Octal Game - See Also

See Also

Octal games like Nim, in which every move transforms a heap into zero or one heaps, are called quaternary games because the only digits that appear are 0, 1, 2, and 3. The octal notation may also be extended to include hexadecimal games, in which digits permit division of a heap into three parts. In fact, arbitrarily large bases are possible. The analysis of quaternary, octal, and hexadecimal games show that these classes of games are markedly different from each other, and the behavior of larger bases has not received as much scrutiny.

Some octal games with different codes are closely related to each other. In the game 0.07, called Dawson's Kayles, a move is to remove exactly two tokens from a heap and to distribute the remainder into zero, one, or two heaps. Dawson's Kayles is named for its (non-obvious) similarity to Dawson's Chess, in that Dawson's Kayles heap of n+1 tokens acts exactly like a Dawson's Chess heap of n tokens. Dawson's Kayles is said to be a first cousin of Dawson's Chess.