Interesting/Paradoxical Math Problems for High School Students I am creating a math course for high school students (not necessarily advanced) about interesting/paradoxical math problems (think Monty Hall and Hilbert's Hotel). What are some other interesting math problems that are accessible to average high school students? So no calculus or higher required (unless the necessary machinery can be taught within 30 minutes). Thanks!

Zeno's paradox could be fun. I had a lively discussion with some high school students about whether $0.999999... = 1$, and we enjoyed looking at pictures such as this one:

While this topic comes up against the idea of a limit and infinite series, it doesn't have to be presented with that language.
