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  • 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.

After a massive storm tears through the Hex Archipelago,

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B1 TED-Ed island treasure pirate buried archipelago

Can you solve the buried treasure riddle? - Daniel Griller

  • 69 1
    林宜悉 posted on 2020/07/03
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