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A characterization of achievable patterns of the MN-puzzle problem

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Abstract

One important MN-puzzle problem is to find a sequence of up-down and right-left movements of the empty-cell so that a goal-pattern can be achieved from a given initial-pattern. The second problem is to characterize the totality of the goal-pattern from a given initial-pattern. The third problem is finding the fewest movements to achieve it. In this paper, these problems will be completely solved.

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References

  1. Marshall Hall, Jr, The Theory of Groups, The Macmillan Co., 1959.

  2. N.J. Nilsson, Principles of Artificial Intelligence, Tiogo Publising Co., 1980.

  3. P.H. Wiston, Artificial Intelligence, Addison-Wesley, 1977.

  4. H. Dudeney, The Canterbury Puzzles, Dover Publications, 1958.

  5. W. Ball, Mathematical Recreations and Essays, Macmillan And Co., 1931.

  6. H. Dudeney, Puzzles and Curious Problems, edited by M. Gardner, Charles Scribner’s Sons, 1967.

  7. M. Gardner, The Scientific American Book of Mathematical Puzzles and Diversions, Simon and Schuster, 1961.

  8. M. Gardner, The Second Scientific American Book of Mathematic Puzzles and Dicersions, Simon and Schuster, 1961.

  9. M. Gardner, Mathematical Games, Scientific American, 210(2) 213(3), 222–236, September 1965.

    Article  Google Scholar 

  10. W.A. Wickelgren, How to Solve Problems, W.H. Freeman, 1974.

  11. W. Woolsey Johson and W.E. Story, Notes on the “15” Puzzle,The American Journal of Mathematicals, 11(1879), 397–404.

    Article  Google Scholar 

  12. Neal H. Mccoy, Introduction to Modern Algebra, Allyn and Bacon, Inc., 1975.

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Authors and Affiliations

  1. Institute of Computing Technology, Academia Sinica, Beijing, China

    Yang Hongqing

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  1. Yang Hongqing
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Yang, H. A characterization of achievable patterns of the MN-puzzle problem. J. of Comput. Sci. & Technol. 5, 266–274 (1990). https://doi.org/10.1007/BF02945315

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  • DOI: https://doi.org/10.1007/BF02945315

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