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Dawson’s chess revisited

Author

Listed:
  • Keivan Borna

    (Kharazmi University
    Institute for Research in Fundamental Sciences (IPM))

  • N. A. Ashrafi Payaman

    (Kharazmi University)

Abstract

In this paper we prove that in a Quasi-Dawson’s Chess (a restricted version of Dawson’s Chess) playing on a 3 × d board, the first player is loser if and only if d (mod)5 = 1 or d (mod)5 = 2. Furthermore, we have designed two algorithms that are responsible for storing the results of Quasi-Dawson’s Chess games having less than d + 1 files and finding the strategy that leads to win, if there is a possibility of winning (by a wining position, we mean one from which one can win with best play). Moreover we show that the total complexity of our algorithms is O(d 2). Finally we have implemented our algorithm in C++ which admits the main results of the paper even for large values of d.

Suggested Citation

  • Keivan Borna & N. A. Ashrafi Payaman, 2013. "Dawson’s chess revisited," Indian Journal of Pure and Applied Mathematics, Springer, vol. 44(6), pages 771-794, December.
    • Handle: RePEc:spr:indpam:v:44:y:2013:i:6:d:10.1007_s13226-013-0042-7
    DOI: 10.1007/s13226-013-0042-7
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