You have a sheet of graph paper and a compass. Draw a circle that passes through more than 8 grid intersections. Specifically, draw the smallest possible such circle.
For example, the following circle only passes through 8 grid intersections, and so is not a solution.
To post your answer, just post a comment with the
radius of the circle (please do not post an image). For example, if you were posting the example above as an answer, post "r=square root of 5" or similar text. I will post the correct answer (and winner) as another blog post.
(FYI, this has also been posted on Facebook. Facebook comments will also be in the running to win.)
Adding whitespace so you have to scroll down to see the solution in the comments.