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.
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?