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?
(In reply to
re: Solution by Jer)
Assume statement 1 is true.
If statement 2 is true, then it is the second true statement, which would make statement 2 false, which is a contradiction.
If statement 2 is false, then it is the first false statement, which would make statement 2 true, which is a contradiction.
It's not really a paradox, we've just exhausted the possible cases where we assumed 1 was true, and found that they both lead to contradictions.
So 1 must be false, which doesn't have any paradoxical implications. If 2 is true, then it's the first true statement. If 2 is false, then it's the second false statement. Either possibility is logically consistent.

Posted by tomarken
on 20140509 00:07:08 