The problem is that there is no way to know how many people were given the chance to play these games. But when we go to a game, we might encounter a random person that would like to play and then decide to go back to the original date. We don’t know the random person who is getting the chance to play, and we can’t know the person’s name. So we could just play random person.
So we have to figure out how to know the name of the random person that decided to play. It could be someone who was around when the original date was made, or someone that has been around since the game was released. Or it could be someone who just randomly decided to play. The solution is simple, though: we have to figure out the time.