One day after having his morning Bat-coffee, Batman received the following message on his Bat-computer:
Hello there Dark Knight. I, the Riddler, along with Joker, Two-Face, and Penguin, are preparing to pull off the heist of the century. But before we go, we're going to play a little game. If you win, we'll surrender to the police. If we win, the heist goes off as planned. Here's how the game works, in 1 hour you'll call the number at the bottom of this message. One of us will pick up the phone, and you'll ask 1 yes/no question. Try to ask any other kind of question, and we hang up and you lose. After you ask and we answer, we pass the phone to another of our members. We know the order we'll pass in, but you won't. The following facts will hold:
I, the Riddler, will always answer truthfully.
Penguin will always lie.
Two-face will flip his coin, if it comes up heads he will tell the truth, tails he lies.
Joker will lie or tell the truth depending on what he feels will most disrupt you.
Each of us will answer before anyone repeats, and the cycle will not change while we talk.(i.e. The order we answer will be the same each round)
If we do not know the answer to a question, we will say "Pass". Note: Joker will never pass.
The task is simple, figure out our order. Good luck.
What is the smallest number of questions Batman will have to ask in order to figure out the villain's order, regardless of what it is?
Bonus: Does it matter if a villain decides to hang-up if they hear a repeated question?
Note: I just came up with this puzzle, so I do not know the answer at this point in time.
Clarification of Joker's behavior: If a) Joker knows the answer to a question AND b) There is a way to answer the question while remaining logically consistent, then the Joker answers the question (lying or truthing depending on how to most screw-up Batman)
If a) Joker doesn't know the answer OR b) There is no way to remain logically consistent while answering, then Joker will pick yes/no based on what he believes would most screw-up Batman.