Can you solve the troll's paradox riddle? - Daniel Finkel

View full lesson: https://ed.ted.com/lessons/can-you-solve-the-troll-s-paradox-riddle-dan-finkel

You and your brother have discovered another realm and set off exploring the new wonderful world. Along the way, you see a troll catching creatures in an enormous net. The troll agrees to release the creatures if you can come up with a statement that is both truth and false. Can you come up with the correct sentence and force the troll to release them? Dan Finkel shows how.

Lesson by Dan Finkel, directed by Artrake Studio.

You’ve discovered a doorway
to another realm,

and now you and your brother

are off exploring the wonderful
world of Paradoxica.

Fantastically paradoxical creatures crawl,
run, and fly around you.

And then you see the troll.

It’s catching all the creatures
in an enormous net.

You bravely step forward
and demand it let them go.

The troll laughs.

“If you’re such a
fan of paradoxes,” it says,

“then I’ll make you an offer.

If you say something true,
I’ll release all these creatures."

You’re about to say, “You are a troll,”

but before you can,
the troll grabs your brother.

“If you say something false,”
he continues,

“then I’ll release your brother."

Your statement can
only be a single sentence.

And as you can see,
I hate paradoxes more than anything.

If you try to cheat
by saying something paradoxical,

like, ‘this statement is false,’

then I'll eat your brother
and the creatures."

What true/false statement
can you say to force the troll

to free your brother
and the paradoxical creatures?

[Pause the video now if you
want to figure it out for yourself!]

Answer in: 3

Answer in: 2

Answer in: 1

This seems like an impossible situation,

but incredibly, you can say something

that will force the troll to
release all its prisoners.

This is an example of coercive logic,

invented by the great logician
and puzzle creator Raymond Smullyan.

The trick Smullyan came up with
involves saying a statement

whose truth or falseness depends on
what you want the troll to do.

Your statement still
has to be carefully crafted.

For example, if you were to say,

“You are going to free the
creatures and my brother,”

the troll could respond, “that’s false…
I’m only going to free your brother.”

Similarly, if you said, “You will free
the paradoxes,”

the troll could say, “That’s true,”
and free the paradoxes.

But watch what happens if you say,
“You will free my brother.”

The statement can’t be false,

because if it were, the troll,
by its own rules,

would have to free your brother.

That would make the statement
paradoxically true and false.

But the troll hates paradoxes

and would never willingly create one.

So his only option
is for the statement to be true.

If “you will free my brother” is true,

then the troll
has to release your brother.

And by its own rules, the troll
has to free the creatures as well,

since you said a true statement.

By wielding just 5 words
like a logical scalpel,

you’ve forced the troll
to free all its prisoners.

As the troll stomps off in anger,

the paradoxes cheer you
for winning them their freedom,

and promise to lead you to the
treasure at the top of the stairs.

If you can reach it.