Well, it occurs to me that you need two pieces of information. 1) Which guard is the Knave/Knight 2) Which door has the treasure.
Asking either guard which door has the treasure is not going to do it. What if that guard is the Knave? You die. Wouldn't want that to happen. So, the only way to ensure that you know the truth is to guarantee that you are being lied to.
Asking Guard 1 what guard 2 would say works because if Guard 1 is the Knave then he will lie about the Knight's response (which would have been a truthful answer. Likewise, if Guard 1 is the Knight, he will tell you the truth about Guard 2's response (which would have been a lie). Either way, you are being lied to, making the actual identities of the guards irrelevant. That being the case, take the door they say is certain death.
The hard challenge is much more interesting. Now you only need one set of information, but the sources of said information are less reliable.
So, let's try talking it through. Label the islanders A, B, and C for simplicity (we'll need as much of that as we can get).
Question 1:
Ask A, "Would B say he is certain he could predict C's answer, if B knew what I was going to ask C?" Complicated, but a Yes/No question none the less.
What does A answer? If Yes, then you are either talking to the Random and B could be either of the others or you are talking to the Knave/Knight and B is the other non-Random. We really don't know a whole lot here, just that B is not Random. Worst case scenario. We'll come back to this in a moment.
If No, then you are talking to the Random. Neither Knight nor Knave will ever answer this question with a No. Proceed to ask B "Would C say you are the Knave?" This guarantees you are being lied to, just like the first challenge. Just switch the answers and use your last question to find out if there's a nice place to get a drink nearby.
If anything else, you are talking to either the Knave/Knight and B is the Random. Neither the Knight nor the Knave can answer this question with a yes or no, because they don't know if they would be lying or telling the truth. In that case, guarantee you are being lied to and go enjoy that drink.
Worst case scenario Question 2: We know B is non-Random in this scenario, so who better to ask? Let's try that same trick again. "Would A say he is certain he could predict C's answer, if A knew what I was going to ask C?"
What does B answer? If yes, then both A and B are non-Random. Use your last question to guarantee you are being lied to.
If no, then you did something very wrong. This should not be a possible answer.
If anything else, then A is the Random. Ask B about C for the Phobos Guarantee and go home.
Convoluted? You bet. Effective, though.
As for the third riddle, word play is less my thing. I prefer the logic puzzles. I might take a look at it later, though.
-Phobos, master strategist and professional Knave
