A big circle
Thirty fans hire a bus to attend a football game. On the way to the stadium they realize that exactly half of them are fans of one team, and the other half are fans of the other team. With still some way to go before reaching the stadium, the bus develops mechanical problems and the driver announces to his passengers that the only way to continue the journey is for half of them to get out and walk. There is a huge fight that doesn’t stop until the driver speaks to them again and suggests a way of selecting the passengers who are to get off the bus.
“All of you,” he said, “get into a big circle. When you are ready, beginning at this spot, I’ll count nine people clockwise. The ninth person leaves the circle and continues on foot. Then I’ll count another nine starting from where I stopped, and the ninth person leaves the circle and continues on foot. And so on until fifteen people have left the circle.”
Suppose that you are one of the fans. How should you arrange all the other fans of your team so that none of them will have to walk?
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If the two teams are A and B and you are a supporter of team A and you do not want any of your fellow supporters to end up walking to the stadium organize them in a circle starting at the point where the driver starts and reading clockwise as follows; A, A, A, A, B, B, B, B, B, A, A, B, A, A, A, B, A, B, B, A, A, B, B, B, A, B, B, A, A, B.