There is a tournament in table tennis (ping-pong) in which 8 players take place.
these are the rules of the tournament:
1 ) each player plays with every other only 1 game.
2 ) if in the i-th round there is a game between a and b, and a game between c and d, and in the i+1-th round there is a game between a and c, then in the i+1-th there must be a game between b and d.
on how many different ways can we make a schedule for all rounds if it's not important which player plays on which table?