Fermat's Room (2007) - full transcript

Do you know
what prime numbers are?

Because if you don't,
you should just leave now.

In 1742, the mathematician
Christian Goldbach

observed that even numbers
could be expressed

as the sum
of two prime numbers.

It's easy to see
with small numbers.

18, an even number, is 7 + 11,
which are prime.

24 is 5 + 19,
which are prime.

50 is 13 + 37, and so on.

Say an even number.

100.



1,000.

100 is 83 + 17.

And 1,000 is 521 + 479.

It works with much
larger numbers too.

Let's see, any number...

7,112.

7,112...

is...

5,119 +...

1,993...

both prime numbers.

But you can't check it
with all even numbers

because numbers are infinite.

A law had to be found
that would cover them all.



And finding it became
the most difficult problem

in the history of mathematics.

Will you sign this?

Yes, of course.
Your name?

In?s.

For In?s.

For In?s
Kisses'!

- Here you are, In?s.
- Thank you.

- And good luck!
- Thanks.

Why "good luck"?

On February 20 I'm presenting
my demonstration

of Goldbach's Conjecture.

Come up! Hurry!

- Your demonstration's ruined.
- Fuck!

- What will you do?
- I can repeat it, but I need time.

I don't know how
they got in without being heard.

FERMAT'S ROOM

FOUR MONTHS LATER

You like puzzles, don't you?

See if you can answer this.

What is the link

between Georg Cantor,
Yutaka Taniyama and Kurt G?del?

Let's see.

The three were mathematicians.

- The three went down in history...
- And the three went mad.

Kurt G?del formulated
the Theorem of Incompleteness.

Kurt G?del committed suicide.

I was very tempted to commit
suicide a few days ago.

But I remembered we had
this game,

something that you forget
very often.

You can't go on like this.

You have to get out. I'm speaking
as a doctor, not as a friend.

You tell me three times a day.
Three!

I'm speaking as a mathematician,
not as a friend.

In fact, I'm going to go away.

Want to see what I got
in the mail today?

Rook F to E 8.

You'll see.

"If you are capable of solving
the following puzzle,

which I don't doubt,

you will be invited
to a weekend gathering

with the most ingenious
mathematical minds.

Sincerely,

Fermat. "

What's the puzzle?

It's...

a sequence of numbers.
You have to find the pattern.

I've got ten days,

but it isn't easy.

TEN DAYS LATER

...8, 5, 4, 9, 1, 7...

Well? Have you solved
the problem?

No, I haven't.

And this was the last day.

If you want to stay late,
I'll leave you the key.

Drop it in the mailbox
afterwards.

Thanks.

One thing...

put back any books you use
in alphabetical order.

In which order are
the following numbers?

Eight, five, four...

they're in alphabetical order!

It's their alphabetical order!

"Dear Sir,

only you
and three other people

were able to resolve
the puzzle.

As I said in my last letter,

the mathematical society
I preside over

would value your presence

at one of the meetings we arrange
to exchange knowledge.

I hope you weren't offended
by the test.

Now I know I can trust you.

If you trust me,
follow my directions.

On Friday, July 25, at 19:00,
come to the meeting point.

Take Highway 141 to Km 18.

Take the turn-off
and continue to the end.

Remember
I am relying on you

to put to you
what I believe to be

the most ingenious,
unedited enigma ever set out.

Do not bring a cell phone.

Give no information about your
identity to the other guests.

Your pseudonym
during the gathering

will be Pascal.

Sincerely, Fermat. "

I'm sorry,
I've broken down here.

It happens with old cars...

Mr. Hilbert.

- We're going to the same place!
- Yes. What a coincidence.

The more you study logic,

the more you value
coincidence.

Do you know
whose phrase that is?

No.

Mine!

Hello.

Are you going
to the mysterious gathering?

According to my invitation,

I should call myself Oliva.

That'll be
for Oliva Sabuco, right?

The 16th century scientist.

I'm an inventor.

Have you invented anything
I might have used?

I don't know.

Lots of things,
from huge hydraulic presses to...

look, things like this.

You'll like this.

This is...

well, you put the corn
in here and then...

the popcorn
comes out of his mouth...

a duck.

Why the nicknames?

Well,

in theory because what matters
at these meetings are the ideas,

not the people.

That's nice.

I'm sick of people saying
I'm right because of who I am.

Yes, it's best
if we don't know each other.

But I do know you.

I saw your photo in a magazine.

It said that you'd resolved...

Goldbach's Conjecture.

Is it true?

If it is, it's best if no one knows.

You'd all say I was right,
just because of who I am.

Hi, there!

We're all here now.

We weren't
supposed to know each other.

And we don't.

Mr. Galois picked me up
on the road.

It's 19:00. Now what?

To be precise,
there's half a minute to go.

I suppose they'll come
and get us.

You've done this before?

Yes.

There are always games
and things.

I bet they'll pick us up

in a luxury car.

Whoever is coming
won't be punctual.

In 5 seconds it'll be 19:00.

Well, 3 seconds,

2, 1...

Lights!

Hey! Hey!

Hey!

Hey!

I think you've
just found the luxury car.

PYTHAGORAS

Well, this reminds me...

of the riddle
about the shepherd

who has to cross
the river in a boat

with a sheep, a wolf
and a cabbage.

You know it?

Only two can go in the boat...

for example,
the shepherd and the sheep;

or the shepherd and the cabbage.

You have to work out
how he can cross the river

without the wolf eating the sheep
or the sheep eating the cabbage.

Why would
a shepherd bring a wolf?

What's more,

I don't see what it has to do
with this situation.

Perhaps Professor Hilbert meant
that one of us is the shepherd,

another, the wolf; another, the sheep;
and another, the cabbage.

They connected the car's
system to a PDA.

They probably programmed it
to switch on the lights at 19:00.

Now what?
Where do we go?

We're here,

and we have to drive to there.

We have to go in here.

Here?

In a grain store?

I've certainly seen
more stylish chicken farms.

The usual place
for these gatherings would be

an elegant drawing room...

a library

filled with books
on mathematics,

a blackboard
for doing calculations,

a nice couch, armchairs,

a tea table.

So, anything missing?

Well, at first sight,

Mr. Fermat is missing.

What time is it?

21:50.

Does anyone know anything
about our host?

I only know
that I know nothing.

We can't know anything.

I know something.

I checked up and I discovered
a few things about Fermat.

Shall I tell you?

That's against the rules.
I'd rather not know.

True,

but now that one of us has got
more information than the others,

isn't it best to share it,
so we're all on the same level?

Okay.

A month ago,

we had to send the solution
to Fermat's P.O. Box.

P.O. Box 325.

Well,

I looked for the name
of the owner of 325.

To discover Fermat's real name.

The Post Office can't
tell you that. It's confidential.

In theory, yes.

I went to the Post Office
and said I was president

of "Defend the Brown Bear. "

I said there were only 325
brown bears left in our mountains

and we wanted that P.O. Box
as a symbolic number.

The employee said
that the number had been taken.

I insisted on how important
the number was for us

and how 325 brown bears
would be very grateful.

And he gave you the name
of the P.O. Box owner?

And a donation for the bears.

Yes, he gave me Fermat's name.

I looked on the Internet,
and here's the good part.

There isn't one file
in his name...

nothing.

Right.

That's all?

Congratulations, you've discovered
that you've discovered nothing.

At least,

what is Fermat's name?

Yes, it was...

something with F,
like... Fran, no, Fer...

Wait, wait.
A bit slower.

We can't process
so much information at once.

You discovered something else.

Good evening.

Forgive me for being late.

I'm Fermat.

It's worth waiting
if the enigma is really original.

- The enigma you're talking about...
- Well,

there's no hurry.

We can sit down first
and take things calmly.

No, no.

The greatest enigma
ever set out is:

how is it that four people
are in here together

and still haven't
touched the supper?

The last gathering
of this kind that I attended

was about this.

Oranges?

No, Kepler's old problem
about how to pile up spherical forms.

It's still unsolved, isn't it?

The fact is, mathematicians
worry about stupidities

with no practical application.

It's not stupid to be famous
for solving a problem.

It should be
any mathematician's dream.

Then I'm not any mathematician.

I recently read a study
about the human being's

most common
impossible wishes...

to fly and to be invisible,
not to resolve mathematical enigmas.

What do you think?

I'd prefer to fly.

Why?

I don't know,

to fly,

to see places,

to enjoy it.

I'd ask to fly too.

But if we could all fly,
it wouldn't be special.

It's special
if only you can do it.

I think flying is overrated.

I think it's much more practical
to be invisible.

For what?

To see without being seen.

I think being invisible
is only useful for doing harm.

What would a person
want to do if he were invisible?

Go into
the girls' changing rooms,

steal tips in bars,
go to Mass naked...

nothing good.

When we do something good,
we like to be seen.

Yes, but if I were invisible,

I'd use it to do good for all
of humanity without being seen.

And no one
would have to thank me.

When is this guy going
to tell us the damn enigma?

Well,

I guess that we'll start now

with the greatest enigma.

I don't know. I guess so.

- Excuse me.
- Yes.

Yes?

When you investigated Fermat

and got so much information,

do you remember
if he was a murderer?

- Why would he be?
- Come on!

Because of the five
of us who are here,

he's the only one with a cell!

Get it? A cell!

It's not funny.

I think I have to leave.

Is anything wrong?

I think that was the hospital,
but I couldn't hear well.

And then I was cut off.

What's happening
at the hospital?

My daughter is there.
She's in a coma.

In that case,
it may be good news.

Or it may be bad.

Maybe they just need
some information,

and I'll be back in an hour.

You'd better carry on
without me.

I know what you're thinking.

All this is too weird.

Fermat forgot his jacket.

Fermat!

Fermat! Your jacket!

All right!

Well, let's see what we'll do

now that we're alone!

Where's Pascal?

Fermat's jacket!

Of course!

Let's see.

Rom?n...

Rom?n, Rom?n...

Fermat is called
Rom?n Naranjo L?pez.

Sound familiar?

Rom?n Naranjo...
I've never heard of him.

I don't know any Rom?n.

The P.O. Box
I checked out wasn't in that name.

It was like...

It was Ferm?n de la Vega,
or De la Cuadra...

Or De las Vegas,

or De las Cuevas...

Maybe it wasn't Ferm?n.

"You've got one minute
to solve the following enigma.

A sweet seller receives
three opaque boxes.

One box contains mint sweets,

another aniseed sweets,

and another a mixture
of mint and aniseed.

The boxes have labels which say
"Mint", "Aniseed"

or "Mixture. "

But the sweet seller is told that
all the boxes are wrongly labeled.

What is the minimum number of sweets
the man will have to take out

to verify the content of each box?"

Don't tell me the greatest enigma
ever set out is this rubbish!

A stimulating problem!

Listen to me.

What happens if we don't
solve it in a minute?

Read it again, Oliva.

There are three boxes,

one with mint sweets,
one with aniseed sweets

and one with a mixture.

They're wrongly labeled.

How can you label them, removing
the smallest number of sweets?

It's easy,
you take one from each box.

No, because you'd have
one of mint, one of aniseed

and one that could be of either.

How do you know
where the mixture is?

This wall is moving.

Let's see,

to know which is the mixture,

you have to take out
more than one.

So, you take out three,
and all are aniseed.

Can you be sure
it's the box of aniseed?

It's a problem of probabilities.

Just take out one sweet.
It's an infantile problem.

The key is in the statement:

all the boxes... all the boxes...
are wrongly labeled.

If that is so,

you just have to take
one sweet from the "Mixture"

because the mixture
can't be in there.

If the sweet is mint,
the box is mint.

So where is the mixture?

They can't be here,

because then the aniseed
would be here

and the box would be
correctly labeled.

But as they're
all wrongly labeled,

the mixture is in here
and the aniseed sweets are here.

Answer: one sweet.

Okay, I'll put it here
and see what happens.

CORRECT.

Now will you listen to me?

The room is shrinking.

Didn't it open outwards?

An enigma.

"You've got one minute
to break the following code:

- One, one... "
- What's the code?

It's a huge list
of ones and zeros.

If we take longer than a minute,

the room will shrink again.

This must be a game. It's...

a joke by our host.

Let me see. 1, 1, 1, 0, 1...

- How many numbers?
- I'm counting them...

it's 169.

You know what 169 is,
don't you?

I've got an idea.
I need pieces of something.

This...

Look,

over two months ago
Mr. Rom?n Naranjo

bought four hydraulic
presses.

Is it normal for a host to go
to so much trouble to play a joke?

I don't know.

You said you'd been in lots
of gatherings like this.

No, not in lots,
I've been in two...

two, counting this one.

Fermat,
Rom?n Naranjo, whatever,

doesn't want to play a joke.

He wants to commit a crime.

He's bought four Poseid?n
hydraulic presses,

one for each wall.

And I guess he's connected
the system to the PDA.

He's assigned a time to each riddle
and, if we take longer,

the presses move again.

- Will you be much longer?
- Not much.

This room is
about 50 sq. meters.

If each press advances
10 cm per minute...

That means in an hour this room
will be the size of an elevator.

An elevator
with too much furniture.

We'll fix this another way.

Will someone help me?

- Where do you want to go?
- You're wasting your time.

Do you know what a press like that
is used for in real life?

Inform us.

Have you ever seen

the presses that turn cars
into a cube of scrap?

When those presses
are no use anymore,

they're made into a cube
by a press like the one back there.

There's another one there,

and there,

and there too.

All right!

Push!

All right!

That's it!

That's it!

Shit! What fucking kind
of gathering is this?

What have we done
to that guy?

Just sit down and keep trying
to find the answer!

We have to solve the enigmas
in the time we're given.

Yes, but we're human,
we'll get tired.

The machines won't.

Why do you think
he wants to crush us?

No, not you lot.
You're just extras.

He wants to kill me.

It has to do with his daughter.

A few months ago,
I managed something important.

I sold a patent.

It was for a doll...

that made popcorn.
You've seen it.

They organized a party.
The company director was coming,

but he rang to say he'd be late,
it was raining

and impossible to find a taxi.

I offered to go and get him.

I got in my car, started it
and drove to his house.

I'd gone about a kilometer,

when suddenly

I noticed a strange
smell in the car.

It was dog shit.

What would the director think

if he got into that gas
chamber on wheels?

You didn't open the windows?

It was raining too hard.

I thought of something better.

I'd put my shoe
in the glove compartment.

I took off my shoe.

I put it in the glove compartment.

When I looked up,

there was a girl in front of me,

crossing without looking,
without traffic lights, nothing.

I wasn't going fast.

If I'd braked then,
nothing would have happened.

But I didn't.

At that moment,

I imagined my bare foot...

pressing the brake pedal
smeared with shit.

Even so, I braked.

But those milliseconds of doubt
had delayed me...

and I hit the girl.

I called an ambulance
and waited for it to arrive,

but then I drove off.

But she had crossed where
she shouldn't.

All you did wrong was
to run away.

I went to the police station
the next day.

When the effect of the drinks
from the party had worn off?

I tried to apologize
to her family,

but they wouldn't
let me see them.

When I saw this photo...

in Rom?n's wallet,

I put it all together.

And the cynic said he was going
to see his daughter!

I've got it!

169 must be 13 by 13,
the coordinates of a square.

The ones and zeros
form a face. See?

0, 1, 1, 0, 0, 0...

So the answer to the problem:

a face. I'll put it in.

It hasn't stopped.

It's not a face.

It's a skull.

I'll put it in.

CORRECT

Fermat wants to kill you.
I understand that much.

But what about us?

Do we have to die because
you knocked someone down?

You're circumstantial victims.
He wants to kill me.

You're all part of this trap.

A new enigma!

Come on,
we've got one minute.

Stop drinking.
We need clear neurons.

Let's see:

"Inside a hermetically sealed
room there is a light bulb,

and outside the room
there are three switches.

Only one
of the three lights the bulb.

While the door is closed,

you can press the switches
as often as you want.

But when you open the door,

you have to say which of the three
switches lights the bulb. "

Shit!

Let's imagine we push
two switches, #1 and #2.

We open the door
and the bulb isn't lit.

That would mean
the correct switch is number three.

- But if...
- And we parked at the lake!

...we still don't know
if the right one is #1 or #2.

He'll be sinking our cars
now to leave no trace.

Let's concentrate.

Something doesn't fit.

What if I hadn't solved
the enigma on the invitation?

The numbers were
in alphabetical order, it was easy.

Did anyone help you
or give you a clue?

No.

Put back any books you use
in alphabetical order.

Let's concentrate on the switches
and the light bulb.

Time's running out.

Why is he going to so much trouble
to get his revenge?

- Why doesn't he just shoot you?
- Stop it!

I don't know
what Fermat wants from us,

but he thinks
the simplest way to get it

- is with this room.
- I've got a theory,

but let's solve this first.

Great!
Now we'll be in the dark!

- What is it?
- Nothing.

I burned myself.

You burned yourself.

The trick is
in the temperature of the bulbs!

We turn on a switch, #1,
and leave it on for a while.

Then we switch it off,
switch on #2 and open the door.

If the bulb is lit,
the right switch is #2.

If it's off and is hot,
the right switch is #1,

which we'd left on for a while.

If it's off and cold,
the right switch is #3.

Case resolved.

That's the solution.

Come on...

Correct.

Oliva,

what's your theory
about what's going on?

For me, the jacket is the key.

Did Fermat forget it
or leave it behind on purpose?

I think he left it on purpose

so Pascal would
find the girl's photo.

Without that jacket,

Pascal wouldn't know
why Fermat wants to kill him.

But there is a reason...
the accident.

We three don't know
why Fermat wants to kill us.

I don't know what,

but we've done something.

Hot, isn't it?

The Audi, how much is it?

- Which Audi? The maroon one?
- Yes.

There is only one.

I'm in a hurry, really.

45 euros, please.

45, Christ's age.

Shit, I forgot my wallet.

You don't leave without paying.

But...

- Did you know Fermat before?
- No.

This is me.

Without any pseudonym,
I don't know what I did to be here.

I knocked his daughter down,
I told you that.

I'm a mathematician because
it's the only thing I can do.

Apart from that,

I return video tapes
without rewinding them,

I lie in electoral surveys,

I take communion
without fasting,

I pick fruit without using
plastic gloves.

Could anyone hate me
for things like that?

I've got no enemies.

THE HISTORY OF MATHEMATICS
I harm no one, so no one harms me.

Are you sure?

I spent five years working
on Goldbach's Conjecture.

Three weeks before the presentation
someone got into my room

and destroyed everything.

You're 26.

And?

That's the age
at which Oliva Sabuco died.

How old are you?

Twenty-two.

Evariste Galois died at 22.

And Blas Pascal died at 39,
the age I am now.

And at what age
did David Hilbert die?

Pierre Fermat died at 64.

Rom?n Naranjo is 64!

I'm sick of this guy!
I bet he's here,

looking at us
from some hiding place.

Rom?n!

What do you want?

Now we'll have
seven years of bad luck.

Anyone want to hear
the new enigma?

"How can you time
a period of nine minutes,

using two sandglasses,

one of four minutes
and one of seven?"

We've got two minutes.

Here, these might help you.

Pascal,

do you think
the presses will stop

when the shelves
are all together?

Only one thing
can stop a Poseid?n press...

two Poseid?n presses.

We've got four.

Can't we set them
against each other?

All right.

This is the plan of the room.

The door was here,

the blackboard,

this is the table...

and here,

here and here
are the bookcases.

Maybe we can
neutralize the forces.

Sooner or later,

you'll have to tell them
what you know.

What's the length
of the bookcases?

- About two meters high.
- And the width?

All together,
no more than four meters.

So, if we do...

this...

- I know what you want to do.
- Will it work?

There's just one way
to find out.

The way
to find out is by doing it.

Oh, right.

I've got it.
I'll send the answer.

How long have we got?

20 seconds.

Check the answer.
We need the time.

I'm sure.

We start the two sandglasses
at the same time.

When the first one finishes,
four minutes will have passed.

We turn it upside down.

Three minutes later, the sand is
finished in the seven-minute one.

We turn it upside down.

When the sand is finished
in the four-minute one the second time,

eight minutes have passed.

The seven-minute one
will have timed one minute.

We turn it over and we've got
the nine minutes.

- You see it?
- Yes, absolutely.

One second left.
I'll send it now.

A new enigma.
I'll read it out loud.

"A student asks his teacher:

How old are your daughters?
The teacher answers:

If you multiply their ages,
you get 36.

If you add them,
you get your house number.

I'm missing a detail,
protests the student.

The teacher answers: You're right,
the eldest plays the piano.

How old are
the three daughters?"

That's surrealistic!

One daughter is nine,
and there are twins of two.

But don't send it yet.
We need time.

- How do you know?
- It's a classic, I can't explain now.

You think it'll resist?

Pressure is unpredictable.
It can turn coal into dust or a diamond.

Was that Archimedes?

No, MacGyver.

Hurry! Come on!

Put the answer in the PDA!

I haven't got it!

What?

Who's got it?

It was on the table
when you overturned it!

It had to fall here!

What's that?

Fermat's invitation.

- What?
- The invitation he brought.

Why did the host bring
an invitation?

It's addressed
to Rom?n Naranjo L?pez.

"Only you and four others

have been invited
to the gathering I'm organizing.

On Friday, July 25, at 22:00,
come to the warehouse... "

He was told to come here!

"Remember
to bring your cell phone.

Your pseudonym during
the gathering will be...

Fermat. "

What is this?

We should look for the PDA
while there's room.

Don't you get it?

They arranged for Rom?n to arrive
ten minutes after we did,

and he was told
to introduce himself as Fermat.

When Rom?n arrived,
as he was the last,

we all assumed he was the host.

If he wasn't the host,

why did he sit
at the head of the table?

He sat in the seat we left for him,
thinking he was the host.

So he impersonated the host?

No, Rom?n never knew
he was our host.

That's why he seemed odd.

You'd better carry on
without me.

How could we carry on
without him?

Why was only he told
to bring a cell phone?

To tell him the story
about the hospital.

Yes?

Rom?n is innocent.

I'm sure of it.

I think he didn't
even recognize you.

The PDA!

I'll send it.

CORRECT

You rang me, I left a meeting,
I forgot my wallet,

I drove 60 km,
I ran out of gas,

I have to go back
to pay for it...

But I'm saying
we didn't call you!

Maybe you didn't,
but someone here did.

Speak to the nurse.

Speak to the nurse!

Mr. Naranjo, listen to me.

We're in a hospital!

Okay.

Show me the number
on your cell phone.

It says "Private number. "

When we call, the switchboard
number comes up.

Mr. Naranjo, your daughter
is still stable.

We didn't call you.

All I know is I have to drive
60 km to the meeting,

get my wallet,

go back
and pay for the gas

and drive another 60 km.

Mr. Naranjo,

why not leave it
for tomorrow?

Go home and rest.

Yes, thank you.

My house keys
are in the jacket too.

You realize?

The keys, the jacket, the gas...

I feel so sorry for him.

What I don't understand is,

if Rom?n didn't organize
all this, who did?

The person who
destroyed your demonstration?

That was some kid
who was jealous.

Come on, a kid doesn't go
into a hall of residence,

destroy documents
and leave without being seen.

Miss Oliva, you shouldn't
solve a problem

with information that isn't
in the formulation.

How do you know
where it happened?

We were dating for two years.

Then, we broke up.

Why did you break up?

Ask her.

- She might tell you.
- We broke up, that's all.

Soon after, I got
the invitation to come here.

I thought it was your doing.
If I called you, it was to clarify it.

I thought if we pretended not
to know each other, started again...

That was your idea.

Yes, and I stick by it.

"In the False Land,
all the inhabitants always lie.

In the True Land,

all the inhabitants
always tell the truth.

A stranger is trapped
in a room that has two doors.

One door leads to freedom,
the other doesn't.

The doors are guarded by a jailer
from the False Land

and by another
from the True Land.

To find the door to freedom,

the stranger can only ask
one question to one of the jailers,

but he doesn't know
which is from the False Land

and which is from the True Land.
What question did he ask?"

We've got less than a minute.

I saw that in a film.

One jailer always tells the truth.
Imagine that it's you.

- The other lies... you.
- It should be the other way round.

You're the man locked
in the room.

If I ask which door is
the right one...

You don't know
which is lying.

I've got an idea.

If I asked you which door
he'd tell me is the right one...

As I always tell the truth,
I'd tell you

he'd say that one.

I've got it.
You have to ask one of them

which door the other one
would tell me is the right one.

As you would both point
at the wrong door,

I take the opposite one.
Get it?

Careful!

Correct.

Why did you two break up?

He got it into his head
that I had a lover.

You couldn't
convince him otherwise?

It's a problem of ages.

I'll calculate it,
I'm the most aged.

I never...

I never liked Internet.

But one day I went in

to play chess.

What's more innocent than playing
chess with someone you can't see?

From time to time,

we sent messages

until...

one day something
happened with him

that had never happened
to me before with anyone.

He beat me.

We played chess dozens of times
and he always beat me.

So I got interested in him.

One day the idea came up...

of meeting
to play face to face.

He invited me to a party where
there would be important people.

In his house?

No.

Not in his house...

on a boat.

On a boat? Why?

That's what I wondered too.
Why on a boat?

Then I found out.

It had to be out at sea
because at that party...

things happened that would be
illegal in any country.

You want to know
what things?

Come on.

Dare to ask.

No, forget it.

At that party...

things happened,

and the things that happened

made me go back more times.

Wait a minute.

Couldn't that guy
have organized all this?

No.

Why not? He's idle, eccentric,
smart, rich. Why can't he be...

It can't be him
because he's in here!

Time's up.

Want to hear the problem?

"The mother is 21 years older
than the son. "

I never thought he'd be here.

"In six years he will be
five times younger than the mother.

What's the father doing?"

We've got 10 seconds.

You both deserve to die here!

What are you doing?
You'll die too!

I don't care!

You don't care if you die?

All this is too interesting

for the person
who organized it to miss it.

If I'd organized all this,
I wouldn't settle just for revenge.

I'd want to see it all.

What do you mean?

The culprit could be someone
so keen to kill his victim

that he doesn't mind dying.

Are you saying I'm capable
of organizing all this?

You said that they deserve to die
and you don't care about anything.

Breaking this PDA

is the closest thing
you could do to killing us.

You knew there was
something between us.

All this is just your style,
so childish.

Those pedantic enigmas,
those stupid brain teasers...

Did you have
to organize all this?

You could have
bought four hydraulic presses

in Rom?n Naranjo's name.

You could have set up the room,
sent the invitations.

You could have done it.

But you didn't.

What?

I've just realized he didn't do it.

Remember after the supper.

We were moving around,
clearing the table

and waiting for Fermat
to set out the famous enigma.

Then there was
an unexpected sound.

That call was
a fundamental part of the plan.

Fermat would have to leave
the room and we'd suspect him.

Whoever made the call

was the person
who organized all this.

He couldn't have done it because
he was next to me on the couch.

Only one person
could have made that call...

the one who wasn't in the room
when Fermat was on the phone.

Is anything wrong?

You just have to resolve one X.

Efr?n Cuevas!

He sent the letters.

It wasn't Ferm?n.

It was Efr?n!

The last call was made
at 22:55.

You called
Fermat from this phone.

Call for help!

There's no time.

Call Fermat.
Maybe he's on his way back.

Fermat is dead.

Good evening.
Your driving license, please.

I haven't got it.

Well, I do, but it's in a house
5 km from here.

Follow me
and I'll show it to you.

Please, I'm asking you.

Follow me, it's very close.

Why don't you come with me?

Please, I'm begging you, really.

Please.

No answer.

How do you stop this?
How do we get out?

There is no way out.

You'll die too.

I've been preparing
this moment for some time.

I even made a model.

May I?

Here it is.

My demonstration that Goldbach's
Conjecture is correct.

You destroyed
his demonstration?

Me?

Two months ago I was so close
to demonstrating it.

I was only missing
a few minor verifications.

And, suddenly I saw this!

35 years looking for the solution

and a kid finds it ten days
before you.

And saying things like:

"My only merit is being young. "

I didn't know what to do.

I considered
committing suicide.

But I felt a...

a brutal curiosity
to meet you.

Then, I read this in the press.

"The solution to the greatest
mathematical enigma

sabotaged. "

I sent you an e-mail,
but your girlfriend answered.

That's how we met.

She confirmed what
I found so hard to believe...

your work was sabotaged

and you had to redo everything.

I was immersed night and day
in Goldbach's Conjecture

until I managed to prove it.

Here it is.

Thank you.

This is brilliant.

I demonstrated the Conjecture,
but you did it first.

Even if you take another three years,
you'll still be the first.

Unless you don't manage
to recover it.

And why can't you see
what the father's doing

if the mother is 21 years older
than the son?

- I can't take any more! I can't!
- Come on!

In six years, the son will be five times
younger than the mother!

What is the father doing?
It's a negative result!

It's possible!

The son has minus
three quarters of a year.

What is the father doing?

- I don't know!
- Leave him alone!

Minus three quarters
is minus nine months!

The father is screwing
the mother.

I set up this room
to put your intelligence

to the test.

I'll give you your grades.

What have Rom?n and I
to do with this?

Tomorrow they'll think Rom?n
took his revenge on you

and we were all sacrificed.

When they blame Rom?n,
he'll defend himself.

I told you, he's dead.

He can't be.
I saw him drive away.

After supper,

we cleared the table.

I couldn't imagine the situation
with the false host

would be so much fun.

Before things
got out of my control,

I went out
to make the famous call.

Yes?

Good evening, Mr. Naranjo.
I'm calling from the hospital.

- Yes?
- Just a moment, please.

You cleverly discovered that.

But you don't know
that while I was talking to him,

I put phosgene in the clasp
of his safety belt.

You have to come here
immediately.

Your daughter...

If inhaled, phosgene causes
asphyxia in less than two minutes.

It leaves no trace

and if you're driving...

I think I have to leave.

Is anything wrong?

...the accident hides
the cause of death.

- What are you doing?
- Calling Fermat.

I never answer if I'm driving.

One must be careful.

Don't you know that 28%
of people who die on the roads

travel like you,

without their safety belt?

So all the rest, the other 72%,

die with their belt on.

I don't believe
you don't mind dying.

When they find us,
I'll be clinging to this dossier.

I'll go down in history
as the mathematician

who demonstrated
Goldbach's Conjecture.

That's enough for me.

It's my fault for lying.

What?

I didn't resolve
Goldbach's Conjecture.

I told you I was working on it
so you'd notice me.

And it worked.

Then the lie got bigger,

there were interviews,

they asked for a demonstration.
I didn't know how to gain time.

No one went into my room.

I destroyed everything.

I didn't know what to do.

I did it for you.

I did it for you!

Then,

I really was the first.

I resolved Goldbach's
Conjecture before anyone.

- What are you doing?
- He deserved it!

He's thought of some way
of getting out at the last minute!

I don't believe that story
about dying with the dossier.

I'm sure he had
an escape planned.

Why don't we just admit
we're going to die?

We'll die at the same age
as Galois, Sabuco, Pascal,

but David Hilbert died
in his 80s.

This guy
wasn't intending to die.

This room was a test
of our intelligence.

There must be a way
of passing it.

FREEDOM

It's breaking!

It's a bolt!

Come on.
There's only room for one.

- No, I won't fit!
- If your head fits, your body fits.

Try putting your ass in a helmet!

- I'm out!
- Send it up!

- The exit is blocked!
- I can't!

Push it up!

- Push it up!
- I can't. It's too heavy!

- Try to push it!
- I'll try with this.

Go on, you next.

- Hurry up!
- No, no, wait!

- What is it?
- Just a second!

- We don't have a second!
- Got it!

- Shit!
- What's wrong?

My pants have got caught!

Look...

the last quarter...

how ironic.

It's shrinking too.

What will you do with that?

It's a problem.

If I publish this demonstration
just as it is,

Efr?n Cuevas will go down
in history and he'll have won.

But if I publish it with my name,
it wouldn't be ethical,

but it would be the easiest for me,
and take a load off my mind.

- What are you doing?
- Problem resolved.

But why?

It was the solution to a problem
unsolved for over 250 years.

How can you
do that to the world?

The world is as it was.

Shit.

FERMAT'S ROOM