Greetings, Not sure if my solution is worth posting.... I took a naive axis-aligned bounding box approach. http://tastyspleen.net/~billk/ruby/quiz/157-smallest-circle/157_naive_aabb.rb I knew it would be inaccurate, but I was curious how bad it would be, so I wrote an OpenGL/GLUT based visualizer: http://tastyspleen.net/~billk/ruby/quiz/157-smallest-circle/157_smallest_circle_visualization.rb (The visualizer will work with any quiz solution that provides the encircle() and generate_samples(n) methods, and Point#x and Point#y.) Occasionally the naive approach lucks out with a dataset that allows it to look good: http://tastyspleen.net/~billk/ruby/quiz/157-smallest-circle/157_vis.png But more often it looks something like this: http://tastyspleen.net/~billk/ruby/quiz/157-smallest-circle/157_vis_naive.png I had planned to improve my solution by taking an approach similar to Justin Ethier's. . . . By iterating and "moving the circle center towards the outlier as the radius is reduced, while all points still are within the radius." I may still code that if I have time... but then again, it's already been done. :) Regards, Bill