

Shape, color, size and topology (with or without a hole) are the four characteristics of a Quarto! piece. Since each has two possible values, the players facing off in this thrilling combinatorial game — one of the most award-winning in the world — must contend with sixteen pieces.



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Two players take turns moving a queen across a chessboard. This seemingly innocuous game offers a way to discover and illustrate a major result in game theory: the Sprague–Grundy theorem. It also has another mathematical surprise in store…

What's presented here isn't a game of five families, but a family of five games (siblings and cousins!) — blocking games, in which a player leaves the game once they can no longer play. All of them concern geometry. In particular, the pieces in these games take many forms, made up of squares, triangles, line segments and cubes.

Graphs are crucial to strategies in games of complete information, provided the positions are not too numerous and can be represented. Patrick Grundy devised a game to formalize these strategies.
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