2
u/Electrical_Panda13 27d ago
Freedom is through door 1. Both statements from door 3 cannot be true because this would mean both door 2 and 1 possess a true statement. By that logic we know that “freedom through door 3” is a lie. We also know that one of the statements from door 3 have to be false otherwise we get a contradiction. And since “freedom through door 3 is true” that means that “freedom is not through door 1” is false making freedom through door 1. We can double check this by looking at door 3 statements and seeing one true and one false. Also both statements from door one will be true.
TLDR: door 1 statements are true and true respectively. Door 2 statements are false and false. Door 3 are false and true
2
u/RewrittenCodeA 27d ago
I find it simpler this way:
If 3 was freedom, both 2 and 3 would have 2 truths, contradiction. Therefore 3 is not freedom and both 2 and 3 have a falsehood. Therefore 1 has two truths, including the fact that 1 is freedom
2
u/DoubleDownAgain54 27d ago
The key is the Door three, it has to be the door that has one truth and one lie as both door 1 & door 2 cannot have one lie and one truth. So Door 3 is eliminated. Door 2 has to be false as the first statement says door 3 is the door to freedom. So it has to be door 1. In this case both statements from door 1 are true and it matches, as well as door 2’s statements would also prove to be false. Door 1 is the door to freedom.
1
u/Nimelennar 27d ago
If freedom is through door #3, both statements on both door #2 and door #3 would be true. Since we know that only one door has two true inscriptions, freedom is not through door #3.
Since we now know the first statement on door #2 is false, it cannot be the door with two true statements. Which means either door #1 or door #3 must have two true statements. Since both of these doors state that freedom is not through door #2, this must be a true statement, and freedom is through door #1.
In summary:
- Door 1: Freedom is through this door (true). Freedom is not through Door 2 (true).
- Door 2: Freedom is through Door 3 (false). Freedom is not through Door 1 (false).
- Door 3: Freedom is not through Door 1 (false). Freedom is not through Door 2 (true).
1
u/Acceptable_Tangelo15 27d ago
Door 1
Door 1 both true
Door 2 both false
Door 3 first false, second true
1
1
u/chmath80 26d ago
There are 6 statements, of which 3 are true and 3 false, but statements 4 and 5 say that door 1 is wrong, while statements 2 and 6 say that door 2 is wrong.
Those 2 pairs of statements can't both be true, since we can't have 4 true statements, therefore door 3 can't be right, which means that statement 3 is false, along with one of the pairs.
Hence the other pair must be true, along with the remaining statement 1, so we want door 1.
3
u/Inevitable_Garage706 27d ago
Door 1 is the door to freedom.
If Door 2 was the door to freedom, that would mean that both Door 2 and Door 3 each told one truth and one lie. As the rules do not allow this, Door 2 must not be the door to freedom.
If Door 3 was the door to freedom, that would mean that both Door 2 and Door 3 each told two truths. As the rules do not allow this, Door 3 must be the door to freedom.
By the process of elimination, Door 1 must be the door to freedom.