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Musical Chairs, by Popa
Start with 1000 boys and 1000 girls. The boys are the chairs, and the girls are the players. Now, every year, we will add 103% to the game, but we will assume the boys are dating the younger girls.
Now, we will assume that there are different circles of chairs, and each girl chooses which game she will play in. And both players and chairs can move among the different games, and do. We don’t know how many are moving, and we don’t know if it is more chairs moving or more players moving.
Some of the players and chairs, leave the game altogether, and don’t play in any of the games. We don’t know how many, or it is unevenly divided.
Some new people join the game, both as players and as chairs. These people were not in the game at all, but join at different times. We don’t know how many or how it is divided.
Someone noticed lots of players with no chairs, so he decided the problem was that the players were choosing older chairs. He did a study which showed that there were indeed some players with no chairs. But he didn’t bother to find out if there was an equal number of unoccupied chairs, or if the chairless players were even still playing the game. Or if there chairs had been taken by new players who had joined the game from the outside. Or if some of the chairs had left the game.