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 2n+1 Statements (Posted on 2005-06-13)
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)

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 not so sure | Comment 1 of 15

In a quick approach:

Statements from n+1 from 2n + 1 are always false (not logic).

Statement n is always false (with n even or odd).

Statement 1 to n-1 are some true and some false:

They are false when states to be true a number of statements superior to n-1, so: odd terms (statements) higher than n/2 and inferior or equal to n-1 are also false.

So, the number of false statements is superior to

(n + 1) + 1 + (n-2)/4 (is > than (5n + 6)/4 con n even).

=====

NB: Last part was needed of some correction, so I've changed the original = in >, and the problem hasn't been solved (but I can't do it now).

Edited on June 13, 2005, 3:38 pm

Edited on June 13, 2005, 4:50 pm
 Posted by armando on 2005-06-13 14:59:09

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