Computation Records
A complete analysis of an octal game results in finding its period and preperiod of its nim-sequence. It is shown in Winning Ways for your Mathematical Plays that only a finite number of values of the nim-sequence is needed to prove that a finite octal game is periodic, which opened the door to computations with computers.
Octal games with at most 3 octal-digits have been analyzed through the years. There are 79 non-trivial octal games, among which 14 have been solved :
- .156 by Jack Kenyon in 1967
- .356, .055, .644 and .165 by Richard Austin in 1976
- .16, .56, .127 and .376 by Anil Gangolli and Thane Plambeck in 1989
- .454, .104, .106, .054 and .354 by Achim Flammenkamp between 2000 and 2002
There remain 63 of these games, despite the computation of millions of nim-values by Achim Flammenkamp.
Read more about this topic: Octal Game
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