Hint 1: Search for reliable purple statements

[prof]

Even the dumbest idiot wouldn't try swallowing a roll whole if there might be a needle inside.
True. If we accept the purple blindly, there's no chance the truth will come to light.
A roll with a needle in it... I like that analogy. The precious votal information might all be wasted thanks to one, tiny lie.
Just which ones of this vast collection of purple have lies in them? Just thinking about it makes my head hurt.
Then why don't we try turning the chessboard over?
Huh? What do you mean?
It's simple. Forget which ones are lies. Let's concentrate on finding out which ones must be true.
Are there any purple statements that we know must be true?
That's what we're looking for. We'll look for people who couldn't possibly be the culprit. If we can do that, then all of their purple statements are the same as red truth.
I see. Instead of searching for the culprit, we'll start by searching for those who couldn't be the culprit! Hmm, quite a fundamental strategy!
That's it. There's got to be someone, so let's look through it carefully.
In other words, you have to start with the first step?
Let's see what they can do.