You are organizing the following game:
Participants: About 15 players. You are Player 1, and the other 14 players have (preferably) no prior knowledge of the game.
Equipment: A basket containing 5 tennis balls (or easier yet, 5 beanbags). You, Player 1, hold the basket the whole time.
Space: Any flat, unobstructed ground, 30 x 30 feet (9 x 9 meters) or larger, indoors or outdoors
You instruct the players as follows:
“This is a game with no winners or losers, but it has a surprise ending, so I’m not going to tell you everything in advance. Just follow the instructions, and watch what happens. And don’t worry, this is a safe game. Everybody, please stand in a circle of about 20 feet (6 meters) in diameter.”
“I am Player 1, and I am tossing this ball to another player who is standing somewhere on the other side of the circle from me. Good catch, Player 2! Now, Player 2, toss the ball to another player who is standing somewhere on the other side of the circle from you, who has not already received the ball. Good! Everybody, please remember who you tossed the ball to. Now, Player 3, toss the ball to a new player who is standing somewhere on the other side of the circle from you. Each player, continue tossing the ball to a new player who is standing somewhere on the other side of the circle from you, until each player has received the ball once. If you haven’t received the ball yet, raise your hand so we know who's left … Now, Player 15, toss the ball back to me, Player 1.”
“Just to make sure everybody remembers who they’re tossing the ball to, let’s do one more round, tossing the ball to the same player that you did before, from Player 1 through Player 15, who tosses it back to me, Player 1 … Good!” At this point, everybody is still standing in a circle.
“Now, when I say Go, keep passing the ball to the same player that you've been passing to, but instead of tossing the ball, walk over to the player and hand the ball to them. And instead of one ball being in play, I’m going to add a new ball every 5 or 10 seconds, until there are 5 balls going at once. Keep passing the ball to the same player that you've been passing to, by walking to them and handing them the ball … Ready, Go!”
Within a minute or two, an interesting pattern emerges. What happens, and why?
I was introduced to this game in the late 1990's by a professional game organizer during (I think) a weekend getaway at Omega Institute in New York state. I don't know who invented it, or what it's called. If anybody knows, please add it to the comments, or to your answer, and I will update this puzzle to give credit to the inventor.