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2n+1 Statements (Posted on 2005-06-13) Difficulty: 2 of 5
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 (4n-1) 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?

No Solution Yet Submitted by Dustin    
Rating: 4.0000 (7 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts re: Hypothesis | Comment 3 of 15 |
(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 2005-06-13 21:46:26
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