Academic Games: On-Sets

The Game of On-Sets®

Students Playing On-Sets

On-Sets is a mathematical game involving logic and set theory. Cards ontaining 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 cubes to the Required, Permitted, or Forbidden sections of the playing 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 "Now" or "Never" against the last Mover. "Now" means the player can make a Solution using the cubes in Required and Permitted and one more cube from Resources (the cubes not yet played to the mat). "Never" means the player believes the Mover cannot make a Solution using the cubes in Required, Permitted, and Resources. 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 6 points.
The loser of the challenge scores 2.
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.

Special rules called variations are in force in each division to make the game more interesting and challenging. Before the cubes are rolled, each player selects a variation from the list for the division.

On-Sets forces players to revise their solutions in response to opponents' moves. Quick and logical thinking is required to win the match.

"On-Sets" is copyrighted by
WFF'N PROOF
1490 South Boulevard
Ann Arbor MI 48104