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ERIC Number: EJ925658
Record Type: Journal
Publication Date: 2011
Pages: 10
Abstractor: As Provided
Reference Count: 2
ISSN: ISSN-0020-739X
Yet More Frogs
Shutler, Paul M. E.
International Journal of Mathematical Education in Science and Technology, v42 n4 p524-533 2011
Extending a recent paper by Derek Holton, we show how to represent the algorithm for the Frog Problem diagrammatically. This diagrammatic representation suggests a simpler proof of the symmetrical case (equal numbers of frogs of each colour) by allowing the even and odd cases to be treated together. It also provides a proof in the asymmetrical case (unequal numbers of frogs) as an extension of the symmetrical case. The issue of whether frogs of a given colour should be allowed to move in either direction is discussed. While it is possible to restrict to the case of movement in a single direction, results for bi-directional movement can be obtained by making the correspondence between the algorithm and its diagrammatic representation more concrete. The Frog Problem then becomes a form of constrained shortest path problem around the diagram, and from this point of view optimality of the algorithm becomes much clearer. (Contains 10 figures.)
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A