Skip to content # The 1-to-100 problem

## Activity Guide

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

Zucker, Josh. (2020). The 1-to-100 problem. In S. Bowen (Ed.), Math Circle Activity Database. American Institute of Mathematics. https://mathcircles.org/activity/https://mathcircles.org/activity/the-1-to-100-problem/

Contributor(s): Joshua Zucker

Math Circles: MTC Network

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

This exercise can be used for middle school students and older. The original problem seems almost impossibly difficult, but there are obviously many ways to approach it by considering simpler problems. As they investigate it, students are actually drilling their multiplication and addition facts. In addition, depending on how detailed a study you want to make, the students will be forced to do a lot of simple algebra to obtain the results they need. They may also learn something about commutativity, associativity, and symmetric functions.