Can you solve the world’s most evil wizard riddle? - Dan Finkel

The evil wizard MoldeVort has
been trying to kill you for years,

and today it looks like he’s
going to succeed.

But your friends are on their way, and
if you can survive until they arrive,

they should be able to help stop him.

The evil wizard’s protective charms ward
off every spell you know,

so in an act of desperation you throw
the only object in reach at him:

Pythagoras’s cursed chessboard.

It works, but with a catch.

Moldevort starts in one corner
of the 5x5 board.

You have a few minutes to choose
four distinct positive whole numbers.

MoldeVort gets to say one of them,
and if you can pick a square on the board

whose center is exactly that
distance away,

the curse will force him to
move to that spot.

Then he’ll have to choose any of
the four numbers,

and the process repeats until you can’t keep
him inside the board

with legal moves.

Then he’ll break free of the spell and
almost certainly kill you.

What four numbers can you choose
to keep MoldeVort trapped by your spell

long enough for help to arrive?
And what’s your strategy?

The trick here is to keep MoldeVort where
you want him.

And one way to figure out how to do that

is to play out the game as
MoldeVort would:

always trying to escape.

You’re dealing with a relatively
small board,

so the numbers can’t be too big.

Let’s start by trying 1, 2, 3, 4 to
see what happens.

Moldevort could escape those numbers
in just three moves.

By saying 2, then 3,

he would force you to let him into one
of the middle points of the grid,

and then a 4 would break him free.

But that means you’ll need to allow
a number larger than 4,

which is the distance from one
end of a row to another.

How is that even possible?

Through diagonal moves.

There are, in fact, points that are
distance 5 from each other,

which we know thanks to the Pythagorean
Theorem.

That states that the squares of the sides
of a right triangle

add up to the square of its hypotenuse.

One of the most famous Pythagorean
triples is 3, 4, 5,

and that triangle is hiding all over
your chessboard.

So if MoldeVort was here, and he said 5,
you could move him to these spaces.

There’s another insight that will help.

The board is very symmetrical: If
Moldevort is in a corner,

it doesn’t really matter to you which
corner it is.

So we can think of the corners as
being functionally the same,

and color them all blue.

Similarly, the spaces neighboring the
corners behave the same as each other,

and we’ll make them red.

Finally, the midpoints of the sides are a
third type.

So instead of having to develop a strategy

for each of the 16 spaces on the
outside of the board,

we can reduce the problem to just three.

Meanwhile, all the inside spaces are bad
for us,

because if Moldevort ever reaches one,

he’ll be able to say any number larger
than 3 and go free.

Orange spaces are trouble too, since
any number except 1, 2, or 4

would take him to an inside space or
off the board.

So orange is out and you’ll need to
keep him on blue and red.

That means 2 is bad,

since that it could take Moldevort
to orange on the first turn.

But the four other smallest numbers,
1, 3, 4, and 5, might work.

Let’s try them and see what happens.

If Moldevort says 1, you can make him
go from blue to red or red to blue.

And the same works if he says 3.

Thanks to our diagonals, this is even
true if he says “5”.

If he says 4, you can keep him on the
color he’s already on

by moving the length of a row or column.

So these four numbers work!

Even if your friends don’t get here
right away,

you’ll be able to keep the world’s most
evil wizard contained

for as long as you need.