NotaKnot

Notaknot is a term that appears in several contexts within recreational mathematics and puzzle culture. In knot theory discussions, it is sometimes used informally to refer to the unknot, the simplest possible knot that is equivalent to a plain circle. The standard technical term for this is unknot, and notaknot remains a colloquial or casual variant rather than a formal designation.

Notakto, often encountered as Notakto rather than Notaknot, is a distinct two-player game derived from tic-tac-toe. It is played on one or more boards; players take turns placing marks on any board. If a move completes a three-in-a-row on that board, that board becomes unusable for the remainder of the game. Play continues until no boards have legal moves left. The objective is to avoid being the player who is forced to make the final move on the last usable board.

In game-theory terms, Notakto on a single board reproduces the standard tic-tac-toe outcome with optimal play, typically ending in a draw. When multiple boards are used, the situation becomes a disjunctive sum of games and can be analyzed with nimber theory. Winning strategies often rely on symmetry, move pairing, and leaving the opponent with boards in which every available move creates a forced loss.

The name Notakto is a playful contraction suggesting “not a tic-tac-toe” or a variant thereof, and Notaknot appears primarily as a common misspelling. See also Notakto, tic-tac-toe, and unknot for related concepts.