There are 10 statements written on a piece of paper:

1. At least one of statements 9 and 10 is true.
2. This either is the first true or the first false statement.
3. There are three consecutive statements, which are false.
4. The difference between the serial numbers of the last true and the first true statement divides the positive integer that is to be found.
5. The sum of the numbers of the true statements is the positive integer that is to be found.
6. This is not the last true statement.
7. The number of each true statement divides the positive integer that is to be found.
8. The positive integer that is to be found is the percentage of true statements.
9. The number of divisors of the number that is to be found, (apart from 1 and itself) is greater than the sum of the numbers of the true statements.
10. There are no three consecutive true statements.

What is the smallest possible value of the positive integer that is to be found?

(In reply to Solution by tomarken)

While overall I agree with your reasoning - it seems what the problem's intention is.   Statements 1 and 2 together struck me. 

What if statement 1 is true?  Statement 2 doesn't actually contradict this because it is a paradox.  But does that mean 2 is neither the first true nor the first false statement - paradox averted?

Posted by Jer on 2014-05-08 23:31:24