Can you solve the riddle of Pandora’s box? - Alex Rosenthal
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زیرنویسها (76 segments)
DownloadPandora was having a decisively bad day.
She didn’t set out to open the box;
if anything, she’d resisted with every ounce of her will.
But her curiosity got the better of her,
and a cavalcade of evils of every shape and size spilled out.
By the time she'd slammed the front door of her home shut,
only 10 minor imps— of wrath, greed, gluttony, and sloth varieties—
and three greater demons remained.
Pandora tried desperately to get them under control,
but they resisted and pounded at the windows.
“This is hopeless!” she cried.
The first greater demon turned to Pandora and said,
“Hope? Hope is still here. I just made her look like an imp.
Because that’s the kind of bad guy I am!”
He whispered in the ears of the two other demons and continued.
“To make things interesting,
I just told Abaddon which variety of imp Hope is,
and Beelzebub how many eyes she has. Bye!”
Abaddon taunted Beelzebub by saying,
“I know you don’t know which one she is.”
Beelzebub responded, “Well, I didn’t before, but now I know.”
To which Abaddon replied in a huff, “Then I also know which one she is.”
And both left in a hurry, without so much as a farewell.
Pandora knows her only chance to fix this mess is to capture Hope
before the imps all escape her home.
But which one is she?
Pause here to figure it out yourself. Answer in 3
Answer in 2
Answer in 1
This problem originally took the world by storm in 2015
when Dr. Joseph Yeo Boon Wooi posed it as Cheryl’s birthday problem,
and for good reason.
The logic requires simultaneously modeling three different perspectives—
ours, Abaddon’s and Beelzebub’s, whom we’ll call A and B from now on.
This puzzle is much more approachable if we start by doing what Pandora could not:
cramming all of these imps into a box...
in this case, of the table variety.
One key thing to note is that unlike many logic problems,
the order of statements matters here,
because the two demons’ knowledge changes over the course of the dialogue.
So let's start with the first statement
and milk it for all it's worth before moving on.
In it, A says to B, “I know you don’t know which one she is.”
At this point, A knows the imp type,
but since there are multiple imps of each type, A doesn’t know who Hope is.
The eyes, however, work differently;
if Hope had 3 or 5 eyes, B would know who she is.
This step is where a lot of people succumb to a common pitfall.
Because the important takeaway here isn’t to just eliminate
the three- and five-eyed imps.
It’s to eliminate the entire rows of the table that they’re in.
Why?
The trick is to think about B’s perspective from A’s perspective.
Through A’s eyes, the entire table boils down to one of these four options,
because he knows which type the imp is.
If he knew Hope was a greed imp, she could have five eyes.
There’s only one imp with five eyes, so B could know who Hope is.
But A knows that B doesn’t know,
so greed isn’t possible, nor, by the same reasoning, is wrath.
Now we’re down to just five possible imps, and we can move on to the next statement,
which we have to consider through B’s eyes.
Critically, B is an expert logician, so anything we’ve figured out—
like that wrath and greed are off the table—
he’s also figured out.
That, plus knowing how many eyes Hope has,
allows him to figure out who she is.
So she must be in a column that has only one imp left,
meaning we can eliminate both one-eyed imps.
Finally, let’s examine the last statement and switch back to A’s perspective.
For A to now know who Hope is,
there must be only one option left in that row.
Therefore, Hope must be the six-eyed sloth imp.
Before anyone else can escape,
Pandora leaps into action and wrestles Hope to the ground.
The world may be a mess,
but at least she’s got a glimmer of... well, you know.
Key Vocabulary (50)
toward
"Go to school."
belonging
"Cup of tea."
also
"You and me."
inside
"In the house."
specific
"That book."
A third-person singular pronoun used to refer to an object, animal, or situation that has already been mentioned or is clear from context. It is also frequently used as a dummy subject to talk about time, weather, or distance.
Used to show who is intended to have or use something, or to explain the purpose or reason for an action. It is also frequently used to indicate a specific duration of time.
A preposition used to indicate that people or things are together, in the same place, or performing an action together. It can also describe the instrument used to perform an action or a characteristic that someone or something has.
A pronoun used to refer to a male person or animal that has already been mentioned or is easily identified. It functions as the subject of a sentence.
Used to refer to the person or people that the speaker is addressing. It is the second-person pronoun used for both singular and plural subjects and objects.
A preposition used to indicate a specific point, location, or position in space. It is also used to specify a particular point in time or a certain state or activity.
Used to identify a specific person, thing, or idea that is physically close to the speaker or has just been mentioned. It can also refer to the present time or a situation that is currently happening.
A coordinating conjunction used to connect two statements that contrast with each other. It is used to introduce an added statement that is different from what has already been mentioned.
A preposition used to show the method or means of doing something, or to identify the person or thing that performs an action. It frequently appears in passive sentences to indicate the agent or before modes of transport.
The word 'we' is a first-person plural pronoun used to refer to the speaker and one or more other people collectively. It is used as the subject of a sentence or clause.
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TED-Ed has launched its first ever physical game: Pandora's Legacy! Learn more and get your copy here: https://ed.ted.com/pandora -- Pandora is having a decisively bad day. She didn’t set...
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