back and forth through the intersection. The base and top angles change during the rotation, while the height and 90 degree angle remain constant. Now do it with the other pencil while the first remains constant. Now do both. The range is not the same since the lengths are unequal though there will be overlap.

It's a great problem because it causes one to think beyond having the necessary two sides, side-angle-side, or angle-side-angle. To put a quadratic equation to work in practical terms rather than for school work is probably more valuable than all the hum drum grinding out of school equations just to get a grade.

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