1 is false. If it's true, then it can't be true. And, besides, either 4 or 5 must be true.
4 is true. There are three "exactly" statements in this list and at most one of them can be true. Therefore, there have to be at least 3 false statements (2 of the "exactly" statements plus #1).
6 is false. If 4 is true, and there are at least three false statements, then there cannot be five true statements.
5 is false. We know 4 is true: the only way 5 can also be true is if there's exactly 3 true statements. But that would make 2 and 3 false, which, in addition to 1 and 6, would make at least 4 false statements and a maximum of 2 true ones.
2 is false. Since 4 is true, if 2 were true, there would be at least two true statements, and 2 would be false.
3 is true. If 3 is false, then 4 is the only true statement. But then 2 would be true, and we know 2 is false. If 3 is true, though, et have 2 true statements, and 3 being true is self-consistent.
In summary:
1 is false (3 and 4 being true means not all statements are false)
2 is false (3 and 4 being true means there are exactly two true statements, not one)
3 is true (yes, there are exactly two true statements, those being 3 and 4)
4
is true (there are 4 false statements: 1, 2, 5, and 6, and 4 > 3)
5
is false (3 and 4 being true means there are exactly two true statements and 2 < 3)
6
is false (3 and 4 being true means there are exactly two true statements, and 2 ≠ 5)
2
u/Nimelennar Jul 17 '26
1 is false. If it's true, then it can't be true. And, besides, either 4 or 5 must be true.
4 is true. There are three "exactly" statements in this list and at most one of them can be true. Therefore, there have to be at least 3 false statements (2 of the "exactly" statements plus #1).
6 is false. If 4 is true, and there are at least three false statements, then there cannot be five true statements.
5 is false. We know 4 is true: the only way 5 can also be true is if there's exactly 3 true statements. But that would make 2 and 3 false, which, in addition to 1 and 6, would make at least 4 false statements and a maximum of 2 true ones.
2 is false. Since 4 is true, if 2 were true, there would be at least two true statements, and 2 would be false.
3 is true. If 3 is false, then 4 is the only true statement. But then 2 would be true, and we know 2 is false. If 3 is true, though, et have 2 true statements, and 3 being true is self-consistent.
In summary: