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 How often does he lie? (Posted on 2004-07-02)
In the "Not-always-lying politician" problem, what's the probability that a particular sentence is true?

 Submitted by Federico Kereki Rating: 2.5000 (4 votes) Solution: (Hide) Call S(i) the number of valid sequences of i statements; as per the solution of the other problem, S(1)=2, S(2)=3, S(3)=5, and generally, S(i)=S(i-2)+S(i-1). Call F(i) the total number of false statements taking into account all the possible sequences in S(i); F(1)=1, F(2)=2, and in general, F(i)=F(i-1)+F(i-2)+S(i-2). [To see why, see the solution to the other problem] The average of false sentences is F(i)/(i*S(i)), which experimentally converges to about 0.27... [more on this to follow] so the answer we are looking for is 0.73... or 73%.

 Subject Author Date Given answer is wrong! Math Man 2012-05-16 09:25:43 i c it this way Ady TZIDON 2004-07-03 02:09:44 A different take Tristan 2004-07-02 15:37:22 Maybe Max 2004-07-02 15:37:21 re: Solution Charlie 2004-07-02 15:15:02 Solution Eric 2004-07-02 14:49:49

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