Solving nine layer Triangular Nim

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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.

Original languageEnglish
Pages (from-to)99-113
Number of pages15
JournalJournal of Information Science and Engineering
Issue number1
StatePublished - 1 Jan 2012


  • Impartial games
  • Misère games
  • Nim
  • Retrograde
  • Triangular nim

Fingerprint Dive into the research topics of 'Solving nine layer Triangular Nim'. Together they form a unique fingerprint.

Cite this