# Two Doors and a Guard

While trekking through the swamp of Knights and Knaves, you come upon a pair of doorways: One leading out of the swamp, the other leading to your doom. The swamp of Knights and Knaves is a strange place, where everyone either always lies or always tells truth. Before the doorways is a great two-headed thurse, guarding the door. "One of us always tells the truth.." begins one head, "..and one always lies" finishes the other. You may only ask a single question to one of the heads

What question can you ask to determine which door you should go through?

Hint:

The guards were the ones who informed you of the rules

• @JeffZeitlin Please read the hint Mar 1 at 20:50
• @IchthysKing Vs obgu bs gur thneqf ner enaqbz va jurgure gurl gryy gur gehgu be yvr, naq obgu unccra gb or vavgvnyyl ylvat, gura lbh ner fheryl qbbzrq. Mar 2 at 0:00
• @DanDan0101 I've edited the question. On your second point, this riddle does not contain a contradiction Mar 2 at 0:31
• Not really a duplicate. Mar 2 at 8:17
• And as always, a solution to this riddle only works if knaves lie with the algorithm: "Generate a truthful answer to the statement and logically negate it" - Otherwise a liar could always answer "I don't know" (which is a perfeclty fine lie) when you ask him for the right door. Mar 3 at 10:22

## 2 Answers

Consider the following possibilities for heads 1 and 2 respectively (where T is a truth-teller and L is a liar).

TT : this is impossible as, while the first statement "one of us always tells the truth" imay be argued to be technically true (if you accept that it is not making any comment about the other of us), the second statement "...and one always lies" cannot be true.

TL : this is impossible as the second statement "...and one always lies" is true, so cannot be spoken by a liar.

LT : this is also impossible as the first statement is true, so cannot be made by a liar.

LL : this appears to be a valid option as "one of us always tells the truth" is clearly a lie however you interpret the one of us bit (only one of us, exactly one of us, or at least one of us), and if you interpret "...and one always lies" to mean exactly one always lies, then it is also a lie. So no inconsistency.

So you can ask

does this door lead to safety"

and who ever answers

you take the opposite to their advice.

• If we take the current Text of the riddle verbatim, the second one says "...and one always lies". The "and" implies "I concur with the first statement and also say (the other) one always lies" which supports this solution. Mar 3 at 10:19

With this information

The swamp of Knights and Knaves is a strange place, where everyone either always lies or always tells truth.

I assume the great two-headed thurse is a single identity.

Let's find out if this thurse tells truth or lies. By considering this sentence comes from different heads of the same identity. I assume the sentence comes from the thurse regardless of which head said it. So, it becomes

"One of us always tells the truth and one always lies"

This sentence is a lie because both heads will either tell the truth or lies.

Therefore, this thurse is a liar.

To find the exit, just ask any head at any door

Is this the exit to safety?

and consider the answer regarding that question is a total lie, you can act accordingly.