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!
...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."
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?
Forgive me.
I'm so sorry!
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!