Quote:
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Originally Posted by Ian Mackenzie
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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Absolutely perfect! Score one cookie for Ian Mackenzie!
How long did that take you? For me, I drew some pictures and started rotating them around in front of me, keeping track of all the combinations for about a half hour. Then I realized that you could just draw lines like you said. Congrats, that's not an easy one to figure out.
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