Guess the Last Ball: An Exercise in Mathematical Modeling

Guess the Last Ball: An Exercise in Mathematical Modeling


Fakhar Lohdi
National University of Computer and Emerging Technologies (NUCES)
Lahore, Pakistan

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This video lesson uses the technique of induction to show students how to analyze a seemingly random occurrence in order to understand it through the development of a mathematical model. Using the medium of a simple game, Dr. Lodhi demonstrates how students can first apply the ‘rules’ to small examples of the game and then, through careful observation, can begin to see the emergence of a possible pattern. Students will learn that they can move from observing a pattern to proving that their observation is correct by the development of a mathematical model. Dr. Lodhi provides a second game for students in the Teacher Guide downloadable on this page. There are no prerequisites for this lesson and needed materials include only a blackboard and objects of two different varieties - such as plain and striped balls, apples and oranges, etc. The lesson can be completed in a 50-minute class period.

这节视频课利用归纳法向学生展示如何建立一个数学模型来分析理解看似随机的事件。通过一个简单的游戏,Dr. Lodhi 演示了学生是如何在一开始将“规则”运用到游戏中的小部分例子上,然后通过细致的观察,开始发现一个可能的规律。学生们将学习从观察一种规律到建立一个数学模型来证明观察的正确性。Dr. Lodhi 在教师指导里还为学生们提供了第二种游戏,可以从此网页下载。这节课不需要什么前提条件,也不需要什么教材,只需要一块黑板和两种不同种类的物体,例如纯色球和条形球,苹果和橙子等等。这节课可以在50分钟的课堂里完成。

Instructor Biography

Dr. Lodhi is a professor in the Department of Computer Science and head of the Software Engineering Research Center (SERC) at NUCES. He is a co-founder and former director of engineering at Vroom Technologies. His areas of interest include software engineering, software metrics, and object oriented methods.

Dr. Lodhi 是NUCES计算机系的一名教授 和软件工程研究中心(SERC)的负责人。他还是Vroom Technologies 的创始人之一和前工程部主任。他的研究领域包括软件工程,软件度量以及面向对象技术。

Additional Online Resources

This is a lesson on mathematical induction presented by

This is a module on Proof by Induction from the website of Connexions, a place to view and share educational material made of small knowledge chunks called modules that can be organized as courses, books, reports, etc.