Given two closed disks of unit radius, such that center of one passes through lies on the circumference of the other, et let M denote the their closed 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 can not cannot place 10 points, and we have example 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 can not 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.
