Knights or Knaves!

Courtesy of xkcd. I like to think of this as "Knights, Knaves, (K)nuisance". So we looked at a bit of probability with the first, now let's look at logic with the second. Introducing, the 2nd puzzle! The famous Knights or Knaves puzzle!

I came across this puzzle (or rather, was assigned this puzzle) in my Symbolic Logic class in sophomore year. While I had to use truth tables and translating all these sentences into propositions in the formal language, I'll just give you a little sample of what the puzzle entails and build from the ground upwards. So here goes.

There is an island far off in the Pacific, called the island of Knights and Knaves. On this island, there are people called knights (who always tell the truth) and knaves (who always lie). They may be either male or female.

You meet three inhabitants: A, B and C. A says  it s not the case that C is a knave. B says C and A are both knights. C says  A is a knight or B is a knave. Which, if any, are knights? Which, if any, are knaves? 

If that was nothing more than a walk in the park for you, the next one is arguably the most famous case of the Knights or Knaves puzzle and you've probably come across it somewhere.

John and Bill are standing at a fork in the road. You know that one of them is a knight and the other a knave, but you don't know which. You also know that one road leads to Death, and the other leads to Freedom. By asking one yes/no question, can you determine the road to Freedom?

And then if you're REALLY up for the task, check this out. I kid you not when I say this, but this is officially "The Hardest Logic Puzzle Ever". It's actually called that! You get this, and you are easily considered one of the finest logicians today, assuming people can consider themself to be a logician by trade. As if you didn't realize already, this is mad HARD, and I would advise you to actually save yourself before risking your head exploding from the sheer ridiculousness of it. It's also appropriately epic in its polytheistic subject matter and scope. So without further ado, "The Hardest Logic Puzzle Ever".

Three gods A, B, and C are called, in some order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for yes and no are 'da' and 'ja', in some order. You do not know which word means which. 

...So yeah, let's see you how fare with these. As usual, solutions to follow after. In the meantime, give thee brain a workout with these 3 puzzles!

~Shimmy