Knights and knaves puzzle variations

My guess is that nearly all my readers have heard the basic knights/knaves puzzle, but I have recently come across interesting modifications of the problem. (It took four -- count them! -- theory grad students to figure out the "challenge" below, and it is probably within ε (i.e., nigh) of murderously frustrating for non-mathematical laypeople.) I have not solved the last three, although two of them have solutions posted on Wikipedia.

As so often occurs in puzzles, you find yourself shipwrecked on an island. The population of this island can be partitioned into two groups: knights and knaves. Knights answer all questions truthfully; knaves always lie. While wandering, you come upon a building with two doors, each guarded by one native islander. You know that one of the doors leads to a pile of treasure, and the other leads to a hungry, man-eating lion. You may ask a single yes/no question to one of the guards. Then you must select a door, and meet your fortune/death.

Warm-up: If you know that exactly one of the guards is a knave and one is a knight, what question do you ask? This is the standard knights and knaves puzzle.

Challenge: If you know nothing about the distribution of the two islanders (maybe two knights, maybe two knaves, maybe one of each), what question do you ask?

Hard challenge: The island also contains some residents who reply at random. You happen upon three islanders, and know that there is one of each type (Knave, Knight, Random). You may ask three yes/no questions. (Each question can be addressed to only one of the islanders.) What do you ask in order to determine their identities?

Harder challenge: Same as the hard challenge, except that the islanders reply in their language, where {yes, no} = {foo, bar} but the exact correlation is unknown. Wikipedia lists this as "the hardest logic puzzle ever."

Impossible:

This post's theme word: ambisinister, "clumsy with both hands." Unfortunately, it does not mean that you are equally sinister with both sides of your body.

IDoS debriefing

It wasn't really that bad. I think I used up all my sadness over the weekend, and also in looking at apartments yesterday in the rain. Very wet, through my shoes to my socks.

Now life is renewed and delicious:

• Happy birthday to M. and S.!
• My new office is much better-positioned than my old one (people walk by, I am close to the lab, there is some distantly-accessible natural light), and my new officemate is either extremely considerate or afraid of me. Either way is fine.
• The LHC has not yet destroyed the earth. (Check here to see if that's still true.)
• In an overview yesterday, I determined that everything is going well and, in general, I'm in a happy and productive phase.
  

This post's theme word: boggify, "to make boggy."