The Hot Game of Nim is a sub-page of the Alexander Bogomolny?s Cut The Knot! site reviewed elsewhere in MERLOT; in particular, it is one of the CTK interactive monthly columns (May, 2001) contained on the CTK page. This page explains and discusses several versions of the game of Nim and some winning strategies./p> Please see these related reviews:
This is a collection of interactive java applets with accompanying textual explanations.
Recommended Uses:
This site can be used to stimulate creative thinking and problem solving within the context of a classic mathematical game.
Technical Requirements:
A basic browser is all that is required to view the primarily textual material; a java-enabled browser is needed for the interactive java applets. This particular collection of applets is unpredictable in its performance on a MAC ? loading slowly and apparently differently on different occasions. For example the Standard Nim page shows an extra row on the MAC implementation.
Identify Major Learning Goals:
The primary goal of the main Cut the Knot site is to help readers experience mathematical topics in a positive and interactive way and to help them learn to appreciate the beauty and fascination of math. This particular page explores several variations of the game of Nim and is designed to lead students into an examination of impartial game theory.
Target Student Population:
The materials here are suitable for students of game theory and logical reasoning in impartial game settings.
Prerequisite Knowledge or Skills:
Logical reasoning skill is the only prerequisite. All of the material is presented in an accessible manner and the many java applets invite exploration and discovery.
Content Quality
Rating:
Strengths:
The content is of high quality similar to the rest of the Cut the Knot site. This particular page features a column that explores the rich variety of Nim-type games. The history is introduced and references to classic sources such as Gardner and Schwartzman are included. There are several versions of the game embedded in this page and there are links to several others. All have the common feature that the last person to make a move wins the game. Standard Nim includes rules, help and a theory section that discusses Boolean arithmetic and binary representation. Five related games are Nimble, Northcutt's Game, Plainim, Scoring and Training Turtles.
Plainim is a version on a square that allows removal and addition of counters. There are no help or explanation features for this version. Northcutt's Game features sliding black and white checkers on a rectangular board that allows reversible moves. Scoring involves subtraction with a simple slider mechanism and includes good explanations.
These applets provide a comprehensive look at Nim-type games.
Concerns:
Several of the pages have unpredictable MAC implementation.
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
The various Nim applets provide an interactive means by which to play the games with the computer as an opponent, thus allowing the user to experiment with different strategies and get immediate feedback on the results. The game theories are well described and numerous references are provided to other sources.
Concerns:
It would have been helpful to be able to restart the applet using the same configuration after having played it and lost; instead, the reset button creates a new game with a different (randomly generated) initial configuration.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
The applet controls are simple and effective.
Concerns:
None
Creative Commons:
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