# 5 guards, and get rid of the timer!

I like the lies and statistics question, but it is a bit too violent, so I suggest a (slightly harder) and way less violent version.

You are looking at the basement of your house, and you see three doors out of place: one leads to the rest of the basement (you want to explore it, because you are sure it is safe), one leads out of the basement and locks it forever (you don't want it), and one is a ticket room, but you don't know which is which.

You can double back, ask more questions and choose more doors after you enter the ticket room, but not the other two doors.

There are 5 strangers near the doors, called A to E, and you don't know who is who. They all know their own and each others' identities, as well as which door leads where.

• A tells only the truth.
• B answers your first question truthfully, but copies the behaviour (if A, tell the truth, if D, yes or no randomly, etc) of your last asked person after that.
• C answers your first question telling the opposite, but copies the behaviour (if A, tell the truth, if D, yes or no randomly, etc) of your last asked person after that.
• D answers yes or no randomly.
• E behaves like A, but will give you a ticket.

After you have a ticket, you must go to the ticket room to permanently destroy all your tickets. If you ask two questions with at least one ticket with you, you will be sent straight out of the basement, locking the basement.

You can only ask Boolean combinations of the following questions (and, or, not, exactly one of, all of, none of, if and only if), to avoid paradoxes:

• "Is 2+2=4?"
• "Are you / Is this guard [A-E]?"
• "Does this door lead [to the rest of the basement, out of the basement, to the ticket room]?

Question: Can you find out which room leads to the rest of the basement, asking 5 questions or fewer? If so, how?

• in B and C: does "first question" refer to the first question you ask altogether, or to the first question you ask to that specific guard? Feb 14 at 16:20
• @juicifer The first question you ask altogether. Feb 14 at 16:21
• What if you ask B and then C? C should copy the behavior of B, which would be to copy the behavior of the last person asked, but there was no one asked before B. Can you elaborate what it means to "copy the last person"? Copy their answer? Copy the truth value of their answer? Copy how they would answer the current question? Copy how they answered the last question? Feb 14 at 17:18
• B will start off telling the truth, then after you ask C, they should tell you the truth too. Feb 14 at 17:21
• Can you go to the rest of the basement with a ticket? Feb 15 at 4:19