The Case of the Cooling Corpse

I've decided to finally put up something new after a long time. Yes, this has math involved because I had to do this as a story for my precalculus class. The concept is part of a prompt-Sherlock like story problem that you could google, should you ever have to do something like this.

It's slightly inconsistent because: a) I like Germany and am in the process of learning the language. However, I'm not German, nor do I live there, so I guess this is like Death Note Germany or something. x: and b) I picked Germany because England's overused for murder mysteries and...if my teacher would've read it instead of having that whole others-read-and-grade-your-story method, Japan might've been a bit awkward. xP

Last note: I obviously do not own Death Note or the background concept. And L is awesome. 8D

The night was sorrow and stuffy as the storm plowed through the German countryside. There were few street lights along the dirt roads, so one had to rely on his outside sources and his good sense of direction in order to make his way to his destination. Not that many people actually came through this road these days anymore. The few people who lived in these particular parts of the country had few visitors and were often seen as peculiar. Not peculiar in the sense that they were porcelain doll collectors or made friends with the local raccoon population. They were more peculiar in the sense of being involved in shady activities. These activities would not be known to the average person unless he wanted his head jammed between the blades of a windmill at the end of the day. After all, some of the countrymen were still just innocent tobacco-chewing, gun-toting countrymen living on small pensions. Yet this case, for all intents and purposes, will not be focusing on the average countrymen.

On the dark country road, a red convertible sped through with all the arrogance and power that an American car can muster. Two people sat in the front with large sunglasses despite the glowing night. The driver was older, well-dressed with a thick, white mustache, somewhat resembling the Monopoly man. Even with his light suit, he still felt uncomfortable. He was not used to nor enjoyed this weather very much. Los Angeles had smog and big buildings to deflect heat. London was usually wet and cool and with cooling breezes. Now in the German countryside, it was hot and damp, almost like jungle weather, and since it was only approaching dawn, of course he couldn't ask to turn on the air conditioner. Besides, he had to prove to the young whippersnappers that the elderly could take it, whatever "it" implied.

His companion wore a clingy white long-sleeve and baggy jeans. The passenger's whole demeanor screamed awkward with his lanky figure, unkempt hair, and the way he sat hunched in the seat, his bare feet resting on its upholstery. The driver had been partners with him for almost ten years, but he still envied him. His focus in distracting situations was simple remarkable, regardless of how childish he acted at times. And did that man act childish! There were always unpaid bills for the cable, the hotels, and various cake shops. There wasn't a greater detective who loved cake so much…

The driver turned left onto a paved road. Soon their destination would be met. The passenger bit on his thumb and looked ahead in the distance, still amazingly focused. "Watson," he muttered, more to himself than the driver.

He was used to the passenger's sudden outbursts. "The police were really desperate for us to come at this late hour. The chief says they have three suspects. Someone must've had a lot of troubles with Raye Penber."

Watson glanced at the passenger for any visible clues of thought. There were none. "Mr. Penber had many enemies. I've had a couple of encounters with him and read up on him before he decided to come. According to his file, he was a very wealthy man, made 20 to 25 million dollars since he moved to Germany two years ago alone. He was very involved in drug trafficking and loan sharking up until his death tonight, often terrorized partners, allies, and civilians alike, a real nasty guy. Or so it would seem." He bit harder on his thumb. "What the public doesn't know is that he was an informant for the FBI. He's given a lot of his money to various organizations and has caught three drug lords in his short time here. But his suspects all had strong motives to kill him."

"Such as?"

"Such as, Watson?" the passenger repeated. "Yes, such as."

"No, I mean what are their motives?"

"Yes, that's clearer. Out of Mr. Penber's death, his wife, Naomi Penber, would receive a very handsome sum to live off of from his insurance policy. Not nearly quite as much as what he'd been earning, but still pretty substantial. His personal butler, Dimitri Mogisten, or 'Mogi', was waiting for approval to become a German citizen, but there were complications between him and Mr. Penber. Not being a German citizen himself yet, I could see why. And there was his business partner – apparently a fellow informant who flew from Japan to meet with him on his break – a Mr. Light Yagami. Clean-cut, very handsome, the all-around perfect graduate student. Pfft."

"What's wrong, Sir?"

"Hmm? Oh, I've had the pleasure of traveling once with Mr. Yagami to Los Angeles. He beat me in a chess game on our flight. I really hate to lose."

"I know, Sir."

Watson slowed down the convertible as he parked alongside a row of statuesque bushes. The Penber mansion was massive and loomed a dark cloud of silence over them. It was very well-known that his partner hated to lose, but it was also a touchy subject, though he didn't lose very often. It would be very unfortunate if they made the wrong arrest. Watson decided to voice his concern, reluctant to poke with it too much. "Lawliet?"

"…yes, Wammy?"

"I know this may be a difficult case, but-"

The passenger held out his hand in a stopping gesture. Even with the sunglasses, Watson felt that strong sense of arrogance. "My dear Watson, I won't lose."

They sat in silence for a few more minutes before deciding to move forward with more important matters. Watson noticed that as they walked two police cars were ahead with the convertible, front and center by the large doors. It had to be nearing dawn by now, considering the two hour drive they had traveled. If the police were too disoriented from the lack of sleep, Watson's partner would surely be functional enough to handle the case on his own. And despite his wholehearted awkwardness, even down to his crooked posture, this man was very functional.

He took the lead off of Watson's shoulders and went to knock on the massive doors, only to be greeted by a sour-looking man with a stained tank top and loose tie. Watson noticed that this man was scrawny yet eager to shoot both of them at a moment's notice. At least he gave the courtesy of not blowing off their heads yet. "Hallo," he greeted, tight-lipped. "Deutsch oder Englisch?"

"We're American, actually," the detective corrected, "although I am pretty fluent in your native tongue."

"Oh, can it," the man snapped. "I lived in San Francisco up until last year. I can speak English just fine. Who the hell are you? More cops?"

The detective looked taken aback. "Probably in your definition, yes. I'm Detective Lawliet Holmes of an independent subdivision of the LAPD, and this is my assistant, Mr. Wammy Watson. We were requested by the chief, Mr. Sawyer Friend, to assist him in the investigation of Mr. Raye Penber."

SLAM, went the door. Holmes rocked back and forth on his feet, probably slightly annoyed under his sunglasses. Watson placed his hand on his partner's shoulder to calm him. They were not as familiar with German customs as with other countries, but they were expectant for anything. There were crooks, jokers, and roughhousers in this business. Once they even ran into a transvestite banker trying to save its Girl Scout troop from disbandment.

However, they were not expecting a petite blond woman in a stereotypical maid outfit fling open the door. She stood next to the sour-looking man, who was now giving them a glare of death. "Mikey! We've been expecting these poor detectives for hours!" she scolded, pigtails swinging with her overdramatic pouting.

"It's Mihael," the man growled, "and it's not even that to you. It's Mello!"

He stomped away. The maid managed to smack Mihael in the back of his head before he could walk out of her reach. Holmes stared at her with interest, placing the tip of his thumb back in his mouth. "My, are all German women this beautiful?"

"Ohhh." The maid took a step back to observe the two detectives. Shaking her head for whatever reason at Watson, probably due to his age and white whiskers, she smiled at Holmes. "Gee, thanks. Lots of people tell me I should go into the modeling business. Mrs. Penber told me there's also lots of creepy perverts, though, but Missy Missy thinks she could fend for herself. Don'tcha think, Mr. Holmes?"

Holmes bit harder. He watched Missy hop up and down for a few seconds before smiling back. "If not, Detective Holmes will be on the case!" he said, chuckling. "But we cannot press upon such small matters right now. Would you give us the honor of showing us to the scene of the crime?"

"Yes, of course! Leave it to Missy Missy to show you around!"

Missy skipped across to a long staircase and hopped up the stairs by twos. Holmes and Watson followed the bubbly maid, noting the fine details of the Penber estate. Along the staircase railing were detailed carvings of safari animals, such as zebras, giraffes, and tigers. Holmes admired the carvings but also noted that they probably had nothing to do with Penber's murder. Sometimes the most out-of-place details ended up as excellent clues.

Eventually Missy flung open another door to reveal three cops and the suspects. Naomi Penber leaned against her couch armrest, morbid in her black jumpsuit and crying into a tissue. Mogi stood tall and serious against the bookcase, barely blinking an eye. His eyes were only focused on the calm figure of Light Yagami, the ideal businessman in a three-piece-suit despite the stuffy conditions. He seemed to be watching the thermostat. Upon close inspection Holmes saw that it read a 24.4˚C, or 76˚F in American terms. And sprawled on the floor was the cadaver of Raye Penber, motionless and pale.

The clock read 4:30 a.m. Inspector Sawyer Friend greeted Holmes and Watson with a handshake. "Wilkommen, you two. We've been expecting you for some time."

"Yes, yes, our apologies," Holmes rushed. "Now we've already wasted enough time on the trip here, so there's no need of pointless chitchat. Where's the body?"

"Um- by the window. Observations and witnesses say he's been there for several hours. No exact time, probably can't give you a very good estima-"

"Don't touch that window!"

Holmes strode over to the window and smacked the deputy's hand, a young-looking man with 'Mott Suda' on his nametag. Mott looked surprised but kept his arm on the windowsill. Annoyed, Holmes smacked him again. "Deputy Suda, this is a professional job with a serious investigation! Don't screw with me by jeopardizing it!" he snapped. "Watson, please take the temperature of Mr. Penber's body."

Watson nodded and grabbed a thermostat from his pocket. He jabbed the thermostat into the cadaver's mouth and showed the results to the rest of the group, a solid 88˚F. Again Holmes bit on his thumb as he began to pace around the room, focusing on the maid and her angry friend. Missy looked slightly uncomfortable when he stood inches from her face, thumb in mouth, wide eyes scanning her. "I have a question for you. Is it always this hot in here?"

Missy nodded. "Mr. Penber always liked the room so warm, dunno why. Told us never to touch his thermostat. Always kept it at the 24.4…um, 76˚."

"A man's thermostat is his most prized possession," Holmes murmured. "Now that that's settled, let's move onto the testimonies, shall we? Ms. Penber, you may start."

Naomi lowered her tissue and crept close to the body, tears brimming in her eyes. She blew her nose twice before looking straight ahead at the window. Tinges of orange and purple were beginning to rise from the horizon, an indication of morning. "We had a fight earlier today," she began. "Since we married Raye pushed me out of the business, said it was too dangerous. As you can see, there's not much to do unless you drive to town."

She gestured to the fields and forests outside their reach. Holmes took out a notepad and began to write. "We were…fighting in this very same room," Naomi continued. "I told him that I wanted to help him in his deals again, and of course he said no, so we fought for about an hour. I kicked that lamp – the one that's right by his head right now – and stomped out of the room. It was either getting drunk or going out to calm my nerves, so I went out. Went to see a double-feature at the theater, and then I left around 2230, 10:30, and…and…"

The woman began to sob again. Missy put a hand on her back and began to rub it up and down until she could regain her composure. "And as I was driving home, I was thinking these unfair thoughts. I began- I began to think that if I couldn't work together with Raye, I'd go back to Los Angeles and find work there. I came home at 11:00 p.m. and immediately went to my bedroom. I didn't think it would be the last time I saw…him…"

This time no one could stop her from the tears. Missy wrapped an arm around her back, sighing. "Mrs. Penber is usually as cool as a cucumber," the maid stated. "Missy Missy could vouch for her straightforward trip to the bedroom. To be honest, though, I thought they were doing the duty…"

Holmes shook his head. "You don't exactly seem like the most dependable person-"


"-but I suppose it's valid enough. I'd like to hear from Mr. Dimitri Mogisten next."

Mogi lowered his head. The ever-sour Mihael, who had been ignoring most of the conversation up until now, crossed his arms. "He doesn't speak English very well."

"That's all right. Whatever English he speaks will be just fine."

The detective looked at Mogi. The butler swallowed the lump in his throat and nodded, still serious and distant. "I…love this country, da," he started in a thick Russian accent. Germans are so hospitable. They do not expect you to be the same as odda persons. Herr Penber gave this day off to me. I liked this. This day I helped Fraulein Melissa with her shopping up until the evening."

"No, Mogi, how many times do I have to tell you?" Missy cried, pouting. "It's Missy Missy! Missy…Missy!"

Holmes gave her a stern look, promptly silencing her. Mogi cleared his throat. "After this shopping Fraulein…Missy Missy went back to the house to help out Frau Penber. I walked streets with my bag of turnips and radishes, played chess with nice gentlemen. Herr Penber called me 'round at eight o' clock p.m. He said he wasn't feeling good but would join me in an hour at the local pub to discuss citizenship papers. I waited 'til nine-thirty p.m. He did not come. I drove home and went to my bed by ten o'clock-five p.m. My night had lasted."

"And me and the other guys can vouch for this," Mihael added. "This guy always snores pretty angrily."

"Excellent." Holmes grabbed a random strawberry from his pocket and tossed it to Mogi. "That was a good job. I don't hand my sweets to others very often."

Mott Suda pounded his fist against the wall. "Hey, wait a minute! You've got an illegal Russian butler here as a suspect, and you just give him a strawberry like you're best friends? Don't you ever watch the mystery movies, Mr. Holmes? The foreign butler always does it!"

"Innocent until proven guilty, that is the American way. However corrupt it may be, Watson and I follow it. You're not very smart, are you, Mr. Suda?"

The deputy was rendered speechless. Holmes smirked as he walked over to the thermostat where Light Yagami stood. They gave each other a respectable nod before Holmes poked him in the chest. "And what about you, Mr. Yagami? You have had a close connection with Mr. Penber."

"Yes," Light replied, grimacing. "We were to meet in a few days to finalize an important business deal. Of course it's not much of a break, more of an abroad trip. My wife and a few of my servants came with me while I worked in my office in Berlin. As it was such, today I spent the entire evening working on the papers for the deal. For a normal person, it would've been done within a couple of hours, but I strive for perfection. Everything has to be neat, paper-clipped, color-coded, anything that will be easily noticeable for my advantage.

"I've never been too fond of Mr. Raye Penber. He asks too many questions. However, I finished my papers and drove home. It's a half-hour drive from the office to my house, so I arrived home at about 10:30 p.m. I was very exhausted and still am."

He sighed. Holmes finished scribbling on his paper and looked up at the man. "Can you verify this?"

"Yes, Mr. Holmes. My wife can verify this through my cell phone."

A few minutes later, the whole group listened to the thick, strong voice of Mr. Teru Mikami, Light's "wife". He and a couple of the servants confirmed Light's arrival at his home by 10:30. After Watari took a second reading of the cadaver at 6:30 a.m., which was 85.8˚F, Holmes began to pace back and forth again, cake in one hand, notebook in the other. Cake was very essential to his thinking abilities, Holmes claimed. The others watched him closely, particularly Inspector Friend and Deputy Suda. They always thought Americans were strange, but this one was almost as strange and disturbed as a drug addict. He wasn't even bothering to point a finger at anyone yet, and there wasn't any point in taking the temperature of a dead person. It must've been one of their sick quirks.

Eventually he stopped his pacing and turned to face the group. His eyes, so wide and dark, surveyed them with an intense passion only a detective could hold. This was a case for champions. "As I am contemplating the facts of Mr. Raye Penber's death, it seems to me like this is one big jigsaw puzzle," Holmes nodded, licking the frosting from his lips. "Inspector Friend, all of who are involved have a good chance of being the murderer. While there are not sufficient clues to determine the cause of death, I could be the bad guy and point the finger to anyone and say he or she did it, based on the testimonies we gathered tonight. Ms. Penber has stated to us that she was dissatisfied with certain aspects of her life with Mr. Penber. She wanted to be in a business that Mr. Penber would not allow and reap the benefits. However, there was a good sum willed to her, should he ever die. Do you know that amount, Ms. Penber?"

"About $500,000 in U.S. dollars," Naomi answered.

"Right. That's a hefty sum." Holmes smirked again. "Then there is Mr. Mogisten. He had no real connection with Mr. Penber, other than being is employee. His composure toward the situation can be seen as indifferent. During his testimony he mentioned that he loves Germany and was going to meet Mr. Penber at nine o'clock. However, Mr. Penber never showed up, and Mr. Mogisten came back at 10:05. Tell me, Mr. Mogisten, have you been under the influence tonight?"


"Did you drink tonight, Mr. Mogisten?"

"Da, that is what men do at pubs. Vodka is wonderful."

"I've never cared too much for alcohol, but that's your opinion," Holmes said. "As far as Mr. Yagami is concerned, he is a top businessman with a known indifference for Mr. Penber. He is a very busy man – all of you were very busy tonight – yet he can still be with us. And all of you came home at similar times. But alas! I know the time when the murder occurred!"

Inspector Friend looked confused. "Do you?"

"Do I? Yes, do I."

" . . ."

"Would you like me to tell you my method to my madness?"

"Yes, that would be preferable, Mr. Holmes," Inspector Friend growled. "On the dry erase board, please."

"Very well. Watson, hand me the blue marker."

Watson handed him the blue marker. Holmes chewed on the dry erase cap and took it off before drawing a smiley face at the top of the board. "Tell me, have any of you ever heard of Newton's law of cooling? I highly doubt that Deputy Suda has ever heard of it, but perhaps one of the rest of you might have some common knowledge."

"You insulting my intelligence, Yankee?"

"No, I'm insulting you. But I guess that's a no for the rest of you. Anyway, Newton's law of cooling, an equation made by the same man who had an apple dropped on his head. The equation is this:


"In this particular equation, T would be the current temperature, TS would be the surrounding temperature, and To would be the original temperature. The small t would be the amount of time and k would be a constant, while e is your basic math e, the natural log, though I won't explain it.

"In the first round of Newton's law of cooling, the surrounding temperature, or the room temperature, is 76˚F. The original temperature of Mr. Penber's body when Watson first checked him was 88˚F, like so:

T – 76 = (88 - 76)ekt

"In this case of current temperature, we would use the temperature that we took two hours later at 6:30, which is 85.8˚F. The time between the original temperature and the current temperature is two hours, so small t would be 2:

85.8 –76 = (88 – 76)ek2

"Then the subtraction is done:

9.8= 12ek2

"Since you want k by itself, you would divide both sides of the equation by 12, leaving the equation like this:

9.8/12 = ek2

"If we take the natural log, or ln, of the left-hand side of the equation and divide by 2, we should get this:

(ln (9.8/12)) /2 = k

- .10126 = k

"And so k equals -.10126. This would be the constant for the next round of Newton's law of cooling. Does everyone understand up until this point?"

Holmes turned around to face a bunch of blank stares, including Watson. He sighed and turned back around to the board. "I do have a calculator in my pocket, but I'll leave our progress on the board anyway since I doubt you would want to check it. For the second round of Newton's law of cooling, the original temperature would be Raye Penber's temperature before he died. Most people's body temperature is 98.6˚F, and Mr. Penber would not be an exception. The current temperature would be the first reading after his death, 88˚F. The surrounding temperature would remain at 76˚F, and the constant is -10126. So of course we can plug this in to make it look like this:

88-76 = (98.6-76)e-.10126t

"I'm sure you'd rather not hear my explanation twice about this matter, so I'll finish the work to the good stuff. Here is how this problem ends:

12/22.6 = e-.10126t

(ln (12/22.6))/-.10126 = t

6.25 = t

"Since small t equals 6.25, this would mean that 6.25 hours had passed since our initial reading of Mr. Penber's body. Therefore, even though the suspects all arrived home at similar times, there is only one person who could have killed him at the time that I've calculated. As Ms. Penber has noted, it takes a half hour to get to and from the local town. In the opposite direction of which Watari and I drove from Berlin, it also took a half hour to get here." He paused. "Well, actually, it took us about two or three hours to get here, but from Berlin it was only a half hour. My mistake. We drove east, and Ms. Penber drove west, but the amount of time it took was very close to each other. However, Ms. Penber did not come home until 11:00. Mr. Mogisten came home by 10:05. Therefore, the only possible suspect left is Mr. Yagami, who did not arrive home until 10:30, as verified by his wife and servants."

Everyone stared at Holmes with a blank face, then at Light, who sneered. "You'd believe a barefooted detective who leaves cake all over his chin? Surely you have your facts wrong, Mr. Holmes."

Holmes shook his head. "The external calculations prove you're the likeliest suspect, and my hunches usually don't go wrong. It must be hard to lose, Mr. Yagami. I know. I hate to lose. I have a hunch that your planned business deal would have tipped the scales out of your favor and possibly harm your assets. I have a hunch that tonight on your way back home, you stopped by to kill Mr. Penber somehow, that I'm not very interested in. And I have a hunch that I have you in check and mate, Mr. Yagami."

There were a few minutes of silence before Light tried to attack Holmes with his bare hands, a vicious glare in his face. Mott Suda and his silent partner in the background, Issac Washington, apprehended the man by the arms and immediately placed him in handcuffs. Holmes glanced at Ms. Penber, at the serious butler Mogi, and the peculiar help Missy and Mihael and pursed his lips. He gestured Watson to follow him as he began to exit out the door. "My condolences to all of you. I hope you have a pleasant funeral." He glanced at Inspector Friend, who was helping with the apprehension. "Inspector, you may bill us later. We're going out for more cake."

Soon the pair was back in their convertible on their way westward toward Berlin. Watson couldn't help but think of the way Holmes had so calmly solved the case. He was always solving cases calmly, but he usually didn't like doing too much math. Most of his results came from critical thinking and deductions. The old man decided to finally bring it up after what seemed like a long time, like a century or two. "Lawliet?"

"…yes, Wammy?"

"You were very good in your observations, but how did you figure out to use Newton's law?"

Holmes gave him an annoyed look. "Well, I'm not a certified resurrectionist. I couldn't just bring Mr. Penber back from the dead and asked who did it. Equations, my dear Watson, is always helpful in these types of situations, regardless of how much I despise them."

"Yes, Sir."

And they drove off on the country roads, remaining in silence for the remainder of their trip to the fancy cake shops. Soon they would be sitting at a table outside, enjoying the mellowness of a hot summer morning. The cake always helped with Holmes's sharp thinking skills. Watson had been partners with Holmes for almost ten years now. For the longest time, he would probably question and scold the young detective for wasting time. But now there was none of that. Sometimes brilliance was not comprehendible to the naked eye, but Mr. Lawliet Holmes's brilliance escaped even the boundaries of the naked mind. Wonderful, awkward brilliance.


Credits to the participating characters:

Lawliet Holmes - L

Wammy Watson - Watari

Mihael/Mello - Mello

Miss Melissa (Missy Missy) - Misa

Inspector Sawyer Friend - Soichiro Yagami

Raye Penber - ...obvious 8D

Naomi Penber - Naomi Misora

Mott Suda - Matsuda

Dimitri Mogisten - Mogi

Light Yagami - obvious

Teru Mikami - obvious

Issac Washington - Aizawa