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The not-always-lying politician (Posted on 2004-02-27) Difficulty: 3 of 5
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.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
AnswerK Sengupta2008-03-21 12:10:09
No SubjectBryan2004-03-26 14:17:24
No SubjectBryan2004-03-26 14:15:55
No Subjectmichelle2004-03-01 21:59:22
re(2): Repeat: I DID IT MAY WAYTomM2004-03-01 11:02:37
re: Re: FibonacciRichard2004-02-28 12:49:42
Hints/Tipsre: Repeat: I DID IT MAY WAYAdy TZIDON2004-02-28 12:29:03
Some ThoughtsRe: FibonacciPenny2004-02-28 11:31:37
RepeatTomM2004-02-28 10:46:45
Hints/Tipsre: A polite solution and a limit to itAdy TZIDON2004-02-28 09:21:48
SolutionA polite solutionPenny2004-02-28 08:04:16
a gross solutionDan Porter2004-02-27 17:40:47
good problemmatt runchey2004-02-27 17:38:59
Some Thoughtsre(2): Fibo again att:CharlieAdy TZIDON2004-02-27 11:57:21
re: Fibo againCharlie2004-02-27 11:03:24
re(2): Fibo againSilverKnight2004-02-27 10:48:41
Hints/Tipsre(2): Fibo again att: BryanAdy TZIDON2004-02-27 10:48:04
re: Fibo againBryan2004-02-27 10:42:51
SolutionFibo againAdy TZIDON2004-02-27 10:22:03
SolutionsolutionCharlie2004-02-27 08:52:09
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