logical deduction - Two doors with three guards - one lies, one tells the truth, and one is unreliable

This is an extension of Two doors with two guards - one lies, one tells the truth, but in this situation you are a prisoner in a room with 2 doors and 3 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, another always lies, and the third is unreliable and sometimes tells the truth and sometimes lies. You don't know who is who, but the guards do.

After asking two yes/no questions you have to choose and open one of the two doors. You can ask one guard both questions or you can ask two different guards a single question each.

What and who do you ask to lead you to the door of freedom?

Answer

This is a rather weird form of the knight, knave and joker puzzle, with a twist.

This part is from Ben Aaronson in this answer.

So say the people are A, B and C. You ask A:

Is exactly one of these statements true:

• You are the knight


• B is the joker"

If you get back the answer yes, then the possibilities are:

• A is the knight and B is the knave (1 is true, 2 is false, so one statement true, so the answer is yes which knight truthfully gives)


• A is the joker


• A is the knave and B is the knight (both statements false, so the answer is no which knave lies about)

In all three cases, B is safe

If you get back the answer no, then the possibilities are:

• A is the knight and B is the joker (both statements true, so the answer is no which knight truthfully gives)


• A is the joker


• A is the knave and B is the joker (1 is false, 2 is true, so one statement is true so answer is yes which knave lies about)

In all three cases, C is safe

Then, just point to a door and ask the safe person:

"Would your exact opposite say this door leads to freedom?"

If you ask the Knave and:

• 
  

  The Knave says No:

  
  
  
  
  • The Knight would tell the truth (Yes), but the Knave lies (No).
  
  
  • The door is safe; go through.
  
  
  
  



• 
  

  The Knave says Yes:

  
  
  
  
  • The Knight would tell the truth (No), but the Knave lies (Yes).
  
  
  • The door is unsafe; choose the other one.
  
  
  
  

If you ask the Knight and:

• 
  

  The Knight says No:

  
  
  
  
  • The Knave lies (No), and the Knight tells the truth (No).
  
  
  • The door is safe; go through.
  
  
  
  


• 
  

  The Knight says Yes:

  
  
  
  
  
  • The Knave lies (Yes), and the Knight tells the truth (Yes).
  
  
  • The door is unsafe; choose the other one.
  
  
  
  

This puzzle was an interesting mix of two puzzles.