How often does he lie? (Posted on 2004-07-02)

	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
	Puzzle Thoughts	K Sengupta	2024-06-19 08:59:44
	No Subject	Rosepark	2023-10-02 09:40:02
	Puzzle Answer	K Sengupta	2023-10-02 08:02:16
	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