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Journal of Information Science and Engineering, Vol. 28 No. 1, pp. 99-113 (January 2012)

Solving Nine Layer Triangular Nim*

YI-CHANG SHAN, I-CHEN WU, HUNG-HSUAN LIN AND KUO-YUAN KAO+
Department of Computer Science
National Chiao Tung University
Hsinchu, 300 Taiwan
+Department of Information Management
National Penghu University of Science and Technology
Penghu, 880 Taiwan

Triangular Nim, one variant of the game Nim, is a common two-player game in Taiwan and China. In the past, Hsu [9] strongly solved seven layer Triangular Nim while some of the authors recently strongly solved eight layer Triangular Nim. The latter required 8 gigabytes in memory and 8,472 seconds. Using a retrograde method, this paper strongly solves nine layer Triangular Nim. In our first version, the program requires four terabytes in memory and takes about 129.21 days aggregately. In our second version, improved by removing some rotated and mirrored positions, the program reduces the memory by a factor of 5.72 and the computation time by a factor of 4.62. Our experiment result also shows that the loss rate is only 5.0%. This is also used to help improve the performance.

Keywords: Nim, Triangular Nim, retrograde, misere games, impartial games

Full Text () Retrieve PDF document (201201_07.pdf)

Received February 26, 2011; revised August 19, 2011; accepted August 29, 2011.
Communicated by Yuh-Jye Lee.
* This work was supported by the National Science Council of Taiwan, under contracts No. NSC 97-2221-E-009-126-MY3 and NSC 99-2221-E-009-102-MY3.