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 The not-always-lying politician (Posted on 2004-02-27)
There happens to be a politician that might lie at any moment (this isn't unusual) but his conscience bothers him enough (now, that is unusual!) so he won't say two lies in a row.

He said ten consecutive statements.

How many combinations of truths/lies can there be?

 Submitted by Federico Kereki Rating: 4.0000 (5 votes) Solution: (Hide) Every 9-statement sequence ("9SS") can be converted into a 10SS sequence by appending a true statement. Every 8SS can be converted into a 10SS by appending first a true statement, and then a false statement. (The reciprocal processes are also valid; if a 10SS ends in a true statement, remove it and you'll get a 9SS, and if the 10SS ends in a false statement, remove the last two statements, and you'll get a 8SS.) Thus, the number of 10SS= the number of 9SS+ the number of 8SS (let's write 10SS=9SS+8SS) and recursively, in a Fibonacci way, 9SS=8SS+7SS, 8SS=7SS+6SS... Since 1SS=2 and 2SS=3, 10SS=144.

 Subject Author Date Answer K Sengupta 2008-03-21 12:10:09 No Subject Bryan 2004-03-26 14:17:24 No Subject Bryan 2004-03-26 14:15:55 No Subject michelle 2004-03-01 21:59:22 re(2): Repeat: I DID IT MAY WAY TomM 2004-03-01 11:02:37 re: Re: Fibonacci Richard 2004-02-28 12:49:42 re: Repeat: I DID IT MAY WAY Ady TZIDON 2004-02-28 12:29:03 Re: Fibonacci Penny 2004-02-28 11:31:37 Repeat TomM 2004-02-28 10:46:45 re: A polite solution and a limit to it Ady TZIDON 2004-02-28 09:21:48 A polite solution Penny 2004-02-28 08:04:16 a gross solution Dan Porter 2004-02-27 17:40:47 good problem matt runchey 2004-02-27 17:38:59 re(2): Fibo again att:Charlie Ady TZIDON 2004-02-27 11:57:21 re: Fibo again Charlie 2004-02-27 11:03:24 re(2): Fibo again SilverKnight 2004-02-27 10:48:41 re(2): Fibo again att: Bryan Ady TZIDON 2004-02-27 10:48:04 re: Fibo again Bryan 2004-02-27 10:42:51 Fibo again Ady TZIDON 2004-02-27 10:22:03 solution Charlie 2004-02-27 08:52:09

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