Everything changed when the fire crystal got stolen - Alex Gendler
Someone has tripped the magical alarms
in the Element Temple.
By the time you and the other monks
arrive on the scene,
you know you have a disaster
on your hands.
Overnight, four young apprentices
broke into the temple’s inner chamber
to steal the sacred element crystals.
But when the alarm went off
they panicked,
and each of them swallowed the crystal
they held right before they were caught.
With no idea how to control
the crystals’ vast powers,
they’ll soon transform
into uncontrollable elemental spirits.
Improbably enough,
the old monk next to you
has seen something similar happen before.
He explains:
“You must determine who ate which crystal
and get each into the proper containment
field before they transform.
The elements compel their masters:
those who ate the Earth and Water Crystals
must speak the truth,
while those who consumed Fire and Air
must lie."
The youths are too scared to confess
their own transgressions.
Instead, they fall to accusing each other.
“Rikku took the Water crystal!”
Sumi blurts out.
Rikku interrupts angrily.
“It was Bella,
she stole the Fire crystal!”
So Bella yells:
“Jonah ate the Air crystal, I saw him!”
Jonah looks up timidly
and shakes his head.
“I… I don’t know what happened,
but Sumi doesn’t have the Earth crystal.”
So who ate which crystal?
Pause now to figure it out for yourself.
There’s no getting around it—
this will take some trial and error.
But that’s not a bad thing.
If we make a wrong guess,
we’ll eventually reach a point where
our conclusions contradict each other.
That would allow us to confirm
that our initial guess was wrong
and work from there.
This is a technique
known as proof by contradiction.
The trick is in being strategic
about where we begin our guessing.
Some assumptions
might not lead to contradictions
without making further assumptions.
We want to pick one that creates
the most constraints on its own,
and thus gives us the most information
when it turns out to be right or wrong.
Take, for example, Sumi’s statement.
If we assume she’s telling the truth,
we’d know the identity
of both truth tellers.
Rikku would have the Water crystal,
and since she’s not lying about him,
Sumi would have Earth.
So Bella would have the Fire crystal,
as Rikku says.
But then Bella would have to be lying
about Jonah having the Air crystal.
And yet that’s the only remaining option.
This is a contradiction, and it tells us
our initial assumption was wrong.
So now we can go back to the start,
but with the added knowledge
that Sumi is lying.
As a liar, Sumi
must either have the Fire or Air crystal.
That means Jonah
was telling the truth about her,
so he can’t have taken either of those.
And that means Bella was lying about him,
so she must also have either Fire or Air.
Since Sumi was lying,
Rikku can’t have taken the Water crystal—
the only one left
who could have it is Jonah.
And because we’ve already identified
the two liars,
Rikku must have the Earth crystal.
That means Bella has the Fire crystal
and Sumi has Air.
You manage to get them all
in the proper containment fields
just as the crystals’ magic
begins to manifest.
Compared with the difficult task
of training these kids
to control their new powers,
figuring out who had which crystal
was elementary.
