Draft:Bpow51

Yesterday I watched a group of kids play a game at the park with a Frisbee -- a flying disk. As best I could tell, these were the rules to their game:

One of them, the King, started the game by shouting, "GREEN LIGHT", after which all the others would run around randomly with much yelling and screaming, (kids!), until the King shouted, "RED LIGHT", freezing them where they were. The King then picked up the disk and threw it to the person furthest away from herself; that person would then throw the disk to the person furthest away from himself, and so on until someone was unable to catch the disk without moving. That person then became the new King and a new round of the game would start.

After watching a while, it seemed that one of the following two things always happened: (a) whoever the king threw the Frisbee to would throw it back and the two of them would form a "tea party", throwing the disk back and forth to each other, or (b) the King would never be thrown the Frisbee back.

Explain why this was necessarily the case.

Problem by Alberto L Delgado, from the now extinct Bradley Problem of the Week.