Solving 9 layer Triangular Nim

Yi Chang Shan*, I-Chen Wu, Hung Hsuan Lin, Kuo Yuan Kao

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

Triangular Nim, one variant of the game Nim, is a common two-player game in Taiwan and China. In the past, Hsu strongly solved 7 layer Triangular Nim while some of the authors recently strongly solved 8 layer Triangular Nim. The latter required 8 gigabytes in memory and 8878 seconds. Using a retrograde method, this paper strongly solves 9 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 5.86 and the computation time by a factor of 4.38. Our experiment result also shows that the loss rate is only 5.0%. This is also used to help improve the performance.

Original languageEnglish
Title of host publicationProceedings - International Conference on Technologies and Applications of Artificial Intelligence, TAAI 2010
Pages421-426
Number of pages6
DOIs
StatePublished - 1 Dec 2010
Event2010 15th Conference on Technologies and Applications of Artificial Intelligence, TAAI 2010 - Hsinchu, Taiwan
Duration: 18 Nov 201020 Nov 2010

Publication series

NameProceedings - International Conference on Technologies and Applications of Artificial Intelligence, TAAI 2010

Conference

Conference2010 15th Conference on Technologies and Applications of Artificial Intelligence, TAAI 2010
CountryTaiwan
CityHsinchu
Period18/11/1020/11/10

Keywords

  • Nim
  • Retrograde
  • Triangular Nim

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    Shan, Y. C., Wu, I-C., Lin, H. H., & Kao, K. Y. (2010). Solving 9 layer Triangular Nim. In Proceedings - International Conference on Technologies and Applications of Artificial Intelligence, TAAI 2010 (pp. 421-426). [5695486] (Proceedings - International Conference on Technologies and Applications of Artificial Intelligence, TAAI 2010). https://doi.org/10.1109/TAAI.2010.73