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February 22nd, 2011, 02:58 PM   #1
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How many sequences of colors are possible...

You pass through five traffic signals on your way to work. Each is either red, yellow, or green. A red is always immediately followed by a yellow; a green is never followed immediately by a green. How many sequences of colors are possible for the five signals?
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February 22nd, 2011, 05:41 PM   #2
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Re: How many sequences of colors are possible...

Just draw a game tree and count the number of different outcomes. Can the last light be red? It seems not.

Alternatively, keep a count of (R)ed, (Y)ellow, (G)reen, and in each row let new R = Y+G, new Y = R+Y+G, and new G = Y.

1, 1, 1
2, 3, 1
4, 6, 3
etc
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