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.
