Unfortunately, Twilight's bad feeling soon proves to be entirely correct, because as soon as you return to Canterlot Castle, you find the entire staff in a state of panic. As soon as the mountain in Ponyville disappeared, Princess Celestia, Princess Luna, and Princess Cadance, who happened to be visiting, suddenly became afflicted with a strange and mysterious condition. They've started babbling in some sort of strange and alien language, and absolutely nothing that any of the best experts can do can seemingly break the curse.
You borrow the tools and quickly send a letter to Twilight, who quickly teleports herself to the throne-room, having regained the ability to use her magic. As it turns out, after everypony left, Twilight discovered a strange text right in the centre of the rubble where the mountain used to be. The bad news is that Starlight Glimmer's...unfortunate accident unleashed three evil spirits who seem to have chosen Celestia, Luna and Cadance as their hosts to render the population of Canterlot into a catatonic state, as they feed on their brainwave energy and the magic of friendship all over Equestria. The good news is that these spirits were sealed away by Star-Swirl the Bearded long ago, and with it, instructions in the text on how to send the spirits back to from whence they came, thanks to a rather handy spell known as the 'Hero's Sporting Chance For The Sake Of Drama' Spell, which he perfected while vacationing in Olde Trottingham. This prevents the spirits from trying to flee should anypony make an attempt to banish them, so at least all hope isn't lost.
His text describes the problem as such: one of the spirits tells nothing but the truth, one spirit tells nothing but lies, and the other answers questions posed to it randomly. A quick asterisk at the bottom of the page states that the random spirit decides whether to answer 'yes' or 'no' through some sort of coin toss in its mind, so not even it knows how it will answer: it's truly random in every aspect. To banish them, their identities must be ascertained in two or fewer questions. However, there is a rather major problem impeding your progress.
The spirits dwell in another world, and speak in a language that bears no resemblance to any language on this planet today, and not even a pony as brilliant as he has managed to decipher even one recognisable word. In other words, you have absolutely no way to actually understand any of their answers, regardless of whether they are the truth, or a lie. Well, horseapples.
One last thing he also notes is that the spirits are omniscient and don't take kindly to those too smart for their liking, and should the questioner pose a question that is paradoxical and cannot be answered, they spirits will automatically 'rage-quit' and just render their host body totally unconscious, preventing you from asking them any more questions, for being a smart-flank. The exception is the spirit of randomness, who cares nothing for truth, lies, or even if the answer makes sense.
Having gathered all three possessed princesses in one place, it is now up to you to prevent Equestria from turning into a nation of apathetic losers and save Equestria from certain doom. Your country needs you, citizen, so cranks those brain cells like never before!
And don't go thinking that just a general summary of the answer is enough! With only one, complicated answer, we couldn't make it that simple!
Uploaded missing answers. Figured this is the one that REALLY matters
I've seen the TED video, so I'll refrain from answering.
9429024
Nope. There's three changes to this puzzle that make it WAY harder.
1. You have 2 questions, not three.
2. The random princess doesn't decide whether to lie or tell the truth randomly - she decides whether to answer yes or no randomly, so she's COMPLETELY random.
3. You don't know what the words meaning yes or no in their language even are before you start.
Oh god this is complex
ask any princess if they will answer this question with no?
If we asked the truthful one she passes out
We then ask either princess if they will answer this question with a yes?
This causes the liar to pass out and the random one to be random, problem solved
But what if the first question is asked to the liar or random? They wont pass out
9429056
Heh...you're sort of on the right lines.
Quick hint: the questions you need to ask are...slightly longer than that
Oh i think i have it
ask pony X: if i ask pony Y "are you the liar?" Will their results be the same if i ask you "are you liar?" ?
If pony Y is random,pony X passes out as they cant guess weather or not they can answer the same
If pony Y is truthful and X lies,X responds with a yes
If X is truthful and Y lies,X responds with no
And if X is random,we cant trust the response
If X does pass out, ask pony Z if they will answer this question with a yes? If they pass out, they tell the lie, if they answer, they tell truth
If X doesn't pass out ask Y: if i ask pony X "are you the liar?" will the result be the same if i ask you "are you the liar?"?
If X is random, Y passes out
If X isnt random, Z must be random and if Y answers the same as X did we use that to determine who is the liar
9429453
This doesn't work. You have complete language ignorance at the start. Without a way to tell yes and no apart, how are you going to interpret the answers correctly?
What if, for example, pony X is random and Y lies, but X happens to respond with the word that means no? Without a way to tell them apart you're going to fail.
9430105
So wait, we dont know what yes or no is, but are they diffrent words?
9430274
Yes and No are, logically, different in some noticeable way.
I have a question, spoilering because it might give away something:
Obviously, I do not know what the words are going into this. However, if I were to hear the two of them, would I be able to put them in some sort of pre-determined order, alphabetical or otherwise - an order that has nothing to do with the order I initially heard those two words? I assume this is the case, but this is an alien language so I thought I would check.