I enjoy mathematical nuggets and puzzles, e.g. from: @mathisstillfun, @mathssolutionz, Mirangu. They are an invitation to explore.

Here are some of the more interesting, surprising, and/or fun. My answers with discussion and extensions are written up as PDFs.

• Problem 1 - sum of squared distances from polygon corners to enclosed circle
• Problem 2 - an invariant expression for all roots of unity
• Problem 3 - a power bound on factorial