Wythoff?s Nim is a sub-page of the Alexander Bogomolny?s Cut The Knot! site reviewed elsewhere in MERLOT; in particular, it is a sub-page of the Games and Puzzles section of the site. This page includes a java applet embodying a two-player strategy game that involves cornering a queen on a chessboard of sorts. An accompanying strategy analysis by Martin Gardner reveals that this game is isomorphic to Wythoff?s Nim, a version of the famous game of Nim. The recursively determined winning strategy is then analyzed as a set of numerical sequences with very deep and interesting results./p> Please see these related reviews:
This is an interactive java applet with accompanying analysis.
Recommended Uses:
This applet 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 textual material; a java-enabled browser is needed for the interactive java applets.
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 a variation of the game of Nim and a determination of a winning strategy.
Target Student Population:
The materials here are suitable for students of all levels and abilities.
Prerequisite Knowledge or Skills:
Simple logical reasoning is all that is required here.
Content Quality
Rating:
Strengths:
The content is of high quality similar to the rest of the Cut the Knot site. The applet is simple and effective and the ensuing development and analysis of strategy is excellent. The numerical sequence analysis invites the reader to explore this area in greater depth.
Concerns:
None
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
The java applet can be set at various levels of difficulty, from a 10x10 board to a 44x44 board, allowing for more in-depth analysis. The game is simple and lightly challenging.
Concerns:
It would have been helpful to be able to restart the same game 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 controls are very simple and basic.
Concerns:
Realizing that the computer moves immediately after your move takes a bit of getting used to; it would have been clearer if there had been a bit of delay programmed into the applet so that there was some differentiation between the player?s move and the computer?s move.
Creative Commons:
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