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Three evil queens, accompanied by their magic mirrors, go for a girls' night out. At some point of the night they decide to finally settle the eternal question: who's the fairest of them all? Of course, the best way to do that is to ask the mirrors! But nothing is ever easy, especially if by this time none of the queens is quite sure which of the mirrors is theirs, and no mirror is crazy enough to tell any evil queen that she's not the fairest...

The queen's mirrors look identical but have different approaches to answering the questions: one of them always tells the truth, another always lies, and the third one will tell the truth to the owner and lie to anyone else. The queens decided that each of them will ask each of the mirrors one question, and they'll use the answers to figure out who owns each mirror and who is the fairest of them all.

Here are the questions they came up with, and the mirrors' answers to them.

The table with questions and answers

And here is a "checksum" for the answer: if you got all connections right, you'll get the name you're looking for.

The checksum image

So, who's the fairest of them all?

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Truthfulness: T(ruth), L(ies), F(aithful)

Let's start with Mirror 3. It

Cannot be F or L, and therefore must be T and belong to Queen A.
The double negative to B and C defines this.
If it is F, it belongs to all queens...or no queens. If it is L, it belongs to both B and C.
Therefore, Queen B > Queen C.

With only 2 truthfulness options left, Mirror 1

Cannot be F, and therefore must be L and belong to Queen C.
F forces us to look at all 3 combinations.
If it belongs to Queen A (so far so good), it also belongs to Queen C. Same thing if it belonged to Queen B. If it belongs to Queen C, then it also doesn't belong to Queen C. No go.
Which means Queen A > Queen C.

And with that, Mirror 2

is F and belongs to Queen B. Which means that Queen B > Queen A.

Summary of findings so far:

Summary of findings so far

Queen B > Queen A > Queen C.

With our good friend the checksum (thanks for that, OP!), here's what we get.

Almost there!

So this is where I'm scratching my head. If I go by the connections being the letters to look at, I get

OMORSL

And if the lines are strike outs, I get

LRECZIUA

Based on a comment from Exal and clarified by athin, using the strikeout method, you can simply read the name

Lucrezia, which is an actual name.
Lucrezia (Borgia), if we take the most well-known of the name. Reading through the article, she marries a couple of dukes, which makes her a duchess instead of a queen... But a name's a name.

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    $\begingroup$ I promise I worked the rest of the puzzle on my own! I think the answer is (rot13) na nantenz bs YERPMVHN, anzryl YRPEHMVN, juvpu vf n tbbq Rivy Dhrra anzr rira vs lbh vtaber gur Obetvn. $\endgroup$ – Exal Aug 28 '20 at 6:47
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    $\begingroup$ Btw it's not an anagram, it's simply a reading order :) $\endgroup$ – athin Aug 28 '20 at 7:14
  • $\begingroup$ @athin Oh, you mean like a normal person. facepalm at self $\endgroup$ – KarmaFodder Aug 28 '20 at 17:56

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