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.