Grundy's game is an impartial game played by the following rules. Given a heap of size 
, two players alternately select a heap and divide it into
two unequal heaps. A player loses when he cannot make a legal move because all heaps
have size 1 or 2. Flammenkamp gives a table of the extremal nim-values
for this game. The nim-values of a single heap of size
, starting with 
, are 0, 0, 0, 1, 0, 2, 1, 0, 2, ... (OEIS A002188).
Grundy's Game
See also
Nim-ValueExplore with Wolfram|Alpha
References
Bogomolny, A. "Grundy's Game." https://cut-the-knot.org/Curriculum/Games/Grundy.shtml.Flammenkamp, A. "Sprague-Grundy Values of Grundy's Game." https://wwwhomes.uni-bielefeld.de/achim/grundy.html.Sloane, N. J. A. Sequence A002188/M0044 in "The On-Line Encyclopedia of Integer Sequences."Referenced on Wolfram|Alpha
Grundy's GameCite this as:
Weisstein, Eric W. "Grundy's Game." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GrundysGame.html