Education Technology

Pebbling the Chessboard

Published on 05/18/2016

Activity Overview

It’s amazing how often sequences and series pop up in problem solving. In this deceptively challenging problem three discs are placed on a chessboard in a bounded region. The task is to move the pieces out of this region with the only complication being that pieces double when moved. After you’ve struggled to find the solution a geometric sequence comes to the rescue!

Objectives

  • Understand the limiting behaviour as n approaches infinity in a geometric sequence and its dependence on the value of the common ratio (ACMMM074)
  • Use geometric sequences in contexts involving geometric growth or decay, such as compound interest. (ACMMM076)

Vocabulary

Sum, infinity

About the Lesson

Students begin by exploring the Pebbling the Chessboard problem. It is not long before students challenge whether or not the problem has a solution. Rather than continuing with trial and error attempts, numbers are used to record the moves, leading to the discovery that a geometric sequence is produced. The sum of the terms in the sequence holds the answer to the problem.
A PowerPoint file is also included so that teachers can demonstrate the problem (and solution) to students.