A Logic Quiz

 

Assume 1 is true. It has 2 being true, but 2 being true is inconsistent with 1 being true (eg 3 cannot both be true and false). So it's not 1.

Assume 2 is true. In that case 4 will be false, and thus out of statements 1, 2, 3, either all are false, 2 of them are true, or all of them are true (but just one of them alone cannot be true). Can't all be false since this contradicts 2, which we are assuming is correct. Can't be 1 and 2 as we've already argued these are inconsistent. Cannot be 2 and 3 since 3 being true entails 1 being true, which again is inconsistent with 2 being true. And all cannot be true since, yet again, we know 1 & 2 are not both true. So it's not 2.

Assume 3 is true. Again this has both 1 & 2 being true, which we know is inconsistent. Hence it's not 3.

Assume 4 is true. This is inconsistent with 3. Inconsistent with 2. Inconsistent with 1. But either 1 or 2 or 3 has to be true in order for 4 to be correct. Hence it's not 4.

Assume 5 is true. Well, my above reasoning shows that 5 is correct.

Assume 6 is correct. But 5 is correct, so 6 must be incorrect.

Hence the answer is 5. Incidentally, where I originally saw this on facebook the most popular answer was 6. But it clearly cannot be 6! For that would make 5 false and if 5 is false then at least one out of 1, 2, 3, 4 is correct. But that contradicts 6.

This underscores the fact that people just say things without even thinking about it!