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.

Algebra / Arithmetic
Problem Solving / General

Problem Posing
Try a Smaller Problem

MP1 - Make sense of problems and persevere in solving them.
MP7 - Look for and make use of structure.
MP8 - Look for and express regularity in repeated reasoning.