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.
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Posted by tomarken
on 2014-05-09 00:07:08 |
re(2): Solution
