Can you solve the buried treasure riddle? - Daniel Griller

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After a massive storm tears through the Hex Archipelago, you find five grizzled survivors in the water. As an act of gratitude for saving them, they reveal a secret – the island they were just on holds some buried treasure. But when the sailors try to describe the island, something seems off. Can you find the booty despite their strange instructions? Daniel Griller shows how.

Lesson by Daniel Griller, animation by Patrick Smith.

After a massive storm tears
through the Hex Archipelago,

you find five grizzled
survivors in the water.

Shivering their timbers,

they explain that they’re the former crew
of the great pirate Greenbeard,

who marooned them
after they tried to mutiny.

Each was bound up in a different
spot on a small island,

until the storm washed them out to sea.

In gratitude for saving them,
they reveal a secret:

the island they were on is also where
Greenbeard has buried his treasure hoard.

But when the sailors try to describe
the island, something seems off.

All agree it was flat and barren with no
prominent features except for some trees.

Yet each pirate claims they saw
a different number of trees,

ranging from two to six.

The pirate who saw two trees says the
treasure was buried right at his feet.

When you fly your hot air balloon
over the area to investigate,

you see hundreds of small islands,
each with exactly six trees.

The next storm will be here soon,

so you’ll have to hurry
and narrow your search.

What does the island with Greenbeard’s
treasure look like from the sky?

And where will the treasure be
on that island?

Pause here if you want
to figure it out for yourself!

Answer in 3

Answer in 2

Answer in 1

It might seem like the pirates
are delirious from dehydration.

But that’s not what’s going on.

Remember, each was confined
to a separate point on the island,

and no two of them could see
the same number of trees.

That means that for all but one pirate,
something was blocking their view.

And since there are no other
features on the island,

that something could only
have been other trees.

A pirate would see fewer trees
when two or more

fell along a straight line
from their vantage point.

So we need to find the island

where five different pirates standing
in different spots

would each see a
different number of trees.

Virtually every island has a position
from which you can see six trees.

And on most islands there’s a
position where 5 trees can be seen

by standing in line with two of them.

It turns out that the hardest locations
to find are those with fewer visible trees

precisely because they require more trees
to line up with the viewer’s position.

So how can we see just two trees?

One way would be if all the trees
were lined up in single file,

such as on this island.

Then, you could stand at the end
of the line and see one,

stand in the middle and see two,

or stand anywhere else and see all six.

But there’s no place from
which you can see only three,

four,

or five,

so one straight line of trees is out.

So what about two lines of trees?

So long as the lines aren’t parallel
and they intersect over land,

there’ll always be a position
where the two lines converge

from which you could
see exactly two trees.

And if they’re grouped two and four,

or three and three,

there are many arrangements in which
you could also see three,

four,

five,

and six trees.

Fortunately for us, there’s only
one island in the archipelago

with two non-parallel lines of trees,

and it’ll be buried at the intersection
of the two lines.

You land on this island and dig up a chest
containing a massive pile of tree seeds,

ready for planting.

Was this treasure really worth
all that trouble?

That’s a matter of perspective.