The Hexad Game
Joseph Kahane, A. J. E. Ryba · The Electronic Journal of Combinatorics · 2000
We give a non-enumerative proof that the $P$-positions of the hexad game give the Steiner system $S(5,6,12)$. We show that the distributions of nim sums and Welter values of these $P$-positions have simple and surprising regularities.