That's pretty neat, I wouldn't have thought to look for planar solutions. My original hope was a solution with unit circles in R^3 where the circles are Fano lines and circle intersection points the Fano points. You are saying that's not possible?
-----Original Message----- From: math-fun [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Fred Lunnon Sent: Monday, June 22, 2015 9:15 PM To: math-fun Subject: Re: [math-fun] Fano Plane puzzle
<< Does one circle really contain 4 vertices, or does it just look that way? >> DA
I hadn't noticed that rather ugly feature --- one point is rather close to a circle to which it does not belong. Another example avoiding that infelicity: https://www.dropbox.com/s/yl819xpiy716qwh/fano7pt7rg_1.gif?dl=0
Adam seems to have nailed the whole problem very neatly --- I haven't checked his reference yet, but it presumably gives an explicit construction. Incidentally, I also tried relaxation based on 14 points and centres, but it was a total failure!
WFL