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5 circles in a hexagon. (Posted on 2018-11-25) Difficulty: 5 of 5
Pack five unit circles in the smallest regular hexagon possible.

The exact solution for the smallest possible side length of the hexagon is given by the largest real root of a fourth degree polynomial:

P(x)=ax4+b√(3)x3+cx2+d√(3)x+e

Where a,b,c,d,e are integers. Find them.

No Solution Yet Submitted by Jer    
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re: soln | Comment 6 of 9 |
(In reply to soln by Steven Lord)

Kudos!  Your longhand solution looks great.  It's pretty much the way I did it.  The algebra is quite a slog.   The first link doesn't work though.


The issue with solved/unsolved/no official solution has always been a problem with this site.   Other puzzle sites require you to submit problems with a solution or a least an answer.  Just because a problem has been solved doesn't mean a person can't solve it independently.

One nice thing is you can submit problems that you can't solve here.  I have a problem like that in the queue right now:  colored triangle.

  Posted by Jer on 2018-11-29 15:44:58
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