A number theory approach to problem representation and solution

Authors:
Stewart N. T. Shen;Edward R. Jones
Affiliations:
Virginia Polytechnic Institute and State University;Virginia Polytechnic Institute and State University
Venue:
IJCAI'73 Proceedings of the 3rd international joint conference on Artificial intelligence
Year:
1973

Citing 3
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Abstract

A number theory approach to problem solving is presented using the tower of cubes puzzle as an example. Some conventional methods of solving the puzzle are first discussed. The puzzle is then thoroughly studied using an entirely different approach. Special numbers are used to represent the different colors on the sides of the cubes. A description matrix is used to compress the problem representation. The solution method becomes very efficient because of the concise representation of the problem. Two theorems are developed to verify the solution method. A generalization of the puzzle is also discussed.