Skip to content# Pigeonhole Principle and Parity Problems

**Classifications**

Author(s): Brian Conrey, Corinne Cristiani

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.

Topics covered: Algebra / Arithmetic, Combinatorics, Geometry, Number Theory, Parity / Invariants, Problem Solving / General

Mathematical practices: MP1 – Make sense of problems and persevere in solving them., MP2 – Reason abstractly and quantitatively., MP3 – Construct viable arguments and critique others’ reasoning., MP4 – Model with mathematics., MP5 – Use appropriate tools strategically., MP6 – Attend to precision., MP7 – Look for and make use of structure., MP8 – Look for and express regularity in repeated reasoning.

Supporting materials: Facilitator Guides

Associated Math Circles: MTC Network