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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.)
re(2): Hypothesis | Comment 4 of 15 |
(In reply to re: Hypothesis by pcbouhid)

For n=0, there is only 1 statement:
1) At least 1 statement among this 1 is true.

This can neither be proven true nor false.  It is the equivalent of the statement, "This statement is true."

Also, your induction was done incorrectly.  Induction has two steps.  First you prove a hypothesis when n=1 (or 0).  Next, you prove that if the hypothesis is true for n=k, it is also true for n=k+1.

The hypothesis you tried to prove seems incorrect.  Try other cases with n>1 and you might see a pattern... or not.

  Posted by Tristan on 2005-06-13 23:14:47

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