Wednesday, March 14, 2018

logical deduction - Who poisoned Hugh G. Pokitz? (a murder mystery logic puzzle)


Preface


After your last mishap with a heap full of rabbits, you got sick of being lied to. Isn't life just so much easier when you can conclusively tell if someone's been telling the truth or not? For that very reason, you went out and bought a lie detector. It works, too! Now, when interrogating suspects, it's as easy as asking the right questions, and getting the answers you need.


Unfortunately, no silly rabbits to hide behind this time. An honest-to-god human has been murdered, and it's up to you to figure out, as they say, "whodunit".


Backstory


This town is small. Real small. Not a lot going on here, at all. You wander up to the sheriff's office and slam open the doors. The sheriff looks up at you from his desk.



"Detective. It's about time. I've been waitin' for ya." He shuffles up some papers on his desk and slides them to the side. "This one's a big one. You should sit."


Normally, you're belligerent whenever you get the chance, but this time your feet hurt, so you gladly sit in the chair across from him. Continuing on, he tells you, "Hugh G. Pokitz has been murdered." He pauses, waiting for a reaction, then shrugs. "Right, I forgot you don't live here. Pokitz is the beneficiary of this entire town. He's the reason any of this exists. He's -- well, he was -- the richest man this side of the Poughipasaw."


You nod in understanding. "Tell me the facts."


The sheriff begins to talk, but you pause him. Reaching into your briefcase, you pull out a small metal device and strap it onto his arm. He looks at you, puzzled. "It's a lie detector," you explain. "Just gotta make sure the thing is calibrated."


He nods back, then continues. "The doctor did a preliminary autopsy and discovered foxglove in Pokitz's system. It's been determined that the foxglove was the cause of his death. Here's the thing about this particular strain of foxglove -- it wilts within two days of not being stored properly, which the mansion does not have the means to do. It also has to be administered orally, or else it won't kill. So the poison got into the mansion within the last two days, and Pokitz somehow got tricked into eating it."


"Who would have motive?" You ask, dreading the answer.


The sheriff sighs. "Basically everyone. No one liked him. He abused his employees, extorted the shopkeepers, and catcalled all the women. It's no secret that his wife, Mai, was only with him for his money. And he liked it that way." With a pause, he muses, "A better question would be, who didn't have motive?"


You chuckle, then remember your here on business and steel yourself. "So, to recap:"


TL;DR




  • The poison made it into the mansion within the last two days.

  • The poison must have been administered orally.

  • Basically everyone is a suspect, since he was hated by all.


You finish jotting down your notes. The sheriff sees you close your notebook and makes an offer. "I've brought in the, as I can see it, only possible suspects -- would you like to meet them?"


You grin a devilish grin. "Oh, I'd love to."


Interrogations


Snatching your lie detector, you're escorted down the hall to a holding cell. "I traced the murder out in my head," the sheriff said. "The poison must have been obtained from the apothecary. She's the only one anywhere near here who would have access to it. It was either bought in the store, or delivered in the mail, and I'm not sure which. Hopefully you and your lie detector can trace the poison straight from the apothecary to the victim's mouth."


You stop in front of a glass window. Behind the window sit eight people. The sheriff details them for you. "From left to right, we have: Mai Pokitz, the Pokitz's butler, the Pokitz's chef, the apothecary, the apothecary's apprentice, the postmaster, the Pokitz Mansion gate guard, and the Pokitz's maid."


He walks back to the door you came through. "I'll leave you to it." You smile and walk through the door to the holding cell.




Suspect: Mai Pokitz




    "Why aren't you crying?" You sneer at Mai as you approach. She shrugs. "I hated that guy, and I'm still rich. So 'boo-hoo', I guess, but it's no sweat off my back." She grins. "I didn't kill him, though."
    Slapping the lie detector onto her wrist, you growl, "Say that again." She winces. "Ow! What is that?" You smile. "It's a lie detector! Now I'll know for sure that everything you're saying is true." She scowls, then repeats herself. "Okay, fine. I didn't kill my husband." You eagerly wait for the lie detector to go off, but it doesn't.
    You scowl. "Fine. Who had access to his food between its preparation and its consumption?" She ponders for a moment. "Um...only the chef and the butler had access to his food. No one else could have touched it.
    Sounds like you've narrowed it down. "Thank you for your time."




Suspect: Pokitz's Chef





    "I've got it all figured out, chef," you say as you attach the lie detector to his wrist. "You went out and bought the poison from the apothecary. Then you came back, and you poisoned Hugh's meal, because he mistreated you. Admit it, and I'll read you your rights."
    The chef looks shocked. "No, sir! It's true, I've been mistreated, but due to that, I haven't left the mansion in a week! I haven't even been out of the kitchen, except to relieve myself."
    Well, there goes that idea, you think. "Fine. Did you see the butler do anything odd with the food before he served it?" The chef responded, "No, not at all. He simply took the tray as he always does and carried it out of the kitchen."
    Looks like the butler is your murderer. "Thank you for your time."




Suspect: Pokitz's Butler




    "Okay, butler, the gambit's up." You attach the lie detector to his wrist. "I know you poisoned Hugh's food between the kitchen and the dining room. He abused you, and you were sick of it. Admit it, you filth."

    The butler simply sighs. "No, monsieur, I surely didn't. In fact, I didn't touch anything but the tray between the kitchen and the dining room." You scowl at the lie detector, but he's telling the truth.
    "Did anything seem suspicious to you?" You inquire. The butler shakes his head. "No, monsieur. In fact, I taste the meal for poison every night, as I did last night, so if the meal was poisoned, surely I would be dead now too."
    Back to square one. "Thank you for your time."




Suspect: Apothecary




    Time to at least figure out where the poison came from. With lie detector attached, you accuse the apothecary. "You sold the poison to this woman, didn't you? Shame on you, facilitating a murder like that."
    "How DARE you accuse me!" The apothecary jabs back. "No, I did not sell poison to this woman. In fact, I've never once before made a transaction with Mai Pokitz, nor anyone else in this holding cell. And that includes gifts and donations of any kind."
    You sigh. "Fine then. Who else could have accessed your store?" The apothecary jingles her keys. "These are the keys to my store. Only myself and my apprentice have copies."

    Looks like you've got an apprentice to interrogate. "Thank you for your time."




Suspect: Apothecary's Apprentice




    You circle your next suspect, as he shakes nervously in front of you. You gingerly attach the lie detector to his wrist. "Something wrong, boy? You nervous?"
    "N-no," he stammers. The lie detector lets out a shrill beep. "Good to know that still works," you say. "Don't worry, boy. If you aren't guilty, I'm sure everything's going to go fine for you." He gulps.
    "Now admit it," you continue. "You took the foxglove from the cupboard and sold it to this woman, didn't you?" He shakes his head, and stammers, "Only my boss has keys to the cabinet where the foxglove is kept. She says it's too dangerous for me."
    You frown. Another dead end. "Thank you for your time."





Suspect: Postmaster




    If the package wasn't bought in the store, it must have been delivered, you reason. Scowling, you snap the lie detector to the postmaster's wrist. "I hear all the mail in the town, comes through you. Do I hear the truth?"
    The postmaster nods. "You do, sir. I handle all the mail for the entire town. If something was mailed, I would have seen it. And it's illegal to mail hazardous substances in this town. I check all the packages myself in case someone is breaking the law."
    You grin. Maybe you're finally getting somewhere. "And did you see a package from the apothecary to this mansion?" To your dismay, the postmaster simply shakes his head. "No, sir. There was no package from the apothecary delivered to the mansion."
    You groan. "Thank you for your time."




Suspect: Pokitz Mansion gate guard





    You peer into the guard's eyes as you attach the lie detector to his wrist. "Tell me who left and who entered the mansion in the last two days."
    The guard stands firm. "Sir, no one has left or entered the mansion in the last two days. Three days, even. Not since Master Pokitz's last trip to market." You frown. It must have been delivery then.
    "Tell me, what do you know about the post delivered here?" The guard continues to stand firm. "I check all of the packages delivered to the mansion. It's my duty. If there was poison, I would have seen it."
    You slump your shoulders in defeat. "Thank you for your time."




Suspect: Pokitz's Maid




    You circle around on the maid, and attach the lie detector to her wrist. "I'm told you handle all of the mail once it makes it past the front gate."

    She nods eagerly. "Yes, sir, I handle all of the mail once it gets within the walls of the mansion." You sneer. "And did you see anything suspicious over the last couple of days?"
    She thinks for a moment, then shakes her head. "No, sir. I didn't see anything that struck me as suspicious in the mail over the last three days." Again, your lie detector stays silent.
    Though you should be frustrated upon reaching another dead end, you instead smile. "Thank you for your time."



Conclusion


You leave the holding cell, and find the sheriff waiting for you on the other side of the door. "See? They're just a dead end," he admits in defeat.


You chuckle. "Perhaps to you, pal. Perhaps to you. You've got a lot of truth-tellers in your town, which is a nice change of pace for me. But if you just listen to what everyone has to say, you'll see the real truth through the cracks." The sheriff looks at you, puzzled, but you just beckon for him to follow you.


"Come on in, and let me show you justice at work. And let me borrow those handcuffs. We're gonna need 'em."




Who murdered Hugh G. Pokitz?




Answer



It was a joint effort between



all 8 suspects.

1. Mai Pokitz at some point in the past approached the others with a scheme for getting rid of her hated husband. She masterminded the scheme, but wasn't directly involved in the murder, so she could truthfully say she didn't kill her husband.

2. On the night before the murder, the apothecary "accidentally" left the cabinet unlocked where the foxglove was stored. When apprentice unlocked the shop in the morning, he packaged it up and mailed it to the mansion, thus it did not come from the apothecary (but rather the apothecary's assistant).

3. The postmaster delivered the package to the mansion. He checked the package, as he claimed, knowing it contained poison, but didn't do anything about it.

4. The gate guard checked the package, as he claimed. There was poison, and he saw it; he just chose not to do anything about it.

5. The maid handled the package, but didn't see anything suspicious, because she was expecting the package of poison, being in on the scheme.

6. The chef received the package, and froze the foxglove into some ice cubes. Just before the meal went out, he added the ice cubes to Pokitz's drink.

7. The butler took the tray as he always does, and touched nothing but the tray. He tasted the meal for poison, but since the ice cubes hadn't yet melted, he did not ingest any of the poison.

8. Everyone sat back, and waited for the inevitable, and took the time to figure out the careful phrasing they would use when put under a lie detector in order to be able to escape suspicion.



No comments:

Post a Comment

classical mechanics - Moment of a force about a given axis (Torque) - Scalar or vectorial?

I am studying Statics and saw that: The moment of a force about a given axis (or Torque) is defined by the equation: $M_X = (\vec r \times \...