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This is another brain teaser that deals with people trying

to logically deduce what's on their forehead.

And it's called the Forehead Number Game.

So what's going to happen is I guess you could say the god of

brain teasers is going to get three

people in a room together.

Once again, these three people are perfect logicians.

Which means they have infallible powers of logic.

And they know that the other two people — they're three

people in total — are also all perfect logicians and have

infallible powers of logic.

We get them into the circle, and we'll say

this is the top view.

So this is the top of one guy's forehead.

They're all bald for convenience.

To make it easy to paint things on their head.

This time we're not going to paint blue

paint on their forehead.

We're actually going to paint numbers.

So you could say the dungeon master of this game, or the

the god of this game says I'm going to pick three numbers.

So three numbers will be picked.

They will be unique.

Which means that no two of these numbers are going to be

the same number.

There are going to be three different numbers.

They're all going to be greater than zero.

And this is key: One of the numbers is going to be the sum

of the other two.

And they tell this to all of the logicians.

So this is the method that they use to pick the number.

And they tell this to the three parties right there.

And what they do is they take these three numbers.

And they write them on people's foreheads.

So say the numbers are a, b and c.

And we know that a plus — let me scroll down a little bit b

is equal to c.

We know that a, b and c are different.

And we know that a is greater than zero.

b is greater than zero.

And c is also greater than zero.

What they do is they paint them on their heads.

So this guy will have a on his forehead.

This guy will have b on his forehead.

And let's say this guy has c on his forehead.

And so when this guy looks out — and you know, the reason

we're even putting things on people's foreheads is because

you can't see what's on your own forehead.

No tricks involved here.

All you can see is what's on the forehead of the other two

people in the game.

So this guy is going to see a and b.

This guy right here is going to see the foreheads c and a.

And then this guy's going to see these two

foreheads, c and b.

So that's the rules of the game.

And of course, you don't know; this guy, the number on his

forehead is c.

And it happens to be the sum of a and b.

But he doesn't know that.

He doesn't know whether it's the sum or not.

He doesn't know he has the sum number.

This is just the way I happened to draw it.

So given those rules of the game.

And let's say you're one of the players.

And this is the view you see.

You look at the two other people in the game.

Let me see if I can draw them a little bit better.

So you look at one person.

This is your view.

So this is one person in the game.

On his forehead — which is fairly large — you

see the number 20.

And on the next guy, who I'll draw in purple.

The next guy, you see the number 30.

And what happens is — so this is literally your view.

So they're seeing you with some number on your forehead.

And this guy can see this 20 and

whatever's on your forehead.

This guy can see this 30 and whatever's on your forehead.

And the game show host, or the dungeon master or soon.

whoever, says, OK what's on your forehead?

And you look at these two people, and you say, gee, I

to logically deduce what's on their forehead.

And it's called the Forehead Number Game.

So what's going to happen is I guess you could say the god of

brain teasers is going to get three

people in a room together.

Once again, these three people are perfect logicians.

Which means they have infallible powers of logic.

And they know that the other two people — they're three

people in total — are also all perfect logicians and have

infallible powers of logic.

We get them into the circle, and we'll say

this is the top view.

So this is the top of one guy's forehead.

They're all bald for convenience.

To make it easy to paint things on their head.

This time we're not going to paint blue

paint on their forehead.

We're actually going to paint numbers.

So you could say the dungeon master of this game, or the

the god of this game says I'm going to pick three numbers.

So three numbers will be picked.

They will be unique.

Which means that no two of these numbers are going to be

the same number.

There are going to be three different numbers.

They're all going to be greater than zero.

And this is key: One of the numbers is going to be the sum

of the other two.

And they tell this to all of the logicians.

So this is the method that they use to pick the number.

And they tell this to the three parties right there.

And what they do is they take these three numbers.

And they write them on people's foreheads.

So say the numbers are a, b and c.

And we know that a plus — let me scroll down a little bit b

is equal to c.

We know that a, b and c are different.

And we know that a is greater than zero.

b is greater than zero.

And c is also greater than zero.

What they do is they paint them on their heads.

So this guy will have a on his forehead.

This guy will have b on his forehead.

And let's say this guy has c on his forehead.

And so when this guy looks out — and you know, the reason

we're even putting things on people's foreheads is because

you can't see what's on your own forehead.

No tricks involved here.

All you can see is what's on the forehead of the other two

people in the game.

So this guy is going to see a and b.

This guy right here is going to see the foreheads c and a.

And then this guy's going to see these two

foreheads, c and b.

So that's the rules of the game.

And of course, you don't know; this guy, the number on his

forehead is c.

And it happens to be the sum of a and b.

But he doesn't know that.

He doesn't know whether it's the sum or not.

He doesn't know he has the sum number.

This is just the way I happened to draw it.

So given those rules of the game.

And let's say you're one of the players.

And this is the view you see.

You look at the two other people in the game.

Let me see if I can draw them a little bit better.

So you look at one person.

This is your view.

So this is one person in the game.

On his forehead — which is fairly large — you

see the number 20.

And on the next guy, who I'll draw in purple.

The next guy, you see the number 30.

And what happens is — so this is literally your view.

So they're seeing you with some number on your forehead.

And this guy can see this 20 and

whatever's on your forehead.

This guy can see this 30 and whatever's on your forehead.

And the game show host, or the dungeon master or soon.

whoever, says, OK what's on your forehead?

And you look at these two people, and you say, gee, I

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