Use your knowledge of four common logical argument forms
(Modus Ponens, Modus Tollens, Disjunctive Syllogism, Transitivity).
Can you solve these very short mysteries?
Review
For reference, symbolic versions of the 4 common
argument forms used in
this mystery game are shown below. If you are not
familiar with symbolic notation, you can find
the English versions further below.
Modus Ponens
Modus Tollens
p → q
p → q
p
~q
q
~p
Disjunctive Syllogism
Transitivity
(Hypothetical Syllogism)
p ∨ q
p → q
~p
q → r
q
p → r
Arguments in English
Modus Ponens: Given the premises "if claim 1 then claim 2" and "claim 1", we can
conclude "claim 2".
Example: "If I ate a sandwich, then I ate bread." "I ate a sandwich."
Therefore, "I ate bread."
Modus Tollens: Given the premises "if claim 1 then claim 2" and "NOT claim 2", we can
conclude "NOT claim 1".
Example: "If Timmy did his chores, then he is paid allowance" but "Timmy is not paid allowance."
Therefore, "Timmy did not do his chores."
Disjunctive Syllogism: Given the premises "claim 1 or claim 2" and "NOT claim 1" then
we can conclude "claim 2".
Example: "Today I went to work or I played video games" but "I did not go to work". Therefore,
"I played video games."
Transitivity: Given the premises "If claim 1 then claim 2" and "if claim 2 then claim 3",
we can chain these ideas together to conclude: "if claim 1 then claim 3".
Example: If today is Tuesday I go to work. If I go to work I eat salad for lunch. Therefore,
if today is Tuesday I eat salad for lunch.
An Old West Argument
"You can point that six-shooter at me all you want," said the sheriff,
"I just watched you shoot half a dozen people..."
( What does the sheriff say next? )
( What argument form would have this as its conclusion? )
( Solution will only show when all correct answers are chosen.)
Solution
"I know you're empty." (Modus Ponens)
If "half a dozen" (or 6) people have just been shot from the 6-shooter,
then it is empty. Since the sheriff just saw the 6 shots, he knows the
gun is empty.
Quick note: you could few if-then type (i.e., conditional) statements to create
a "Transitivity" argument, but then its "conclusion" would also need to be
an if-then type statement.
(Modus Ponens)
p = Six shots have been fired.
q = The gun is empty.
p → q
p
q
How Do We Know?
"How do we know if we should arrest him?" asked the rookie, before
knocking on the hotel room door.
"Listen," said Officer Hailey, "If he is here then he is violating
his parole. If he is violating his parole then we arrest him.
And so..."
( How should the rookie finish this argument? )
( What argument form lets him conclude this? )
Solution
"If he's here we arrest him." (Transitivity)
If the suspect is at the hotel, then he is violating his parole and that means
the officers should arrest him. So the rookie's simplified answer should be
"If he is here then we arrest him."
(Transitivity)
p = He is here.
q = He is violating his parole.
r = We arrest him.
p → q
q → r
p → r
An Absurd Accusation
Officer Melissa Jones was out on patrol when a house door swung open
and a crazed man ran right up to her police cruiser.
He pointed back at another man who was standing in the open doorway,
rolling his eyes. "Arrest him!" yelled the man by the cruiser, dramatically.
"For... uh, murder! He murdered me!"
"Um," Officer Jones responded, unamused.
( What did she say next? )
( What argument could be used to support this? )
Solution
"No he didn't." (Modus Tollens)
The crazed man, who is speaking, is obviously not dead. Officer
Jones could present her (Modus Tollens form) argument like so:
"If he murdered you then you would be dead, but you are not dead,
so he did not murder you."
(Modus Tollens)
p = He murdered you.
q = You are dead.
p → q
~q
~p
DNA
The district attorney spoke to the detective, "The DNA has come back, and it matches Mickey Farmay's DNA. We have spent this whole case proving that if it matches, then
Mickey committed this crime."
(What do they conclude now?)
( What argument form lets then conclude this? )
Solution
Mickey Farmay is guilty. (Modus Ponens)
We have been given all the information we need to construct
a direct argument via Modus Ponens.
(Modus Ponens)
p = The DNA matches.
q = Mickey Farmay is guilty.
p → q
p
q
Who Copied Whom?
After his students John and Rebecca had both entered his office, the professor stated,
"I've brought you two here because your essays are identical.
One of you copied the other. Since you two have never gotten along I can
only assume that the one being copied had no idea."
John was quick to reply "She copied me!"
Since Rebecca had not copied John, she knew he was lying. Furthermore,
she knew...
( What did she know? )
( How did she know this? )
Solution
John had copied her. (Disjunctive Syllogism)
"one of you copied the other" means that Rebecca copied John
or John copied Rebecca (possibly both). But Rebecca also knows "she
had not copied John". So the other option (that John copied Rebecca)
must be true.
(Disjunctive Syllogism)
p = Rebecca copied John
q = John copied Rebecca
p ∨ q
~p
q
Yesterday
"I wasn't even at that club yesterday!" cried Sam, the suspect.
"This should be quick," Mary thought to herself. She nodded towards the
unusual blue dragon stamp on his hand.
"What, that?" he said nervously, "Oh, I got that the day before yesterday. The other witnesses
must have gotten the day wrong."
Mary had already spoken to the club manager. They change their
stamp every day, creating a brand new one each time. The first
and only blue dragon they had ever used was yesterday.
( What does Mary conclude about yesterday?)
( What argument tells her this?)
Solution
He was at the club. (Modus Ponens)
The only people who have that unique blue dragon stamp were at the club yesterday.
Clearly Sam has the stamp. Therefore, he was at the club yesterday.
(Modus Ponens)
p = Sam has the blue dragon hand stamp.
q = Sam was at the club yesterday.
p → q
p
q
Opportunity
"You have some nerve, standing right in front of my pistol," said Barney, "You know
I always shoot as soon as I have an opportunity."
"That's all true," Will responded,
( What did Will say next? )
( What argument form does this follow from? )
Solution
"But you can't shoot me now." (Modus Tollens)
Whenever Barney "has the opportunity to shoot", he will, as both speakers agree.
Will is standing right in front of his pistol, so Barney clearly
"has the opportunity" unless he is unable to shoot the gun
(it could be jammed, or out of bullets, or broken, or fake, etc.).
That is, if he is able to shoot, he shoots. But he didn't shoot, so he
must not be able to. This is a Modus Tollens argument.
(Modus Tollens)
p = Barney is able to shoot
q = Barney shoots
p → q
~q
~p
Heading Back
The rookie walked up to Officer Hailey's desk, and begin speaking,
"Remember Malakai, who started his 100% house arrest sentence this morning
for dealing drugs to minors? Weed, PCP, LSD, meth...
Anyway, we just pulled him over on Route 22, heading back
toward the same neighborhood he used to deal from.
What can we do?"
( How does Officer Hailey respond? )
( Which argument do we apply, before Modus Ponens
lets us conclude this? )
Solution
"We can arrest him." (Transitivity)
Officer Hailey responds: "We can arrest him." Even if Malakai does not have drugs on
him, he is still breaking the law.
If the police "pulled him over on Route 22" then he was outside the house, so clearly he was
violating his 100% house arrest. Even without the drugs, if they pulled him over the officers can arrest
him for violating his house arrest.
We can apply Transitivity twice to simplify our statements. We'll draw it
below as one argument.
(Transitivity)
p = The officers pulled Malakai over.
q = Malakai was outside his house.
r = Malakai was violating his 100% house arrest.
s = The officers can arrest Malakai.
p → q
q → r
r → s
p → s
Now we have the information p → s, and since the officers
did pull Malakai over, as the rookie mentioned, then a quick application of Modus Ponens
tells us that the officers can arrest Malakai.
p → s
p
s
Final Girl
Rose and Jeremy sat on other ends of the remote cabin
stared at each other, drenched in blood, and shivering.
"The killer must be one of us campers," Jeremy insisted,
"We are hundreds of miles from civilization. The only people here
are the ones that came in our group.
We have to figure out which one is the killer."
"Everyone else is dead," Rose responded, closing her eyes, "I found each
of their dead bodies, one by one." She looked back at Jeremy and proclaimed,
( What did Rose say? )
( What argument suggests this? )
Solution
"You killed them." (Disjunctive Syllogism)
There is no one else alive at the cabin besides Rose and Jeremy.
Rose did not kill the other campers; in fact she "found each of their
dead bodies", so someone else killed them before she "found" them. Since the only
possible killer is Rose or Jeremy, and it's not Rose, it must be
Jeremy.
(Disjunctive Syllogism)
p = Rose is the killer.
q = Jeremy is the killer.
p ∨ q
~p
q
A Winter's Day
Captain Marrix walked over the 6-inch deep snow in front of her
deputy's house, feeling disappointed, not only for sullying the
otherwise undisturbed white ground, but because she had a
sinking feeling about what she was about to find. Her deputy,
Jason, swung the door open. Captain Marrix looked down at the
corpse next to the deputy's feet.
"I know this doesn't look good," Jason said, "You sent me home before the
storm, but I swear I just got here! I hit some traffic on the way here, and then
I had to pull over because
the storm was so heavy I couldn't see the road,
but then I couldn't even get the truck started again until the storm
had completely passed."
"You walked in here and found her like this, and no one else?"
"Well yeah, on all counts. I mean we've had all the other doors and
windows boarded up to prepare for the storm, so no one else could
have gotten in or out without me noticing. The must have killed her
and left a long time before I got here." Marrix did a quick search of
the house to verify that there was no one else inside,
and felt a rush of disappointment again when she found no one.
( Who does the captain suspect? )
( What argument form arouses this suspicion? )
Solution
The deputy, Jason. (Modus Tollens)
The captain is disappointed to mess up the "otherwise undisturbed
white ground" in front of the house. In particular, there are no other
footprints leading to the front door. Since all the other doors
and window are boarded up, Jason must have entered through the front
door.
Jason claims he just got here, after the storm had completely passed,
and the captain concludes this is a lie, so
she suspects Jason. Her argument is: if Jason got here after the storm, then there
would be footprints in the snow. But there are no footprints in the snow.
So it must not be true that Jason got here after the storm.
Since Jason is lying about his whereabouts, the captain suspects that he
is the person responsible.
(Modus Tollens)
p = He got here after the storm.
q = There are footprints in the snow.
p → q
~q
~p
Two Bodies
Deputy: "Two bodies, each killed by a gunshot to the head. Only one was a suicide."
Chief: "Was the other an accident?"
Deputy: "We don't believe so."
( What did the Chief say next? )
( What might be the first premise to conclude this from Disjunctive Syllogism?)
Solution
"Then it was murder." (It was an accident or murder.)
The second body did not die by suicide, as it was explicitly stated
that "only one [death] was a suicide" and we know that the first body was
that one. This can be viewed as Modus Tollens (see below).
Now the body that did not die by suicide was shot in the head, so
either this person was murdered or was the victim of some sort of
accident involving the gun ( this is our first premise for a
Disjunctive Syllogism argument ).
But the first speaker insists it was not an accident. Then it must have been
murder.
(Modus Tollens)
p = The second body died by suicide.
q = More than one death was a suicide.
p → q
~q
~p
(Disjunctive Syllogism)
p = The second person died from an accident.
q = The second person was murdered.
p ∨ q
~p
q
Two Bodies, Part 2
Deputy: "Two bodies found, one in each of the house's two bedrooms,
on opposite sides of the house.
The victims were each killed by a gunshot to the head,
by the exact same gun. Seems to be a murder-suicide.
But we're not sure which happened first..."
Chief: "Come on..."
( What did the chief say next? )
( "The suicide happened first or the murder happened first"
would begin what argument form? )
Solution
"The murder happened first." (Disjunctive Syllogism)
A murder and a suicide have both occurred, and from the same exact weapon.
Since it was the same weapon, it could not have shot both individuals
simultaneously (at least not from separate rooms on opposite sides of the house).
So the suicide happened first or the murder happened first. If the suicide
happened first, then the person would be dead when they supposedly murdered
the other person. That is absurd. So the murder must have happened first.
(Disjunctive Syllogism)
p = The suicide happened first.
q = The murder happened first.
p ∨ q
~p
q
Name's the Same
Detective Charles Smith held the victim as the blood poured over her. Although he had
not found the killer, he had traced the man down to this location, a possible
childhood home. Smith believed this was the mother, but the blood
loss had made her less than lucid. Nonetheless, he tried to use these last
few moments of her life to extract a clue.
"All I need is his name," begged the detective, "What is his name?"
She just stared up at the sky and repeated over and over, "He has the same name as his father."
The detective sighed, "Okay..., well then, what was his father's name?"
"He... has the same name as his own father, the owner of this house." Those were
her last words before dying in the detective's arms.
( What will the officer do? )
( What argument justifies this? )
Solution
Look up the house owner's name. (Transitivity)
The victim keeps giving clues without saying the actual name, but
she has told us that the killer has the same name as his father, who has
the same name of his own father (the owner of the house).
The detective will look up the owner of the house (who is the killer's
grandfather), because if he knows
that then he knows the father's name, and if he knows that then he knows
the killer's name.
(Transitivity)
p = He knows the homeowner's name.
q = He knows the father's name.
r = He knows the killer's name.
p → q
q → r
p → r
Face the Camera
Rodney smiled at his reflection calmly in the room's two-way mirror,
as the officer played
the surveillance footage from a recent robbery.
The officer gave a comical and exaggerated smile, while staring into in a book labeled
"County Prison Records",
spinning a pair of handcuffs around on the table, and
lightly singing some old song about a "chain gang".
Rodney, who had been subject to various intimidation methods in the past,
was unfazed by all of this.
"It's clear as day,"
said the officer finally said as the robber in the video smiled smugly at the camera,
"That's definitely your face".
"You might think that's proof," laughed Rodney, "But that proves nothing.
See, I have an identical twin- you can check the hospital records back in our
hometown. And so, that just might be him in that video."
"And I'm sure you don't know where to find this twin of yours."
"As luck would have it, I don't." Rodney gave a facetious shrug,
matching the officer's comical exaggeration.
"We had a falling out a few years ago,
haven't kept in touch. And even if we did, it'd be pretty hard to stick this
on either of us. Maybe that's me, maybe it's him." He shrugged.
"All that video proves is that it's one of us. That's all."
"No, you see, that wasn't a question. You say all the video proves is that
it's one of you? Well... that's all it needs to prove. See?"
( What did the officer show him? )
( Now what argument could be used against the suspect? )
Solution
"That's all it needs to prove." (Disjunctive Syllogism)
The officer says "I'm sure you don't know where to find this twin of yours".
This implies that the officer does know where to find
the twin, and that it would affect Rodney's statement if he did too.
The officer shows something to Rodney that will supposedly prove his guilt,
given that the person in the video is one of them.
The handcuffs and mirror seem pretty useless, and the video showing
the same face again would not provide any more evidence that it does now.
The officer saying "See?" must be referring to the book of County Prison
Records. We can conclude that the book has information
that would solve this crime,
in particular, that the estranged twin was in prison on the date of the robbery.
Even Rodney has agreed that the video proves that the robber is
him or his twin.
Since his incarcerated twin could not possibly have
committed the robbery, it must have been him (Disjunctive Syllogism).
Rodney admitting "it's one of us" was an unintentional confession of guilt.
(Disjunctive Syllogism)
p = Rodney's twin committed the robbery.
q = Rodney committed the robbery.
p ∨ q
~p
q
Goody-goody
Joe walked up to the hotel desk clerk, showed his P.I. credentials and asked bluntly,
"Do you know a woman by the name of Jamie Meren?" Jamie had been arrested this morning
for a crime that had been committed on a date over 6 months ago. She felt she
was being set up, and had used her only phone call to hire a private eye, Joe,
who trusted the police about as little as she did.
"Um yeah," the clerk responded, "She's the morning clerk on weekends. Been here about a year."
"Can you describe her for me? Ever seen any signs of aggression, or even violence?"
"Ha! Honestly, she's kind of a goody-goody. She just received a Perfect Attendance Award
for her first year, and employee of the month the past three months in a row. That's why
we don't have to hire any more help for Saturday or Sunday mornings - she handles
everything all by herself."
He pointed to the wall behind him, which hosted the attendance award plaque
and the Employee of the Month picture,
next to a loudly ticking analog clock
and a wall calendar flaunting the current month's bikini model
(which made Joe snicker at its oddity, since it was the middle of December).
"Is that time right?" he asked, and when the clerk raised his eyebrow, explained
"I don't carry a cell phone. I don't really like having
a government-tracked device in my pocket."
The clerk gave Joe an unexpected nod of agreement. "Same here.
I assume it's right but our computers are down, so I'm not 100% sure."
Joe's eyes roamed up to a small security camera up in the corner. "Does that camera work?"
"I mean... it does... records 24-7 and the videos are saved to the cloud somewhere.
I tried to find a tape once when someone said he checked out earlier than he really did.
Eventually I just gave up because the storage system is such a mess. I refunded his money."
"I know how to prove she's innocent. I don't want to go through the trouble
of looking through the video storage system unless I know for sure it will show her."
( What can he check to quickly determine if he would see Jamie on the tapes? )
( What argument suggests this? )
Solution
The bikini calendar (Transitivity)
If Jamie was at work, then the security tapes will prove it. This would make it worth the trouble
of searching for the tapes, since it would definitely prove her innocence. So Joe
is looking for a quick way to ensure that she would actually be in the video.
Jamie works weekends (both Saturday and Sunday as the clerk mentions),
and in fact has worked every weekend over the past year since she has the
Perfect Attendance Award. In other words, if the date was a weekend, then Jamie was at work.
Neither person has a phone, and the computers are down, but a
quick glance through the calendar will show Joe if the date
was on a weekend. (Since it is now December, a date "6 months ago"
would be in the same calendar.) If it was, that would imply
Jamie was at work, which would imply that the tapes will
indeed prove her alibi (and so, Joe will deem it worthwhile to look through them).
(Transitivity)
p = The date was on a weekend.
q = Jamie was at work.
r = The security tapes will prove Jamie's alibi.
p → q
q → r
p → r
He Said, She Said
When detectives Ray Jones and Maya Glan interrogated Felix Smith
about a murder at their neighbor's house,
he swore he was being set up by his wife Tammy. He claimed he
was at home watching their toddler, Junior, all day. Tammy did this most
days while Ray worked on his computer from home, but because of the block-wide power
outage that had left them with no electricity for the past week,
he offered to watch Junior while she went shopping.
It was after she had left that
stories began to diverge.
Felix said he didn't know what Tammy had been up
to today, but it sounded like nothing good. When the detectives
interrogated Tammy about her
whereabouts today, she basically said the same thing about Felix.
"I went to the festival uptown early in the morning, and when I walked back in
around noon,
Felix was stomping around angrily, like he was plotting something. I was so frightened that I
dropped the groceries all over the floor." She pointed down to the bags
scattered around. Junior stomped around, and Maya couldn't decide if she
believed he was emulating his father, or just trying to figure out how to walk.
"I must have passed out in fear, and didn't wake up until
you rang the doorbell. Who knows what Felix could have done during those 5 hours."
"You're sweating," said Maya, "Nervous about anything?"
"No no," Tammy said, pointing to a bead of sweat on Maya's own arm,
"I mean it's warm in here. We don't have air conditioning. We
use electric fans, but the stupid power outage..."
Junior tripped and fell flat on his face. Ray tried not to laugh. Junior begin crying and Maya
almost wanted to cry herself from the piercing sound. "Oh, poor boy," said Tammy,
"He's so awkward and clumsy, just like his father." She picked him up and sat
him in his high chair, then reached into one of the grocery bags on the floor.
"All you gotta do is give him something sweet, and he'll forget all about it. Just
like his father." She winked at Ray.
"Um, so..." Ray said shyly, "You had time to go to the festival and get back before noon? Why not just go to the
store down the streen?"
"Oh, he's allergic to cow's milk," Tammy explained, nodding towards Junior,
"But it's his birthday! I had heard about a kiosk there that sells cake and ice cream
made with almond milk." She opened the carton of ice cream and
handed it to Junior with a thick plastic spoon decorated with the company's logo,
an anthropomorphic almond in a top hat and a pink bowtie.
Junior shoved his spoon down into the ice cream and it snapped in half, causing him to cry again.
Maya was getting frustrated. Tammy reached into the silverware drawer and gave
Junior a stronger, metal spoon.
Someone was lying, and Maya knew who.
( Who was lying? )
( Which argument type helped her deduce this? )
Tammy (Modus Tollens)
Tammy says she got home 5 hours ago, dropped her bags,
and just woke up now. Maya thinks Tammy committed the crime
then brought the groceries home and threw them across the
floor herself as an excuse.
The ice cream that Tammy gave Junior was hard enough to break
the thick plastic spoon. In particular, it was still frozen. This certainly
wouldn't be the case for ice cream that had been lying on the
ground for 5 hours.
Tammy may accuse Felix, and say that he purposefully put the ice cream
in the freezer after she had fainted, and just returned it to
make the detectives suspicious. The problem is, she and Felix had
both verified that the electricity has been out for the past week, so the freezer
would not keep the ice cream frozen hard for 5 hours, and the hot house
would not keep it frozen either. The only possibility
is that Tammy had just recently come home with the ice cream. So
she must have been lying about her alibi.
(Modus Tollens)
p = Tammy has been home for 5 hours.
q = The ice cream has melted.
p → q
~q
~p
Just Us
The crime consultant walked into the victim's house, putting his gloves on, and
yelled upstairs to the suspicious captain, who was looking over the crime scene alone.
"Just us so far, huh? Have you called for ballistics or checked for gun powder residue?"
"No, I just called it in a few minutes ago. How were there no witnesses to this?"
"I assume there are no witnesses because this house in the middle of nowhere,"
the consultant laughed,
as he walked up the stairs and then down the hall toward the room.
The house was indeed in a rather remote area,
and in fact the only reason the captain had come here
was to check in on a person of interest who had escaped from a recent attack
by a man in a mask and gloves. Now the captain had found the woman dead,
with a single bullet wound in her chest, and he instantly
regretted giving in to her wish to have no patrol cars watching the house.
"And yet here we are," called the captain, looking down at the victim's
otherwise pristine blouse,
"I had a sneaking suspicion about this one, so I just called it in now,
a 'Brutal stabbing to the gut. No witnesses.' And yet here we are." They could hear the
sirens approaching.
( Who killed the woman? )
( What was the murder weapon? )
Solution
The consultant (Gun)
We are not asking for a specific argument type here, as many could be applied.
First, as a note to the reader, since the captain "regretted" not being more protective
of the victim, we can assume the captain did not murder the victim himself. That is:
If the captain murdered the victim, he would not regret leaving her vulnerable.
But he does regret leaving her vulnerable. So he did not murder her (Modus Tollens,
after applying the appropriate negations). (You could also write this via Modus Ponens.)
And so, the murderer was the captain or someone else. But it was not the captain.
therefore it was someone else (Disjunctive Syllogism).
The captain has been suspicious, and in particular had a sneaking suspicion
about this crime, so called it in as a stabbing even though it
was a gunshot wound to the chest (the rest of the blouse remained "pristine",
so the stabs to the gut must have been a bluff - Modus Tollens).
The house is remote, so no one would have heard the gunshot, and the only
reason the captain had come by was to check in. Since the consultant agrees
there are no witnesses, we can assume that no witness has contacted him
to tip him off about the gunshot.
The only living person who knew about the gunshot
(besides the captain himself, who we have already ruled out) would be the murderer.
The consultant asking about gunshot residue and ballistics implies that he
knows a gunshot occurred, even before he comes anywhere near the
scene of the crime (up the stairs and down the hall).
Thus the captain concludes that the consultant is in fact the murderer. We
can view this via Modus Ponens, or by applying some negations first, we can
view this via Modus Tollens.
(Modus Ponens)
If the consultant knows about the gunshot, the consultant was the murderer.
The consultant knows about the gunshot. Therefore the consultant was the murderer.
(Modus Tollens)
If the consultant is not the murderer, then he would not know about the gunshot.
But he does know about the gunshot. Therefore he is the murderer.
Papa and the Clown
"So you believe this was an accident?" Detective Amber Neilson looked at Ms. Vernon suspiciously,
after noticing what were clear signs of a struggle.
"Yes, of course," Ms. Vernon answered, "I heard something like footsteps coming
from inside the room
around 4:05pm, even though Papa was supposed to be sleeping,
and when I came to tell him to stay in bed,
I heard him yell 'Woah' like he was starting to trip. I mean, the door and walls are
thick, so the sound was a little muffled, but it definitely sounded like 'Woah' or 'Oh' or
some sound of distress, you know?
He must have fallen and hit his head exactly as I opened the door, because I
didn't really hear the fall."
Amber looked out the window at the garden filling the side of the house. She
noticed a water droplet falling off a sunflower by the window, and then
a large damp spot on the carpet just inside the window.
"Why is the window open?" she asked, "Wasn't it raining earlier?"
"Yes, hm. After the rain stopped, Juniper must have opened it to give Papa some air.
Oh, Juniper is our, well... he's a clown by trade..."
Ms. Vernon gave a sligh chuckle of embarrassment as Amber raised her eyebrows.
"But he specializes in taking care of senior citizens. He works from 3 to 4
every Friday, while I go grocery shopping.
Yes, I remember now. I had just gotten home when he was on his way out.
I was about to offer him an umbrella as he left,
when I noticed the rain had just stopped." She reached into a desk drawer and
handed Amber a business card:
It had a full-body photograph of Juniper in full clown getup: the
white makeup, the red nose, the outrageously oversized shoes, the polka-dot onesie.
"This is what he wears to take care of senior citizens?" Amber asked.
"Yup, exactly that. Papa loved it. Juniper says the onesie and shoes
need special tools to get on or off- which can take over an hour- but that
it's worth it to see Papa's face light up at the sight."
"Well it's not very lit up anymore," Amber thought crudely to herself, looking
down at the corpse.
She knew exactly where she wanted to investigate. Within
a few minutes, she was whispering to herself, "Gotcha."
( Where did Amber find the evidence? )
( What did this evidence confirm?)
Solution
The garden (Juniper murdered Papa)
Though she wasn't sure of the motive, Amber believed Juniper had killed Papa
and since there were signs of a struggle, Amber assumed this
wasn't an accident. Amber started working out a theory.
Juniper had opened the window, but the damp spot suggested that the rain
hadn't actually stopped yet when he did this. Juniper's plan must have
required that the window was open no matter what.
Amber theorizes: after he had left out the front door, Juniper walked
around to the open window. He reached in and bounced his juggling balls
on the floor to give the impression of Papa moving around,
possibly even footsteps (through the muffling
of the thick bedroom wall and door). When Juniper heard
Ms. Vernon approaching, he used his ventriloquism and impressionist skills
to throw his voice, sounding like Papa, to say "Whoa!" then ran off before
Ms. Vernon opened the door. She had not heard Papa fall because the
actual struggle and fall had occurred earlier while she was out shopping.
To test her theory, Amber went outside the investigate the garden.
It had just finished raining on the garden "filling the side of the house"
all the way up to the "sunflower by the window", so the garden
dirt would be muddy and footprints would show. Since the 24EE shoes
take such a long time to take off, Juniper would not have had a chance
to remove them before making the sound at 4:05pm (and he did
this so quickly after leaving to avoid risking Ms. Vernon finding Papa's body first).
After finding footprints of the greatly oversized shoes, Amber assumed that Juniper
had indeed come around to the open window after leaving the house.
She concluded that her theory is correct, and arrested Juniper under suspicion
of murder.
Some notes on arguments: As far as logical arguments are concerned,
a few different ones could
be applied here, in particular Modus Ponens
("If Amber finds footprints for oversized shoes, then Juniper murdered Papa")
and Transitivity:
"If Amber finds footprints for oversized shoes, then Juniper went around the side of the house. If Juniper
went around the side of the house, then Juniper is faking the cause of Papa's death.
If Juniper is faking the cause of Papa's death, then Juniper murdered Papa" all reduces to
"If Amber finds footprints for oversized shoes, then Juniper murdered Papa."
The End
Congratulations! You figured out all of the mini mysteries,
and identified the correct logical argument forms to
solve them.