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Coyotek4


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This story is a sequel to Twilight's Logic Puzzle Adventure


The Cutie Map sends Twilight Sparkle back to the mysterious twin-towns of Utopia and Paradise, where some ponies are always truthful and others always lie. Can Twilight solve the puzzles she will face and unravel the mystery? And why was Ocellus summoned to join her?

Chapters (7)
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Comments ( 15 )
Ri2

His name is Coccyx? Ouch.

Also, all this logic makes my head spin. How do you keep it all straight?!

This is beautiful. I love this fic and its predecessor.

So, when they heard there was a town where earth ponies were impersonating unicorns and pegasi, the changelings must have said to themselves, "Hold my beer." I knew I was going to like this the moment it popped up in my feed!

Oh, my goodness. Now we've got changelings in the mix as well? Whoo boy. I could barely deduce the solutions as it was!

Interesting. How did Zodiac know?

Oh wow, I gotta say, that last puzzle really tripped me up. Ocellus's deduction was rather impressive!

I wonder what Zodiac knows :rainbowhuh:

Ok, I think I've got it.


First we start with the Twilight on the far Right, that Twilight claims to be Coccyx. Since Coccyx must lie, the real Coccyx cannot make that statement. Moreover, since the real Twilight and Ocellus must tell the truth, they cannot be the rightmost Twilight, so the that Twilight must be one of the generic Changelings.

Now, lets look at the leftmost Twilight. That Twilight claims to be the real Twilight. Either this IS the real Twilight telling the truth, or this is one of the non Ocellus Changelings lying. Lets assume it is Twilight and see how it goes out. If this is Twilight, only Ocellus is left that can tell the truth. The middle Twilight claimed that Twilight is on an end, so that one is telling the truth. The Second Twilight however claims to not be Twilight. This would also be true, meaning that we have three Twilights telling the truth. Therefore the Twilight on the left cannot be the real Twilight.

Now that we know the Twilight on the left has to be a lying, we know the middle Twilight is as well. (Since the middle twilight claims Twilight is on the end, but we have proven both ends are lying.) This means we know the pattern of Truth and Lies must be LTLTL. Since Twilight number 2 claims to not be twilight and is telling the truth, this must be Ocellus. This leaves Twilight number 4 to be the real Twilight. Since the real Twilight claims that Coccyx is on an end, and we have already proven that the far right Twilight has to be a generic Changeling, the Leftmost Twilight must be the Real Coccyx.

So the order of Identities is Coccyx, Ocellus, Changeling, Twilight, Changeling

I love this fic, and the series it comes from.

Let's examine the first claim: "I am Twilight". If true, then that would also make statements two and three true, which is impossible if only two of five are telling the truth. So the first claim must be false.

Let us then examine the second claim: Only Ocellus and Twilight would tell the truth, and for "I am not Twilight" to be false then Twilight would need to say it, which she can't since she always tells the truth. None of the liars would admit they aren't Twilight, so the sole pony who can make that statement according to the stated rules is Ocellus. The second pony is Ocellus therefore.

The third statement combined with what we deduced about the first, "Twilight is on an end", can be true only if pony number five is Twilight. But Pony number five claims to be Coccyx. Since Twillight always tells the truth then pony number five can't be Twilight, and the third statement must be false.Therefore, Twilight cannot be on the end. We already identified pony number 2 as Ocellus. This third statement has proven false, which can't therefore be uttered by Twilight. Only pony number four remains as a possibility.

The fourth statement, knowing that we just determined it as truth coming from Twilight, means Coccyx must be one of the ponies on either end, either nr. 1 or nr. 5. But pony nr. 5 states that they are Coccyx, which must be a lie -Coccyx always lies- and thus cannot be Coccyx. Coccyx must be pony nr. 1.

To sum up, Nr. 1 is Coccyx. Nr. 2 is Ocellus. Nr. 4 is Twilight.

This one seems easy,
if 1 is true, then 2&3 are true and there can only be 2 true statements,so 1 is false.
If 2 is true, its Ocellus, it can't be false as only twilight saying it makes it so, and she says the truth.
3 cant be true cause only Ocellus can say so, and i just said she's 2.
If 4 is false that makes them Coccyx, but that means twilight cant be 1 or 5, witch makes her 3, but that cant be correct so 4 is True, so it must be twilight.
As only liars are left, Coccyx must be 1 or 5, but since 5 said he is Coccyx and we know its a lie, Coccyx is 1.
In conclusion, 1 is Coccyx, 2 is Ocellus and 4 is Twilight

I don't usually try these, but here goes...

“I am Twilight.”
“I am not Twilight.”
“Twilight is on an end.”
“Coccyx is on an end.”
“I am Coccyx.”

Let's start with the last one, "I am Coccyx." It cannot be true, because only Twilight or Ocellus would tell the truth, and neither of them is Coccyx, so it must be some anonymous changeling. This means only one of the ends is still uncertain, which means only one (and exactly one) of the previous two statements--"Twilight is on an end" or "Coccyx is on an end"--can be true. (If both were false, Twilight and Ocellus could not have said them, meaning they must be the first two speakers. Then "I am Twilight," the first statement, would be true, thus Twilight would be on an end and thus the "end" statements wouldn't both be false.)

If "Twilight is on an end" is true, so must "I am Twilight" be, and vice versa. This means there are only two options--"Twilight is on an end" and "I am Twilight" are both true and the other two are false, or "I am not Twilight" and "Coccyx is on an end" are true and the other two false. Let's assume the first case--that "I am Twilight" and "Twilight is on an end" are true. But if "I am Twilight" is true, the one saying "I am not Twilight" cannot be Twilight and thus would also be true. But "I am not Twilight" must be false in this system. So we can move on to the second case.

Having ruled out all other options, "I am not Twilight" and "Coccyx is on the end" are true, and "I am Twilight" and "Twilight is on an end" are false. The one saying "I am not Twilight" must be Ocellus, since it must be true and therefore cannot be Twilight. So "Coccyx is on an end" is Twilight, and the only end available ("I am Twilight") is Coccyx. That leaves "Twilight is on an end" to be an as-yet unnamed changeling.

Man, "Twilight" doesn't even look like a word anymore.

I used individual spoiler tags for each paragraph, so you can follow along and stop at any point, and there's an extra spoiler tag inside one of the others for a mini-proof.

Pro tip for puzzle solvers: When someone makes a statement implying that they are a liar, that person definitely is a liar, just not in the specific way they claim. Conversely, if someone makes a statement implying they are "not" a "truth-teller", that person is definitely a truth-teller.

As soon as I read the statement, I knew how he was trapped. I have said this before, and I'll say this again. I love these types of fics.

9094951
There are more? Please tell me where I can read other writers' work of this type.

9095687
It's not EXACTLY this type, but ones that make you use your head. I forget where the last one I read is, but you will ALWAYS get a favourite on these from me.

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