Solving Eight Layer Triangular Nim

Abstract

In the past, Hsu [3][4] solved all Triangular Nim positions with side size seven, In this paper, we propose a new retrograde algorithm to solve all Triangular Nim positions with side size eight. This algorithm makes use of unbalanced ratios of win and loss to reduce greatly the computation time to 2.6 hours. In addition, this algorithm also fits into the traditional 32-bit operating systems. In contrast to another independent result [1], they required 64-bit operating systems and took about 17.1 hours.