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So we had the hundred logicians.

All of their foreheads were painted blue.

And before they entered the room, they were told that at

least one of you hundred logicians has your forehead

painted blue.

And then every time that they turned on the lights, so that

they could see each other, they said OK, once you've

determined that you have a blue forehead, when the lights

get turned off again, we want you to leave the room.

And then once that's kind of settled down, they'll turn the

lights on again.

And people will look at each other again.

And then they'll turn them off again.

And maybe people will leave the room.

And so forth and so on.

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

perfect logician.

They have infallible logic.

So the question was, what happens?

And actually maybe an even more interesting question is

why does it happen?

So I'll answer the first, what happens?

And if just take the answer, and you don't know why, it

almost seems mystical.

That essentially the light gets turned on and off 100

times, and then after the hundredth time that the light

gets turned on, and the lights get turned off again, all of

them leave. They all leave. So I mean, it's

kind of weird, right?

Let's say I'm one of them.

Or you're one of them.

I go into this room.

The lights get turned on.

And I see 99 people with blue foreheads.

And I can't see my own forehead.

They see my forehead, of course.

But to any other person, I'm one of the 99, right?

But I see 99 blue foreheads.

So essentially what happens if we were to watch the show is,

the lights get turned on.

You see 99 blue foreheads.

Then the lights get turned off again.

And then the lights get turned on again.

And everyone's still sitting there.

And I still see 99 blue foreheads.

And that happens 100 times.

And after the hundredth time the light gets turned on,

everyone leaves the room.

And at first glance, that seems crazy,

because nothing changes.

Nothing changes between every time we turn on the light.

But the way you need to think about this — and this is what

makes it interesting — is what happens instead of 100, let's

say there was one person in the room.

So before the show starts — they never told me that there

were going to be 100 people in the room.

They just said, at least one of you, at least one of the

people in the room, has your forehead painted blue.

And as soon as you know that your forehead is painted blue,

you leave the room.

And that everyone's a perfect logician.

So imagine the situation where instead of 100 there's only

one perfect logician.

Let's say it's me.

So that's the room.

I walk in.

And I sit down.

And maybe I should do it with blue.

And then they turn the lights on, and say,

look around the room.

And I look around the room, and I see nobody else, right?

And remember, even in the case of one, we've painted

everyone's forehead blue.

So in this case, this one dude, or me or whoever you

want to call him.

His forehead is painted blue.

So he looks around and he sees no one in the room.

But he remembers the statement, and maybe it's even

written down on a card for him in case he forgets.

That at least one of you has your forehead painted blue.

So if he looks around the room and he says, well I'm the only

dude in the room.

And they told me that at least one of the dudes in the room

is going to have their foreheads blue.

Well, I'm the only dude in the room.

So I must have a blue forehead.

All of their foreheads were painted blue.

And before they entered the room, they were told that at

least one of you hundred logicians has your forehead

painted blue.

And then every time that they turned on the lights, so that

they could see each other, they said OK, once you've

determined that you have a blue forehead, when the lights

get turned off again, we want you to leave the room.

And then once that's kind of settled down, they'll turn the

lights on again.

And people will look at each other again.

And then they'll turn them off again.

And maybe people will leave the room.

And so forth and so on.

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

perfect logician.

They have infallible logic.

So the question was, what happens?

And actually maybe an even more interesting question is

why does it happen?

So I'll answer the first, what happens?

And if just take the answer, and you don't know why, it

almost seems mystical.

That essentially the light gets turned on and off 100

times, and then after the hundredth time that the light

gets turned on, and the lights get turned off again, all of

them leave. They all leave. So I mean, it's

kind of weird, right?

Let's say I'm one of them.

Or you're one of them.

I go into this room.

The lights get turned on.

And I see 99 people with blue foreheads.

And I can't see my own forehead.

They see my forehead, of course.

But to any other person, I'm one of the 99, right?

But I see 99 blue foreheads.

So essentially what happens if we were to watch the show is,

the lights get turned on.

You see 99 blue foreheads.

Then the lights get turned off again.

And then the lights get turned on again.

And everyone's still sitting there.

And I still see 99 blue foreheads.

And that happens 100 times.

And after the hundredth time the light gets turned on,

everyone leaves the room.

And at first glance, that seems crazy,

because nothing changes.

Nothing changes between every time we turn on the light.

But the way you need to think about this — and this is what

makes it interesting — is what happens instead of 100, let's

say there was one person in the room.

So before the show starts — they never told me that there

were going to be 100 people in the room.

They just said, at least one of you, at least one of the

people in the room, has your forehead painted blue.

And as soon as you know that your forehead is painted blue,

you leave the room.

And that everyone's a perfect logician.

So imagine the situation where instead of 100 there's only

one perfect logician.

Let's say it's me.

So that's the room.

I walk in.

And I sit down.

And maybe I should do it with blue.

And then they turn the lights on, and say,

look around the room.

And I look around the room, and I see nobody else, right?

And remember, even in the case of one, we've painted

everyone's forehead blue.

So in this case, this one dude, or me or whoever you

want to call him.

His forehead is painted blue.

So he looks around and he sees no one in the room.

But he remembers the statement, and maybe it's even

written down on a card for him in case he forgets.

That at least one of you has your forehead painted blue.

So if he looks around the room and he says, well I'm the only

dude in the room.

And they told me that at least one of the dudes in the room

is going to have their foreheads blue.

Well, I'm the only dude in the room.

So I must have a blue forehead.

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