Sarah's solution is correct, and very clever, but only if the Blue Guard was telling the truth when he said "one of us always tells the truth, and one of us always lies"!

First, let us proceed on the assumption that the Blue Guard was telling the truth: One of the doors always lies, and one always tells the truth.

Sarah asks the Red Guard to tell her if the Blue Guard would tell her that the door behind the Red Guard was the correct door. The Red Guard answers: "Yes".

From this answer, Sarah can infer which is the correct door because it's now an "either/or" scenario, but both scenarios yield the same answer to the question "Which is the correct door."

Observe:

1. The Red Guard is lying. In that case, the Blue Guard would actually say, "No: The Red Guard's door is not the correct door" and would be telling the truth: The Blue Guard's door is the correct door.

2. The Red Guard is telling the truth. In that case, the Blue Guard would say, "Yes: The Red Guard's door is the correct door"", but he would be the liar: The Blue Guard's door is still the correct door.

Solution: When you ask one of the guards: "Would he tell me you guard the correct door?" the answer will be either a direct lie, or a lie truthfully reported: Open whatever door the guard has told you the other guard would tell you is the wrong door.

Question: Why didn't it work?

Sarah's formulation is the correct solution to the scenario described by the Blue Guard ("One of us always tells the truth, and one of us always lies"); however, she overlooked the possibility that the Blue Guard, when he explained this rule, was lying. If the Blue Guard were lying, other scenarios are possible. In some of these, her formulation is useless—such as one in which all four guards lie and tell the truth inconsistently, and both doors lead to certain death.

Your thoughts.

The poster formerly known as Hydra.