Skip to content# The 1-to-100 problem

**Classifications**

Author(s): Joshua Zucker

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.

Topics covered: Algebra / Arithmetic, Problem Solving / General

Session styles: Problem Posing, Try a Smaller Problem

Supporting materials: Facilitator Guides

Associated Math Circles: MTC Network