The odd numbered color? You don't know how many of each color exists. You can't sort the colors either. If someone has been sorted they've been told their color.

we know there is 200 in the room and a person only goes to stand in either side of the room once they have been to the front of the room and did a count themselves. i am assuming that there is an even spread of coloured hats.

You can't assume an even distribution of hats though.

how devious

No, it doesnt.
"Nobody knows their own hat color, and no one is allowed to signal or speak of each other's individual hats."

You're grabbing two, and then relying on them not being an idiot and doing an "if theyre ____, I must be ____.

Question is not written as clearly as it needs to be if you want a different answer.

The riddle takes place at the Pentagon

September 11, 2001

I said the first step is to form a single file line.
have the first two people stand together against the wall, and then close their eyes.
next person in line stands between them if they are non identical colors, or to the right of them if they are, then they close their eyes.
the fourth person goes to the right if the three previous are the same color, if not they stand between where the Blue and Yellow groups meet.

this eventually forms a line of people. ...BBBB[B]|[Y]YYYY...

and everyone may open their eyes, but not everyone will know their hat color yet. those in brackets do not.

so everyone that DOES know their hat color based on position in line will pull off, leaving two people behind, who based on the instructions given will know their hat to be the opposite color of the person they are left with.

I also said I'd share how one might reach the solution.

which is like a magician revealing a trick, so pay attention.

the ability to assess the utility of information, and the importance when quantified, helps smart people get ahead from those less talented.

In the OP, amidst the bevy of mistakes I made, was a condition of the problem that should have stood out as seeming more Material than it really was.

200 participants.

If the condition was changed to 20, the answer should be similar?

And surely the problem would be easier to solve with only 3.