1. A Four Square Court is a subset of the plane comprising four squares of equal area and pairwise disjoint interiors (under the topology induced by the Euclidean metric) with one point common to all four squares. There shall be a bijection number from the set of these four squares to the set {1,2,3,4} such that number ^-1(1) and number ^-1(3) intersect at a point. If number(x)=y, then it shall be said that x is numbered y.
   
   
2. The maximum distance between two points of a conventional four square court of The Four Square Club of Rutgers, The State University of New Jersey shall be the square root of 3200 times the length of the shorter side of one of the bricks in the courtyard in front of the Hill Center on Busch Campus in Piscataway in New Jersey in the United States of America. On an ordinary summer afternoon, this distance is approximately 150 attoparsecs.
   
   
3. The First Square shall be defined as the union of the interior of the square numbered 1, the boundary of the square numbered 1 not shared by any of the other three numbered squares, and the boundary of the square numbered 1 shared by the square numbered 2.  The Second Square shall be defined as the union of the interior of the square numbered 2, the boundary of the square numbered 2 not shared by any of the other three numbered squares, and the boundary of the square numbered 2 shared by the square numbered 3 alone. The Third Square shall be defined as the union of the interior of the square numbered 3, the boundary of the square numbered 3 not shared by any of the other three numbered squares, and the boundary of the square numbered 3 shared by the square numbered 4 alone. The Fourth Square shall be defined as the union of the interior of the square numbered 4, the boundary of the square numbered 4 not shared by any of the other three numbered squares, and the boundary of the square numbered 4 shared by the square numbered 1 alone.
   
   
4. There shall be a variable N denoting the number of players, and a bijection label from the set {1, 2, ... , N} to the set of players. If label(x)=y, then it shall be said that y is labelled x.
   
   
5. There shall be a function rank from the Cartesian product of the set {1, 2, ... , N} and the set of non-negative real numbers to the set {1, 2, ... , N}. If rank(k,t)=m, then it shall be said that the player labelled k is ranked m at time t. The players ranked 1, 2, 3 and 4, called rank insiders, shall be the owners of the First, Second, Third and Fourth Squares respectively.
   
   
6. A round is the canonical unit of gameplay in four square. A round begins with a legal serve and ends when rank(k,t) > N for some k. For a serve to be legal, the player ranked 1 must stand behind the square numbered 1 from the vantage points of both the square numbered 2 and the square numbered 4, drop The Ball into the interior of the square numbered 1, and hit The Ball.
   
   
7. There shall be a function control from the set of non-negative real numbers to the set {1,2,3,4}. If label(control(t))=x, then it shall be said that x has control at time t. When the round begins, the player ranked 1 will have control. A rank insider gains control on touching, or being touched by, The Ball.
   
   
8. Rule the First (The Rule): If The Ball bounces into a square not belonging to the player who has control, and touches the ground again before any of the rank insiders touch it, then the owner of the square is out.
   Rule the Second (Owning): If The Ball bounces into the square belonging to the player who has control, then that player is out; the player "owned it".
   Rule the Third (Hitting Out): If The Ball bounces out, then the player who had control is out; the player "hit it out".
   Rule the Fourth (Doublehit): If the player who has control touches, or is touched by, The Ball any time after the serve is delivered, then that player is out; the player "doublehit".
   Rule the Fifth (Palming): If a player stays in contact with The Ball for a duration offending the sensibilities of any of the rank insiders, then that player is out; the player "palmed it".
   Thus enumerated are the ways of getting out during a round of four square.
   
   
9. When a player labelled j and ranked k is out at time t, rank(j,t) is set to N+1, terminating the round. Players ranked k+1, k+2, ... , N+1 have their ranks decremented by 1. When all four rank insiders are ready, the next round begins.
   
   
10. When a new player joins a game of four square after the start of play, the value of N shall be incremented by 1 at the end of the current round, and the new player shall be labelled N.
    
    
11. When a player labelled k leaves a game of four square, the players labelled k+1, ... , N have their labels decremented by 1 at the end of the current round. The value of N is also decremented by 1.
    
    
12. A game of four square ends -- rain or shine, snow or storm, angry faculty threatening to call the cops or no angry faculty threatening to call the cops -- when the value of N is less than 4.