Original subtitles

Turning to the cruiser ship explosion that killed a medical school director...

Coast Guard examiners have found no evidence of a bomb onboard.

Examiners believe the explosion may have been caused by a freak accident.

But several weeks ago, the director had received a death threat.

Could someone have fired on the boat from shore?

That would be physically difficult.

Sinking a boat that size...

would require a large military weapon of some kind.

It would leave definite tracks.

And it could easily be traced.

I find it highly unlikely.

"Unlikely"?

There is an explanation to everything.

Take this simple experiment using a Gaussian acceleration device.

A steel ball rolls along a rail, striking a row of stationary balls.

As you can see, the last ball is pushed away...

at the same speed as the striking ball.

The law of energy and momentum conservation.

But now let's add to the rail a powerful neodymium magnet.

Watch.

Prior to impact...

the rolled ball receives instant acceleration from the magnet.

That speed gets transferred to the ball at the end.

What would happen if we multiplied the magnet's strength by many times?

The ball at the end would become a high-speed projectile.

In short, this tiny steel ball... would become a rifle bullet.

A superconducting accelerator.

Let's harness the power of a super-conducting magnet.

Stand by!

Right.

Extinguish!

I'm guessing the perpetrator used a device like this to sink the boat.

But who could build such a device?

Super-conducting magnets are found in large MRI and CT scan equipment.

Umeyashiki Medical Systems?

They do have a research facility near the Haneda coast.

How did you know?

Electromagnetic noise.

There were reports in the area from local residents...

of clocks stopping and disrupted TV signals.

Evidence of a magnetic field generated near the lab.

So the death threat was from someone at Umeyashiki?

That's for you police to answer. I've no interest in that.

Yeah, yeah.

You're only interested in how it happened, right?

Precisely. Now go lead your investigation.

Wise guy.

I bet you're clueless when it comes to questions science can't answer.

Such as?

Such as...

love.

Love?

Yes, that is irrationality at its best.

Why don't we insert it into an equation?

ax� + bx + c = "love"

Can't be solved.

No kidding.

The area of a triangle? Base x height / "love".

Or a circle would be radius� x "love"?

Very funny.

"Love" is a construct, therefore...

Forget I asked. It was a waste of time.

Precisely.

Masaharu FUKUYAMA

Kou SHIBASAKI

Hurry and get up, Misato!

You'll be late!

I know.

I'm going. Don't forget to lock up.

Okay.

See you later.

Bye.

Don't skip breakfast.

< SUSPECT X >

Thank you. Come again!

Good morning.

Lunch special.

One special!

600 yen exactly.

Thank you, as always.

Here you go!

It's getting cold out.

Man, it's cold!

Morning!

Winter's here.

Thanks for waiting.

Early bird special!

Have a good day!

Misato?

Don't you have a key?

Ow, ow, ow!

Surprise!

How'd you?

Can't hide from your ex-husband.

Get out!

Brought your favorite cake.

I'll call the police.

I found work.

I'll work hard this time.

Let's give it another shot.

No way.

Now leave.

I saw your shop.

Congrats. That was your dream.

Hostess savings?

None of your business. I beg you to leave.

Honey...

Don't touch me!

I'm home!

Hi, Misato!

To your room.

Show some manners!

Lower your voice!

Bad attitude.

Just leave us alone.

How rude.

Fine.

I'm going.

What're you doing?

Saying hello to my daughter. Hey, Misato!

She's not your daughter.

She'll be a beaut.

Get her working at a night club in a few years.

You'll never shake me.

Stop trying.

Misato!

What did you do? Give me that!

Misato!

Let go!

That wasn't smart, was it?

You wanna die, kid?

Is that what you want?

Stop it!

Get up! Let me see your face!

Run, Misato!

Move!

Come here.

No!

Stop it!

Oh my God...

what've we done?

Misato, get in your room. Quickly.

Who is it?

Ishigami, from next door.

Just a minute!

I'll be right there!

Is everything okay?

Were we noisy?

I'm sorry... a cockroach.

My daughter and I...

Killed him?

The roach.

Yes. We're fine now.

I'm really sorry.

Ms. Hanaoka...

it wasn't a roach.

Media got here fast.

Brass has arrived.

Sir!

Chief Kusanagi!

How've you been, Utsumi?

Are you heading this?

Yup. This here's Sgt. Kakimoto.

Utsumi... Kaizuka Precinct.

Who found him?

Kids playing baseball.

Effects?

Nothing yet.

That bike could be his.

Probably stolen.

And that?

His clothes were burned.

Coroner?

Arrived 30 minutes ago.

Who's handling the media? That bird's a nuisance.

I'm cold just looking at him.

Heat pad.

You sure?

I've more.

You come prepared.

Prints were burned?

Yes.

Face is crushed, too.

Just great.

Forget dental records.

It'll take time.

Victim's name...

Shinji Togashi, 39, unemployed. From Hamamatsu City.

Blood type: A.

Time of death... between 6 and 10 p.m., Dec. 2nd.

Currently lives in Kawasaki City.

Behind in his rent, he's been staying in boarding houses.

How'd you identify him so quickly?

The day he went missing, he was at an inn in Ota Ward.

The proprietor filed a stolen items report.

He wasn't in his room.

I hate having keys stolen.

Quiet!

DNA from hair in the room matches the victim's.

Prints also match those found on the stolen bicycle.

We can assume the body is that of Shinji Togashi.

What about the weapon? Crime Lab?

It's been identified. He was strangled to death.

No vital signs.

Post-mortem damage.

Cervix.

Deep markings from twined rope cord.

Just like the one you have here.

Heater table cord.

Next, Togashi's associations. Investigation team?

Yes!

Investigation!

The victim was married.

6 years ago to a bar hostess. They divorced after 2 years.

Ex-wife is Yasuko Hanaoka, 35.

She has a teenage daughter. No relation to the victim.

She runs a box lunch shop called "Misato" in Hamacho.

Yasuko Hanaoka's residence?

Yes.

Do you know a Shinji Togashi?

Had you seen him recently?

No, we never spoke.

Thank you.

Were you home the night of Dec. 2nd?

December 2nd?

Several days before his death, Mr. Togashi showed up at the club...

where you used to work.

He left with your shop address.

Did he visit you there?

No.

Nor here?

No.

Where were you the eve of Dec. 2nd?

Let's see.

We went to a movie.

I met my daughter after work.

Misato, right?

What theater?

The Scala in Hibiya.

After that?

We ate dinner and went to a karaoke box.

Different kind of heater cord. She has an alibi, too.

I don't buy it.

A movie and karaoke on a week night?

Good point.

What's more...

she's pretty.

What?

Excuse us.

Know this man?

No.

This your usual return time?

Usually but...

not when classes end early.

Classes?

I'm a high school math teacher.

"Ishigami". Unusual name.

If you'll excuse me.

What time did you return last Tuesday, Dec. 2nd?

"Teito University"

I'd say I was home by 7.

Hear anything next door?

Next door?

Like a visitor.

No, I didn't.

I see.

Thank you for your time.

Hello?

It's Ishigami.

Yes?

The police came, right?

Yes.

That was quick, wasn't it?

Don't worry. That's expected.

Just respond without emotion.

Okay.

Don't show them movie stubs unless they ask.

Where are they now?

In a drawer.

Stick them in the film program.

Not a drawer, but the program.

Okay.

From now on, I'll call only from a public phone.

They might tap mine.

Yes.

Um...

Yes?

Mr. Ishigami?

Are you sure this is the right thing to do?

Yes, I'm sure.

Logic is on our side.

What is logic?

When Einstein posited his particle theory of light...

he added logical beauty to Planck's constant.

As usual, lots of girls.

Cretin.

Obviously, logical thinking demands calm analysis.

Going on "impulse" or "hunches" will lead you astray.

Get that?

Who, me?

I don't always go on hunches.

What brings you here?

We were just passing by.

I think logically, too.

Not here for my help?

Don't flatter yourself. We manage fine.

Actually, yeah.

See the news about the body with the pulverized face?

Our lead suspect has a strong alibi. So we're stuck.

It happens sometimes.

No, it doesn't.

Okay, it doesn't. Help us.

No thanks.

There's no science in a strong alibi.

There might be. A person can't be in two places at the same time.

Explain that.

The suspect's a real beauty.

Want some coffee?

Where's the cable?

I gave it to you!

No, you didn't.

Nitrogen coming through.

We're ready, Professor!

What's the beauty's alibi?

That she was at a movie in Hibiya the time of the crime.

With her daughter.

Professor Yukawa, we're ready.

Then dinner and karaoke afterwards.

Staff at both places corroborate.

At issue is the theater, then. This beauty...

What's with your "beauty" trip?

It's important. She is, right?

Frail but sexy.

Whatever.

Any proof this frail but sexy beauty was at the movies?

She had some.

I bought a film program.

May I see it?

Sorry for intruding again.

Ticket stubs would help, too.

- Ticket stubs? - Yes.

"Little Santa... Dec. 2, 7 p.m."

She's innocent. Why doubt her?

A cop's hunch.

Aha! An illogical and groundless hunch!

And then you say she had to be in two places at once.

Well, that's impossible.

Indeed.

In 1854, a Latvian teacher named Emilie Sagee split in two during class.

What?

Students were shocked to see two Emilys writing on the blackboard.

No way.

It's called a "doppelganger" or "bilocation" phenomenon.

There've been many reports.

By occult freaks.

Can't happen. There's always a reason.

But alas, not one by physicists.

Right! Having ticket stubs doesn't put her in the theater.

She could've left early.

Or bought the tickets in the day.

We know that!

But if that beauty is the culprit, you're in for a hard time.

How so?

An average person wouldn't think about where best to store ticket stubs.

If she did that to strengthen her alibi, you're up against a strong mind.

And an interesting one.

Okay, lab time, Professor.

It's the job of cops, not physicists, to solve crimes.

I enjoyed it, though. Good luck.

By the way...

her next-door-neighbor is an alum of ours. Maybe you know him.

So what? Hurry, Professor.

Ishigami, was it?

Ishigami?

Professor!

Tetsuya Ishigami?

You know him?

I don't use the word "genius" lightly. But Ishigami is one.

Really?

How is he?

He seemed aloof and antisocial.

He's only interested in math.

Math?

Yes, math.

It's not a hard derivative.

It just takes a little creative substitution for alpha.

The police came to Misato's school...

asking about the movie plot.

I'm sure she did fine. Don't worry.

If she followed my directions.

Mr. Ishigami?

Yes?

Why are you helping us?

That man made you suffer, right?

Yes, but...

I'd hate it if I could no longer buy your lunches.

Yes?

Thank you... very much.

I'll call tomorrow.

Yes.

Amazing, huh?

It's going just like he said.

Let's eat.

Still passionate about math, I see.

Our staff doesn't even have material like this.

Please, over here.

Sit anywhere.

Take a cushion.

Thanks.

You can move that.

A friend, you say?

"Bento Misato"

Who gave you my address?

A cop who talked to you. He's an alum, too.

Oh, I see.

This is all I got.

It's been 17 years.

What high schooler could solve the Four Color theorem?

Wasted breath.

Yet nothing could be more fascinating.

Absolutely.

Why high school math?

Hits the spot.

I thought you'd stay and do research.

I planned to.

But my mom was bedridden.

I had to leave the university.

I see.

But math research can be done anywhere.

True.

Still climbing?

Occasionally.

Mountain climbing is like math.

One summit.

The trick is to find the simplest, most logical route to it.

And math has many peaks to be conquered.

Hodge Conjecture, Yang Mills Theory and the Mass Gap...

the P not = NP Problem.

- The Riemann Hypothesis, huh? - That's from the Math Dept.

This tries to disprove it.

I'd like you to assess the proof.

This'll take some time.

I can wait.

Don't forget breakfast, Misato.

I won't.

Bye.

Still working on it?

I figured it out.

Sadly, this refutation is flawed.

Prime number distribution. Admirable try, though.

Just six hours.

The genius has still got it.

I'm glad.

I hear your neighbor's a murder suspect.

Seems so.

You friendly?

No, we just exchange greetings. I buy lunch from her shop.

Too bad. I hear she's pretty.

Interesting route to work.

The scenery never changes. Their lives are like clockwork.

Freed from the clock, humans live more regulated lives.

Interesting.

Yukawa...

how do you stay so young?

I envy that.

That doesn't sound like you.

Sorry I couldn't be a better host.

You kidding? It was great.

- Take care. - Take care.

What's taking so long to get her?

She's our perp, right?

Still missing key evidence. Sorry.

It's Kusanagi's weakness for pretty women.

Yoo-hoo! Hey, Miss!

Utsumi.

Coffee, please.

We're looking into a possible accomplice.

She may have acted alone in the killing, but not the cover-up.

As a former hostess, she's doubtless known enough men.

Watch it, or you might upset the nation's hostess union.

"From Manabu Yukawa. Meet me where the body was found."

Meet me where the body was found.

What kind of batting stroke is that?

Hit with your gut.

When the pitch comes, coil your gut and release!

Totally illogical.

By "gut", you mean generating subumbilical...

Professor?

Well, good luck.

What took you?

I work too, you know.

Where was the body found?

So why the sudden interest in this case?

What's your rundown of the murder?

Ms. Hanaoka...

"the suspect" was meeting the victim here.

The victim came here by stolen bicycle...

and was murdered.

Why assume a bicycle?

It had his prints all over it.

Why were prints on it?

I don't know.

Wouldn't the killer try to wipe them away?

She was flustered.

But she wasn't too flustered to burn his clothes and fingers.

What're you driving at?

That the killer intentionally left prints on the bike.

For what purpose?

To make it look like the victim came by bicycle, and was killed here.

Wait a second.

So Togashi was killed elsewhere and brought here?

The bike was stolen here that day between 4 and 11 p.m.

Why that time frame?

The owner reported it stolen.

A report?

The owner says she tied the bicycle here.

Why choose that particular bike?

Lots of bikes aren't locked up. This one, for instance.

Want my hypothesis?

That bike was brand new, was it not?

Why target a new bicycle?

To ensure it'd be reported stolen.

That would be convenient to the killer.

Convenient how?

I have no idea.

What's up?

I was musing what to eat, and remembered your box lunch place.

So you came all this way?

When I get an idea in my head, I can't let it go.

Hello.

Hello.

It's cold.

Still teach differential equations?

Not anymore.

Physics students could really use it.

Math students, too.

Thank you.

Welcome!

Afternoon.

Afternoon.

What do you recommend?

What's his usual order?

Mr. Ishigami gets the lunch special.

Really?

Then so will I.

One special!

They all look great. I can see why you come every day.

Hello!

Welcome!

Long time, no see.

Mr. Kudo.

You look well, Yasuko.

I heard you opened a shop, and figured I'd help boost sales.

Thank you. What a surprise.

Lunch special!

So you're the boss.

Excuse me.

Your special.

Here you go.

600 yen exactly.

Shall we go?

Thank you.

You haven't changed a bit!

I'll eat this at home.

You're going to take that on the train with you?

Call me eccentric.

I'll part ways here.

Thanks for your company.

Ishigami?

I've a challenge for you. A new math problem.

Which is more difficult?

Inventing an unsolvable problem...

Or solving one.

And there is an answer.

Intriguing. I'll think on it.

I hope you will.

Sorry for surprising you today.

Yukawa's a classmate from college.

He's a very smart man.

Be careful with him.

Understood.

Um...

Yes?

That customer that came into the shop today...

Oh, an old acquaintance.

He helped me out once.

Why? What's wrong?

Nothing. Never mind.

We need to play our next card to stay ahead of Yukawa.

Our next card?

Put Misato on the line.

Misato... it's Mr. Ishigami.

Hello?

What friend did you run into that night?

Kurumi... Kurumi Morino.

You haven't told the police that, right?

No, you told me not to.

Okay, then listen carefully.

Professor Yukawa?

What're you doing?

Burning old reports. I don't trust the shredder.

Did you find out something?

Like what?

You went to her shop.

Just to buy lunch. Ishigami told me it's good.

Don't be cute.

You suspect her, right?

No comment.

I'm doing this out of interest, not to help the police.

- I've been feeding you info! - Please go.

Or arrest me for obstruction.

What's his problem?

Personal interest?

Dr. "Galileo" Yukawa?

Says he's not helping the police. I don't get it.

I do.

Personal interest, right?

She's pretty.

I don't think that's it.

It's all about that.

I bet a lot of regular customers go just to see her.

A lot of cops come here as an excuse to see me.

Regular customer.

Yum, this is addictive.

You're investigating the math teacher.

You're not getting my help.

He goes to that shop.

It stands to reason that he likes her.

That would give him a motive to help her.

She has other regular customers.

And Ishigami has no alibi for Dec. 2nd.

Not conclusive evidence.

There's more.

Like you said, the culprit has to be extremely smart.

He's a "genius", right?

Shinji Togashi's killer... is most likely Yasuko Hanaoka.

And Ishigami helped?

No, he's not directly involved in the murder.

Not involved?

By the time he came along, Togashi was already dead.

How can you be so sure?

If she had sought his help, he'd have devised another plan.

He wouldn't choose murder.

He's not capable of it?

He wouldn't find murder a logical solution.

He's no fool.

Once he learned of the murder, he could help by covering evidence.

He could devise ways to throw off the police.

Give Yasuko an alibi and instruct her.

Like when to provide evidence, how to respond to police.

I bought a film program.

Ishigami created her alibi?

And left prints on the bike, as well as clothing unburned.

Intentionally? Why?

I don't know.

Criminals make mistakes.

Not him. He wouldn't.

But his specialty is math, not homicide.

Yes, but homicide would prove an easier challenge.

Utsumi here.

We got new testimony from the daughter's classmate.

We're sunk.

Okay.

I understand.

It seems Misato just remembered seeing a friend at the movie theater.

At the concession stand prior to the film starting.

The friend corroborates.

The two were certainly in Hibiya that night...

during Togashi's murder.

No... impossible.

Thanks for dinner.

Can we do it again?

That's very kind but... I need to eat dinner with my daughter.

Bring her along next time.

The incident must've frightened her.

I don't know how I can help, but I'd like to try.

It's pouring!

- Sorry! - Be careful.

Thank you.

Well, good night.

Good night.

We're changing the direction of the investigation.

New info on the victim.

He'd been on the run from debt collectors.

Sources say he was on several crime syndicate hit lists.

We're adding the organized crime division to the case.

Get warrants to search crime ring offices and gambling joints.

Investigate Ishigami?

Professor Yukawa still suspects Ms. Hanaoka.

And that Ishigami helped her.

Then we're back to the occult. They were at the theater.

Has Yukawa ever been wrong?

The top brass won't buy it.

I'll work alone. Let me pursue Ishigami.

Don't be stupid.

You, there. Bring a gun and a vest!

Sure thing.

Don't move! Police!

Hands in the air!

Hands up!

Don't touch anything!

Where's the manager? I need the man in charge!

Utsumi here.

Search underway at 1:13 a.m.

Sorry to bother you at work.

That's okay.

Conducting exams?

Makeup tests.

I bet your tests are hard.

No, they're not. Just simple trick questions.

Trick questions?

Like making a functions problem look like a geometry question.

It's easy if you change the way you view it.

I'm sure I'd fail it.

I was terrible at math.

So how may I help you?

The night of Dec. 2nd.

I thought we discussed that.

We borrowed this.

Your work attendance.

This should help your memory.

You were absent from work the morning of Dec. 3rd.

I felt under the weather.

Really?

What do you mean?

Same for Dec. 2nd.

I slept in after a late night doing research.

Is that strange?

We've heard from your staff that you do that on occasion.

They also said never two days in a row... until now.

What's your point?

That something kept you up which made you skip work the next morning.

A cold. I awoke feeling ill.

I see.

Let me confirm one more thing.

There's nothing between you and your neighbor, Ms. Yasuko Hanaoka?

Not a thing. That's the truth.

I checked up on the man you've been seeing.

Let me ask you...

what's your relationship with him?

If it's a romantic one...

I consider it a terrible betrayal.

Do you realize what I've done for you?

Sorry to call you out suddenly.

What's the matter?

I was visited by detectives.

They asked all sorts of questions about you.

I'm sorry that I got you involved in this.

Don't apologize. I'm not upset.

I feel I have a right to make some demands.

Break it off with this man immediately.

Otherwise...

I'll direct my anger at him.

"Four Color Theorem"?

No more than four colors can be used on a map...

without the same colors bordering each other somewhere.

You stumped me.

Hot!

Sichuan food.

My sophomore year in college...

I saw a man on campus frantically scribbling notes.

Yes, this is spicy.

Activates the brain cells.

It does not activate the brain cells.

Continue.

So I asked him...

"Why are you doing that?"

"The Four Color Theorem was proven over 20 years ago."

Know what he said?

"But it's not a beautiful proof."

It made me happy.

I'd found someone I could relate to.

That was Ishigami?

So you had a rivalry.

I never considered him a rival.

Physicists and mathematicians approach problems differently.

Physicists observe and establish hypotheses...

then test those hypotheses.

Mathematicians conduct their simulations in their heads.

Like you understand.

And you do?

Mmm, the smell of jasmine.

Mathematicians solve riddles from a variety of angles.

Ishigami said the same thing.

He said his test questions...

are easy to solve if you change how you view them.

What was it again?

A functions problem disguised as a geometry one.

That's very like him.

A trick question. I had a sneaky teacher like that.

Let me see that copy.

His work attendance.

Hey!

What is it?

"12/2: morning absence. 12/3: morning absence."

Thank you.

Professor?

Yukawa.

It's nothing.

You're picking up the tab?

Yeah.

Thank you. Now, if you'll excuse me.

What?

Yukawa!

Professor Yukawa!

Hello?

It's Yukawa.

I'd like to talk.

I'm sorry.

I'm a little busy tonight.

When can we meet?

Say Yukawa...

you want to go climbing this weekend?

Found this in my mailbox.

"Stay away from Yasuko Hanaoka. You can't make her happy."

Who would do this and why?

Stay away from Yasuko Hanaoka.

You can't make her happy.

Yasuko?

Welcome home.

Hi.

I made curry. Hungry?

Mr. Kudo again?

You think I shouldn't see him?

Well, you don't want to upset Mr. Ishigami.

I'm sure he's helping us because he likes you.

Stop it!

Must I live the rest of my life worrying about what he thinks?

That makes him no different than Togashi!

I didn't expect you'd invite me climbing.

This may be my last chance.

What do you mean?

The police came to my school.

The police have no grounds to suspect you.

But you do, right?

I heard an interesting story.

About your math tests.

Making functions look like geometry.

In short, creating a blind spot.

That's when I remembered them.

The homeless you see every morning.

"Living their lives like clockwork."

I mistook your words.

What you were saying is...

that even the homeless are like parts in a clock...

another gear in the works.

Am I right?

It's not like you to talk in such circles.

It's over, Ishigami.

Is it?

I don't think you're satisfied that you have final proof.

Still, you could tell people your theory.

Why haven't you?

'Cause you're my friend.

I don't... have any friends.

Ishigami!

Ishigami!

Ishigami!

...Either out of range or the phone is switched off.

Utsumi!

The fog will clear soon.

Incredible.

My life feels complete.

I can look at this view and actually be struck by its beauty.

Say Yukawa...

solving that problem won't make anyone happy.

Let it rest.

Why don't you get that?

No, don't!

Hello?

I put two letters in your mailbox.

You'll need the one in the white envelope, so hold onto it.

But make sure you destroy the brown one upon reading it.

And finally...

this will be the last time we speak to each other.

Task Force.

Chief!

Hold on!

A man claiming to be the killer has turned himself in!

What?

Identity?

Tetsuya... Ishigami.

Koto Ward resident, age 38.

High school teacher.

Ishigami gave himself up.

But he's not saying he aided Ms. Hanaoka.

He asserts he killed Togashi!

I met Togashi around 7 p.m. on Dec. 2nd.

I returned home to find him loitering around my apartment.

I immediately knew he was Ms. Hanaoka's ex-husband.

How's that?

I knew that she had been trying to run away from him.

So I spoke to him.

I told him Ms. Hanaoka no longer lived here.

That she'd moved to Omori.

I gave him a memo with a false address.

To lure him to an unpopulated place.

Hold on a second.

Did you plan on killing him from the start?

Of course.

I strangled him to death with a table heater cord.

I smashed his face with a rock so he couldn't be easily identified.

And burned his fingerprints.

I cut away his clothes and burned them in an oil can.

I returned home after midnight.

The cord, burner and knife are all in my apartment.

Found the cord.

Is this the one?

Yes.

Point.

Got the knife.

Please.

Does Ms. Hanaoka know?

No, she doesn't.

I didn't want her saying something that would alarm the police.

I've had no contact with her.

How did you communicate then?

Through a wall mike.

A mike?

Please.

She'd pretend to talk to her daughter...

to send me messages.

Textbook stalker.

What made you give yourself up?

She betrayed me.

Mr. Ishigami?

He says he killed your ex.

Did Mr. Ishigami stalk you?

"Ms. Yasuko Hanaoka"

"I've checked up on the man you've been seeing."

"Let me ask you... what's your relationship to him?"

"If you're romantically involved..."

"I consider it a total betrayal."

Any previous letters?

"Dear Ms. Yasuko Hanaoka..."

"you must destroy this letter after reading it."

"I want you two to follow these instructions."

"The police will visit you again soon."

"I want you to say you were being stalked by someone."

"I want you to continue..."

"answering the police questions with the truth."

"That will protect you."

"Mr. Kuniaki Kudo..."

"seems a sincere and trustworthy gentleman."

"Marrying him..."

"should bring you and Misato happiness."

"Ms. Yasuko Hanaoka..."

"I am eternally grateful to you."

"I was in despair."

"I'd all but given up on life."

"But you saved me."

The same colors cannot border each other.

Is that the Four Color Theorem?

You know about it?

You're testing Appel and Haken's proof.

Without a computer, wow.

It's not a beautiful proof.

Not "beautiful"?

Interesting.

Math student?

No, Physics.

Professor Yukawa...

I'll make coffee.

When I saw Ishigami again...

he asked me something.

"How do you stay so young?"

"I envy that."

It surprised me.

Ishigami was never a man... who cared much how he looked.

That's when I realized...

he was in love.

Please tell me.

What exactly did he do?

My exposing the truth in this case...

won't make anybody happy.

Can you live with that?

You're the one who said he wasn't capable of murder.

The Professor Yukawa I know...

isn't swayed by emotion. He remains logical...

and pursues the truth harder than anyone.

If you find yourself... unable to endure the pain...

let me bear it with you.

Will you listen...

as a friend, not a cop?

As a friend?

Yes.

I want you to let me...

solve this case.

Your alibi is no doubt real.

On the night of Dec. 2nd...

you and your daughter did see a movie.

You've never lied.

No.

That's how you endured the questioning.

But you must've found it strange...

why you didn't need to lie.

Why the police only asked about Dec. 2nd.

That's because...

you killed Shinji Togashi...

the day before on Dec. 1st.

So Ishigami...

to protect you and your daughter...

made the ultimate sacrifice without your knowing.

We're taking you to the detention center.

Just in time.

We need to question him again.

You're kidding.

It'll only set you back 10 minutes.

Come.

What could you ask me now?

Shut up.

You cleared for this?

No.

Kusanagi says to report that he acted on his own.

I'm sorry.

Don't sweat it. No problem.

Enter.

This is what you meant when you said it'd be your last climb.

The police will break the law for you, huh?

You must be something, Yukawa.

Here's my theory.

Togashi's killer...

was Yasuko Hanaoka.

It took place in her apartment.

You heard noises next door.

So you helped them cover up.

I did it.

I'm turning myself in.

No!

But I hit him first, Mom!

Quiet. She's not involved.

That won't work.

Internal bleeding.

Finger marks.

He was strangled from behind, and tried to free himself.

But someone held his arm down.

It was me.

You'd need four hands to strangle him and hold his other arm.

I can't let her be involved. Not my daughter.

I can't let you go to jail, Mom!

"Ogiya"

Let's build an alibi.

Alibi?

But if the body were found, the police would visit them.

They couldn't sustain the act.

So you devised a plan.

Prepare another body...

and make it seem like Togashi's.

The body found by the river was not Togashi.

To protect the girls...

you murdered someone else...

someone whose disappearance... wouldn't be missed.

A homeless person.

I'd like to hire you for some work.

Stay here until evening.

"Ogiya Guesthouse."

"Ogiya Guesthouse."

You intended to leave the man's prints and hair in Togashi's room.

He changed into Togashi's clothes, and met you at night.

Then on a stolen bicycle...

you rode to Omori.

And there...

you killed him.

To make the police think he was Togashi...

you pulverized his face.

Burning his fingertips was just...

to remain consistent with what a murderer would do.

The prints you left on the bike and clothing...

had to match those from the inn.

You wanted the police to think the killer had slipped up.

Then you let the police focus on Ms. Hanaoka...

after giving her an alibi.

The alibi would be airtight.

Because the body found by the river had nothing to do with her.

It looks like a geometry problem. But it's really functions.

An apparent alibi trick was, in fact, a case of switched bodies.

Along with killing a homeless man, you got rid of Togashi's body.

Probably cut him up and scattered the parts.

That's why you missed two mornings of work.

That's the truth of this case.

Very interesting.

You are free to hypothesize.

There's one more rationale for what you did.

While giving yourself up in her stead...

even you might break under police interrogation and spill the truth.

But if you really did kill someone...

you could assert your guilt...

and protect the one you love.

Now you're just babbling.

Ishigami...

you made an innocent man a gear in your clock.

To save someone you love...

you took another life.

A hypothesis becomes fact upon demonstration of proof.

Isn't that right?

It's with the other body.

Let's stop this.

We're done here.

I told her.

I told her everything.

If as you say there is another body...

by the time it's found, my trial will be over.

If I accept the verdict without making an appeal...

the Togashi case is closed.

What a shame.

Such a wonderful mind...

had to be wasted on this.

You're the only one who would say that, Yukawa.

Why go to such lengths to protect her?

What happened?

"Ms. Yasuko Hanaoka..."

"I am eternally grateful to you."

"I was in despair."

"I'd all but given up on life."

"But you saved me."

Good morning. Sorry to disturb you.

We've just moved in next door.

Please accept this.

It's really nothing but...

We'll do our best not to disturb you too much.

Nice meeting you.

Thank you for your time.

Hurry to school.

And you?

Work, but I won't be late.

Okay. See you later!

See you later.

Mr. Ishigami?

You came.

Come in.

Please.

Mr. Ishigami!

Have a nice day!

Who's that, Misato?

Our neighbor.

"I doubt you'll understand what I'm talking about."

"But that's fine."

"Ms. Yasuko..."

"And Ms. Misato..."

"thank you."

"Thank you."

"I wish you both happiness."

"Please forget everything about me."

"You must not have guilty feelings."

"For if you don't find happiness..."

"all my work will go to waste."

Mr. Ishigami...

Why'd you do this for me?

Why?

Mr. Ishigami...

Hold it, madam.

I'm sorry!

I'm so sorry!

What're you talking about?

You can't expect us alone to be happy!

I will atone, too.

I'll accept my punishment with you.

Why?

Why?

Why?

Forgive me.

I'm so sorry!

Forgive me!

Forgive me!

Yasuko Hanaoka admits her guilt.

But Ishigami still refuses to acknowledge it.

I see.

May I sit?

17 years ago...

I first met Ishigami on this bench.

If he had lived his whole life never having felt love...

he'd have never made such a mistake.

Who'd have thought him capable of...

loving someone that deeply?

She's what kept him alive.

What's this?

Come here a second.

Photo!