I learned of the following problem from Alexander Bogomolny: Given a square grid with 25 points, arranged in 5 rows and 5 columns, can you draw five circles that pass through all of the points?
After working on this problem for a while, I found that there are many solutions, so I wrote a Python script to list them all. It turns out that there are exactly 13 distinct solutions up to rotations and reflections. I used D3.js to render the solutions.
There are 54 ways to cover a 6x6 grid with 6 circles.