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.
(In reply to
re: soln by Jer)
Thanks, it was an enjoyable challenge.
I think the figure link works... Could you double check maybe?
As for the site - I believe the vast majority of "no solution" problems have correct user solutions posted, more or less. The author would know. Some don't. For me, that is quite a distinction. However, as one user of the site, I can not search for problems remaining stubbornly unsolved because the label has no sure meaning.
BTW, posting problems you do not know the solution to is fine by me as well.
Edited on November 29, 2018, 7:38 pm
re(2): soln
