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

  • Sequence
  • Series
  • 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.