Thanks go to Nicholas Abruzzo for his explanation of this game.
The Definition of a WFF: A given expression is a WFF if and only if:
a. It is a ‘p’, ‘q’, ‘r’, or ‘s’; or
b. It is an ‘N’ followed by a WFF; or
c. It is a ‘K’, ‘A’, ‘C’, or ‘E’ followed by two WFF’s.
Note: Each letter N, K, A, C, E has a corresponding logical operation.
N: not; K: and; A: or; C: if ... then ...; E: if and only if
Rules of Shake-a-WFF: This game is for two or three players. Each player begins the game with a hand of three cubes: two small cubes and one big cube, and a store of unused cubes. All players will throw their cubes at the same time and then each player tries to come up with a longest WFF. As soon as a player finds a WFF, s/he calls out, “WFF” (pronounce “woof”) or “no WFF” – if s/he can find no WFF. (This person is the caller.) Other player(s) then have to stop and validate the caller’s “WFF” (or “no WFF”).
If a player agrees that the caller is correct, s/he says “check.” If all the players “check,” the caller gains one point. The caller puts his WFF on the mat, replaces the placed cubes with the same number and kind of cubes from her/his store of unused cubes, and also takes one more cube from the store. The rule restricting the kind of extra cube the caller may take is: The player must have either the same number of big cubes as small cubes; or one more small cube than big cubes.
If any player believes that the caller has made a mistake (e.g. A longer WFF exists than the one the caller presented, the caller presented an incorrect ‘WFF’, there is a WFF but the caller said “no WFF”, or there is no WFF but the caller incorrectly presents a ‘WFF’), s/he says, “challenge” and points out the mistake or makes the correct WFF. Others or the referee then check the correction. If the correction is correct, then the checker gains one point and is rewarded an extra cube (restricted by the rule above). The caller has to return one cube (again, according to the restriction stated).
If the correction is wrong, then the checker loses one cube (restricted by the rule above).
After all players are ready with their cubes, the next round can start again. Players can set up a timer or the number of cubes formed from all WFF’s of each player to determine the winner, who puts the most number of cubes on the mat.