Can you solve the rebel supplies riddle? - Alex Gendler
You’re overseeing the delivery
of crucial supplies to a rebel base
deep in the heart of enemy territory.
To get past Imperial customs, all
packages must follow a strict protocol:
if a box is marked with
an even number on the bottom,
it must be sealed with a red top.
The boxes are already being loaded
onto the transport
when you receive an urgent message.
One of the four boxes
was sealed incorrectly,
but they lost track of which one.
All the boxes are still
on the conveyor belt.
Two are facing down:
one marked with a four,
and one with a seven.
The other two are facing up:
one with a black top,
another with a red one.
You know that any violation
of the protocol
will get the entire shipment confiscated
and put your allies in grave danger.
But any boxes you pull off for inspection
won’t make it onto this delivery run,
depriving the rebels
of critically needed supplies.
The transport leaves in a few moments,
with or without its cargo.
Which box or boxes should you
grab off the conveyor belt?
Pause the video now if you want
to figure it out for yourself!
Answer in: 3
Answer in: 2
Answer in: 1
It may seem like you need to inspect
all four boxes
to see what’s on the other side of each.
But in fact, only two of them matter.
Let’s look at the protocol again.
All it says is that even-numbered boxes
must have a red top.
It doesn’t say anything
about odd-numbered boxes,
so we can just ignore
the box marked with a seven.
What about the box with a red top?
Don’t we need to check
that the number on the bottom is even?
As it turns out, we don’t.
The protocol says that
if a box has an even number,
then it should have a red top.
It doesn’t say that only boxes
with even numbers can have red tops,
or that a box with a red top
must have an even number.
The requirement
only goes in one direction.
So we don’t need
to check the box with the red lid.
We do, however,
need to check the one with the black lid,
to make sure it wasn’t incorrectly
placed on an even-numbered box.
If you initially assumed the rules
imply a symmetrical match
between the number on the box
and the type of lid, you’re not alone.
That error is so common,
we even have a name for it:
affirming the consequent,
or the fallacy of the converse.
This fallacy wrongly assumes
that just because a certain condition
is necessary for a given result,
it must also be sufficient for it.
For instance, having an atmosphere
is a necessary condition
for being a habitable planet.
But this doesn’t mean that
it’s a sufficient condition –
planets like Venus have atmospheres
but lack other criteria for habitability.
If that still seems hard
to wrap your head around,
let’s look at
a slightly different problem.
Imagine the boxes contain groceries.
You see one marked for shipment
to a steakhouse
and one to a vegetarian restaurant.
Then you see two more boxes
turned upside down:
one labeled as containing meat,
and another as containing onions.
Which ones do you need to check?
Well, it’s easy –
make sure the meat isn’t being shipped
to the vegetarian restaurant,
and that the box going there
doesn’t contain meat.
The onions can go to either place,
and the box bound for the steakhouse
can contain either product.
Why does this scenario seem easier?
Formally, it’s the same problem –
two possible conditions
for the top of the box,
and two for the bottom.
But in this case, they’re based on
familiar real-world needs,
and we easily understand that
while vegetarians only eat vegetables,
they’re not the only ones who do so.
In the original problem,
the rules seemed more arbitrary,
and when they’re abstracted that way,
the logical connections
become harder to see.
In your case, you’ve managed
to get enough supplies through
to enable the resistance
to fight another day.
And you did it by thinking
outside the box –
both sides of it.
