On-Sets is a mathematical game involving logic and set theory. Cards containing combinations of blue, red, green, and yellow dots are dealt to form the universe, and cubes are rolled to form the resources. The cubes contain the same four color dots, plus symbols for the operations of union (U), intersection (upside-down U), complement ('), and subtraction (-). Three cubes contain the digits 1 to 5.

Students play in groups of two or three. The first player uses the digit cubes to set a Goal, which is the number of cards that must be in the solution set. Each player must use the symbols rolled to form a set equal to the Goal. For example, a Solution for a Goal of 5 might be B U R ("blue union red"), which represents the set of cards which contain either a blue or a red dot.

Players take turns moving to the Required, Permitted, or Forbidden sections of the mat. Any cube moved to Required must be used in any Solution; any cube in Permitted may be used; any cube in Forbidden may not be used. Thus the players themselves shape the Solution, forcing one another to create new Solutions in response to moves.

At any point a player may challenge the last mover, if they feel the last mover has made a mistake. There are three types of Challenges.  A-Flub means that the Challenger can make a Solution using the cubes in Required and Permitted and one more cube from Resources. P-Flub, or Challenge Impossible means the player believes the Mover cannot make a Solution using the cubes in Required, Permitted, and Resources. C-A- Flub means that the Challenger believes that the Mover, or some previous mover, missed an A-Flub.  After a challenge, at least one player must show a correct Solution on paper. The scoring goes like this:
     The player who wins the challenge scores 10 points.
     The loser of the challenge scores 6.
     If there is a third player, he must side with or against the Challenger and scores points depending upon that decision.

A game may also end in a Forceout.

In the adventurous version of the game, Special rules called Variations are in force in each division and reinforce what is taught in the mathematics curriculum. Before the cubes are rolled, each player selects a variation from the list provided for that division.

On-Sets teaches students the basics of set theory and symbolic logic, and helps form the foundation for further study into algebra and advanced math.

On-Sets  is copyrighted by WFF'N PROOF