Conrey, Brian. Cristiani, Corinne. (2022). Pigeonhole Principle and Parity Problems. In S. Bowen (Ed.), Math Circle Activity Database. American Institute of Mathematics. https://mathcircles.org/activity/pigeonhole-principle-and-parity-problems
The pigeonhole principle states that if n pigeons are put into m cubbies, with n > m, then at least one cubby must contain more than one pigeon. Parity problems deal with odd and even integers. Here is a collection of problems that can be used in a single problem solving session, or as individual teaser questions.
Problems are suitable for a math circle or classroom.