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February 22nd, 2011, 02:58 PM  #1 
Senior Member Joined: Jan 2009 Posts: 344 Thanks: 3  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?

February 22nd, 2011, 05:41 PM  #2 
Senior Member Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3  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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