1. At least 1 statement among these 2n+1 are true.
2. At least 3 statements among these 2n+1 are false.
3. At least 5 statements among these 2n+1 are true.
...
2n. At least (4n1) statments among these 2n+1 are false.
2n+1. At least (4n+1) statements among these 2n+1 are true.
How many statements are true? Which?
(In reply to
Hypothesis by Charlie)
For n = 0, there are 2*0+1 = 1 statement, that is :
1) at least 1 statement among these 1 "are" true.======>T
For n = 1, there are 2*1 + 1 = 3 statements, that are :
1) at least 1 statements among these 3 are true.
2) at least 3 statements among these 3 are false.
3) at least 5 statements among these 3 are true.
Statement (3) canīt be made, so we couldnīt test if it is T or F. And since statement (2) reffers to all 3, it also canīt be tested. So, we could consider only statement (1), T.
And this will occur with n= 2, 3,...
By induction, the only statement TRUE is the FIRST.

Posted by pcbouhid
on 20050613 21:46:26 