In one of the answers to this question, reproduced here:
You are a prisoner in a room with 2 doors and 2 guards. One of the doors will guide you to freedom and behind the other is a hangman - you don't know which is which.
One of the guards always tell the truth and the other always lies. You don't know which one is the truth-teller or the liar either.
You have to choose and open one of these doors, but you can only ask a single question from one of the guards.
What do you ask to lead you to the door of freedom?
and the solution:
Here is a twisted solution.
Go to any guard, point at a door and ask: Among the propositions 1. "You are a liar", 2. "You will reply negatively" and 3. "This door leads to freedom", is there an odd number of true propositions?
If you get the answer yes: If the guard is a truthteller, the number of truths is odd, 1. is false, 2. is false, so 3. must be true. If the guard is a liar, the number of truths is even, 1. is true, 2. is false, so 3. must be true.
If you get a negative answer: If the guard is a truthteller, the number of truths is even, 1. is false, 2. is true, so 3. must be true. If the guard is a liar, the number of truths is odd, 1. is true, 2. is true, so 3. must be true.
So regardless of the answer of the guard, the door you pointed at is the door to freedom, you can leave safely.
I fail to follow the logic behind this answer. The answer seems to suggest that no matter what door is pointed to, it becomes the correct door, which does not make sense.
Is there a logical mistake behind this answer, or is there something I missed in my reading?