Skip to content # Pigeonhole Principle and Parity Problems

## Activity Guide

# This guide looks at the activity in detail and goes into the underlying math.

## More Resources

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

Contributor(s): Brian Conrey, Corinne Cristiani

Math Circles: MTC Network

- Activity Description
- Topics Covered
- Session Styles
- Mathematical Practices

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.

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.

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.