Right? Because he's a perfect logician.

And that everyone's a perfect logician.

So imagine the situation where instead of 100 there's only one perfect logician.

So, everyone is also told, and this is true, everyone is a perfect logician.

I'm a perfect logician, but I still can't figure out what's on my forehead.

Von Neumann, and a logician, and a mathematician from the army put this together.

And they're also all told that everyone in the room is a perfect logician.

And this guy, he's a perfect logician, so he makes the exact same conclusion.

And then you, as a perfect logician says, oh, now I know what my number is.

So this guy, because he's a perfect logician, will deduce that he has to have a blue forehead.

And not only are they all perfect logicians, but they all know that everyone else is a perfect logician.

So for example, let's say I enter into the room, and because I'm a perfect logician I see things that allow me to perfectly deduce that I have a blue forehead.

I'm a perfect logician, so if I can assume, if I'm simulating the reality where I don't have a blue forehead, then this guy will see, I don't have a blue forehead.