Given two closed disks of unit radius, such that center of one lies on the circumference of the other, let M denote their union. We want to place the maximum number of points in M such that their pairwise distance is strictly greater than 1. We can show that we cannot place 10 points, and we have examples where we can place 8. Is it possible to place 9 points? We have not been able to prove that 9 points is impossible. Any suggestions welcome. (I cannot seem to place image tags since this is my first question.. but the images showing why 10 points are impossible and a configuration showing 8 points are available at:

http://www.freeimagehosting.net/image.php?3c080eeea5.jpg, and http://www.freeimagehosting.net/image.php?7ff64600b3.jpg

respectively.

cando 10 points? – Vinayak Pathak Sep 20 '10 at 13:22lunein the computational geometry literature... – Joseph O'Rourke Sep 20 '10 at 15:06