I wish to create 5 identical white circles of some lesser radius, which I will place on top of the black circle and completely obscure (cover) the black circle.

What is the smallest radius which I can make the smaller circles and still meet my requirement?

As this is a difficuty level 4 problem, the nice pentagon configuration would seem too easy, and it is! The problem is mentioned in Rouse Ball pp. 97-99 (no spoiler, really) and the radius ratio of .609383:1 is given as optimal whereas the pentagon approach gives .618034:1. The problem is evidently an old one as a solution was published by Neville in 1915. As some people get very upset by Google searches, I won't at this time say what I found using Google. 

Posted by Richard on 2004-10-17 17:42:08