Thread: Odd Escape
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Unread 09-04-2004, 18:44
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Ian Mackenzie Ian Mackenzie is offline
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Re: Odd Escape

No, it isn't possible; here's my geometric proof. Take any four points representing the four lights. Draw lines connecting every pair of points, extending off to infinity in both directions; since the observed order of the lights only changes when one light appears to the observer to pass behind another, crossing a line represents a change in observed order. Since only six lines can be drawn (4 choose 2), and the observer can only cross each one twice in one pass around the circle, the observed order can only change 12 times (one of these being a change back to the originally observed order), so there is a maximum of 12 orders that can be observed (not the full 24).
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