There are 10 statements written on a piece of paper:
- At least one of statements 9 and 10 is true.
- This either is the first true or the first false statement.
- There are three consecutive statements, which are false.
- The difference between the serial numbers of the last true and the first true statement divides the positive integer that is to be found.
- The sum of the numbers of the true statements is the positive integer that is to be found.
- This is not the last true statement.
- The number of each true statement divides the positive integer that is to be found.
- The positive integer that is to be found is the percentage of true statements.
- 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.
- There are no three consecutive true statements.
What is the smallest possible value of the positive integer that is to be found?
