Can you solve the buried treasure riddle? - Daniel Griller

3,254,006 views ใƒป 2018-03-22

TED-Ed


ืื ื ืœื—ืฅ ืคืขืžื™ื™ื ืขืœ ื”ื›ืชื•ื‘ื™ื•ืช ื‘ืื ื’ืœื™ืช ืœืžื˜ื” ื›ื“ื™ ืœื”ืคืขื™ืœ ืืช ื”ืกืจื˜ื•ืŸ.

ืชืจื’ื•ื: Ido Dekkers ืขืจื™ื›ื”: Sigal Tifferet
00:06
After a massive storm tears through the Hex Archipelago,
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ืื—ืจื™ ืฉืกื•ืคื” ื—ื–ืงื” ืžื—ืจื™ื‘ื” ืืช ืืจื›ื™ืคืœื’ ื”ืงืก,
00:10
you find five grizzled survivors in the water.
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ืืชื ืžื•ืฆืื™ื ื—ืžื™ืฉื” ื ื™ืฆื•ืœื™ื ืชืฉื•ืฉื™ื ื‘ืžื™ื.
00:14
Shivering their timbers,
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ืงื•ืคืื™ื ืžืงื•ืจ,
00:16
they explain that theyโ€™re the former crew of the great pirate Greenbeard,
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ื”ื ืžืกื‘ื™ืจื™ื ืฉื”ื ืฉื™ื™ื›ื™ื ืœืฆื•ื•ืช ืœืฉืขื‘ืจ ืฉืœ ื”ืคื™ืจtื˜ ื”ื’ื“ื•ืœ ื–ืงืŸ ื™ืจื•ืง,
00:20
who marooned them after they tried to mutiny.
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ืฉื ื˜ืฉ ืื•ืชื ืื—ืจื™ ืฉื ื™ืกื• ืœืžืจื•ื“.
00:24
Each was bound up in a different spot on a small island,
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ื›ืœ ืื—ื“ ืžื”ื ื”ื™ื” ื›ืคื•ืช ื‘ื ืงื•ื“ื” ืฉื•ื ื” ืขืœ ืื™ ืงื˜ืŸ,
00:27
until the storm washed them out to sea.
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ืขื“ ืฉื”ืกืขืจื” ืฉื˜ืคื” ืื•ืชื ืœื™ื.
00:30
In gratitude for saving them, they reveal a secret:
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ื›ืชื•ื“ื” ืขืœ ื”ืฆืœืชื, ื”ื ืžื’ืœื™ื ืกื•ื“:
00:33
the island they were on is also where Greenbeard has buried his treasure hoard.
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ื”ืื™ ืขืœื™ื• ื”ื™ื• ื”ื•ื ื’ื ื”ืžืงื•ื ื‘ื• ื™ืจื•ืง ื”ื–ืงืŸ ืงื‘ืจ ืืช ื”ืื•ืฆืจ ืฉืœื•.
00:39
But when the sailors try to describe the island, something seems off.
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ืื‘ืœ ื›ืฉื”ืžืœื—ื™ื ืžื ืกื™ื ืœืชืืจ ืืช ื”ืื™, ืžืฉื”ื• ืœื ื ืฉืžืข ื”ื’ื™ื•ื ื™.
00:44
All agree it was flat and barren with no prominent features except for some trees.
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ื›ื•ืœื ืžืกื›ื™ืžื™ื ืฉื”ื•ื ื”ื™ื” ืฉื˜ื•ื— ื•ืฉื•ืžื ื‘ืœื™ ืชื›ื•ื ื•ืช ื‘ื•ืœื˜ื•ืช ื—ื•ืฅ ืžื›ืžื” ืขืฆื™ื.
00:51
Yet each pirate claims they saw a different number of trees,
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ื•ืขื“ื™ื™ืŸ ื›ืœ ืคื™ืจืื˜ ื˜ื•ืขืŸ ืฉื”ื•ื ืจืื” ืžืกืคืจ ืฉื•ื ื” ืฉืœ ืขืฆื™ื,
00:55
ranging from two to six.
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ืฉื ืข ื‘ื™ืŸ ืฉื ื™ื™ื ืœืฉื™ืฉื”.
00:57
The pirate who saw two trees says the treasure was buried right at his feet.
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ื”ืคื™ืจืื˜ ืฉืจืื” ืฉื ื™ ืขืฆื™ื ืื•ืžืจ ืฉื”ืžื˜ืžื•ืŸ ื”ื™ื” ืงื‘ื•ืจ ืžืžืฉ ืžืชื—ืช ืœืจื’ืœื™ื•.
01:02
When you fly your hot air balloon over the area to investigate,
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ื›ืฉืืชื ื˜ืกื™ื ื‘ื›ื“ื•ืจ ื”ืคื•ืจื— ืฉืœื›ื ืžืขืœ ื”ืื™ื–ื•ืจ ื›ื“ื™ ืœื—ืงื•ืจ,
01:05
you see hundreds of small islands, each with exactly six trees.
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ืืชื ืจื•ืื™ื ืžืื•ืช ืื™ื™ื ืงื˜ื ื™ื, ื›ืœ ืื—ื“ ืขื ื‘ื“ื™ื•ืง ืฉื™ืฉื” ืขืฆื™ื.
01:11
The next storm will be here soon,
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ื”ืกืขืจื” ื”ื‘ืื” ืชื’ื™ืข ื‘ืงืจื•ื‘,
01:13
so youโ€™ll have to hurry and narrow your search.
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ืื– ืืชื ืชืฆื˜ืจื›ื• ืœืžื”ืจ ื•ืœืฆืžืฆื ืืช ื”ื—ื™ืคื•ืฉ.
01:16
What does the island with Greenbeardโ€™s treasure look like from the sky?
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ืื™ืš ื ืจืื” ืื™ ื”ืžื˜ืžื•ืŸ ืฉืœ ื™ืจื•ืง ื”ื–ืงืŸ ืžื”ืฉืžื™ื?
01:19
And where will the treasure be on that island?
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ื•ื”ื™ื›ืŸ ืžืžื•ืงื ื”ืžื˜ืžื•ืŸ ืขืœ ื”ืื™?
01:27
Pause here if you want to figure it out for yourself!
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ืขืฆืจื• ืคื” ืื ืืชื ืจื•ืฆื™ื ืœื’ืœื•ืช ืืช ื”ืชืฉื•ื‘ื” ื‘ืขืฆืžื›ื!
01:31
Answer in 3
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ืชืฉื•ื‘ื” ืขื•ื“ 3
01:33
Answer in 2
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ืชืฉื•ื‘ื” ืขื•ื“ 2
01:34
Answer in 1
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ืชืฉื•ื‘ื” ืขื•ื“ 1
01:35
It might seem like the pirates are delirious from dehydration.
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ื–ื” ืื•ืœื™ ื ืจืื” ื›ืื™ืœื• ื”ืคื™ืจืื˜ื™ื ื”ื•ื–ื™ื ืžื”ืชื™ื™ื‘ืฉื•ืช.
01:39
But thatโ€™s not whatโ€™s going on.
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ืื‘ืœ ื–ื” ืœื ืžื” ืฉืงื•ืจื”.
01:41
Remember, each was confined to a separate point on the island,
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ื–ื›ืจื•, ื›ืœ ืื—ื“ ื”ื™ื” ืžื•ื’ื‘ืœ ืœื ืงื•ื“ื” ืฉื•ื ื” ื‘ืื™,
01:45
and no two of them could see the same number of trees.
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ื•ืืฃ ืื—ื“ ืžื”ื ืœื ื™ื›ื•ืœ ืœืจืื•ืช ืžืกืคืจ ื–ื”ื” ืฉืœ ืขืฆื™ื.
01:49
That means that for all but one pirate, something was blocking their view.
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ื–ื” ืื•ืžืจ ืฉืœื›ื•ืœื ื—ื•ืฅ ืžืœืคื™ืจืื˜ ืื—ื“ ืžืฉื”ื• ื”ืกืชื™ืจ ืืช ืงื• ื”ืจืื™ื”.
01:53
And since there are no other features on the island,
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ื•ืžืื—ืจ ืฉืื™ืŸ ืชื›ื•ื ื•ืช ืื—ืจื•ืช ืขืœ ื”ืื™,
01:56
that something could only have been other trees.
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ื”ื“ื‘ืจ ื”ื–ื” ื”ื™ื” ื™ื›ื•ืœ ืœื”ื™ื•ืช ืจืง ืขืฆื™ื ืื—ืจื™ื.
02:01
A pirate would see fewer trees when two or more
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ืคื™ืจืื˜ ื”ื™ื” ืจื•ืื” ืคื—ื•ืช ืขืฆื™ื ื›ืฉืฉื ื™ื™ื ืื• ื™ื•ืชืจ
02:04
fell along a straight line from their vantage point.
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ื”ื™ื• ืขืœ ืงื• ืื—ื“ ืžื ืงื•ื“ืช ื”ืžื‘ื˜ ืฉืœื”ื.
02:08
So we need to find the island
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ืื– ืื ื—ื ื• ืฆืจื™ื›ื™ื ืœืžืฆื•ื ืื™
02:09
where five different pirates standing in different spots
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ื‘ื• ื—ืžื™ืฉื” ืคื™ืจืื˜ื™ื ืฉื•ื ื™ื ืฉืขื•ืžื“ื™ื ื‘ื ืงื•ื“ื•ืช ืฉื•ื ื•ืช
02:12
would each see a different number of trees.
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ื™ืจืื• ื›ืœ ืื—ื“ ืžืกืคืจ ืฉื•ื ื” ืฉืœ ืขืฆื™ื.
02:16
Virtually every island has a position from which you can see six trees.
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ื›ืžืขื˜ ื‘ื›ืœ ืื™ ื™ืฉ ื ืงื•ื“ื” ืžืžื ื” ืืคืฉืจ ืœืจืื•ืช ืฉื™ืฉื” ืขืฆื™ื.
02:21
And on most islands thereโ€™s a position where 5 trees can be seen
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ื•ื‘ืจื•ื‘ ื”ืื™ื™ื ื™ืฉ ื ืงื•ื“ื” ื‘ื” ืืคืฉืจ ืœืจืื•ืช 5,
02:25
by standing in line with two of them.
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ืขืœ ื™ื“ื™ ืขืžื™ื“ื” ื‘ืงื• ืขื ืฉื ื™ื™ื ืžื”ื.
02:28
It turns out that the hardest locations to find are those with fewer visible trees
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ืžืกืชื‘ืจ ืฉื”ืžื™ืงื•ื ื”ืงืฉื” ื‘ื™ื•ืชืจ ืœืžืฆื•ื ื”ื•ื ื–ื” ืขื ืคื—ื•ืช ืขืฆื™ื ื ืจืื™ื
02:33
precisely because they require more trees to line up with the viewerโ€™s position.
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ื‘ื“ื™ื•ืง ื‘ื’ืœืœ ืฉื”ื ื“ื•ืจืฉื™ื ื™ื•ืชืจ ืขืฆื™ื ืฉื™ืขืžื“ื• ื‘ืฉื•ืจื” ืžื ืงื•ื“ืช ืžื‘ื˜ ื”ืฆื•ืคื”.
02:39
So how can we see just two trees?
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ืื– ืื™ืš ืืคืฉืจ ืœืจืื•ืช ืจืง ืฉื ื™ ืขืฆื™ื?
02:42
One way would be if all the trees were lined up in single file,
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ื“ืจืš ืื—ืช ืชื”ื™ื” ืื ื›ืœ ื”ืขืฆื™ื ื”ื™ื• ืžืกื•ื“ืจื™ื ื‘ืฉื•ืจื” ืื—ืช,
02:45
such as on this island.
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ื›ืžื• ืขืœ ื”ืื™ ื”ื–ื”.
02:47
Then, you could stand at the end of the line and see one,
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ืื–, ืชื•ื›ืœื• ืœืขืžื•ื“ ื‘ืงืฆื” ื”ืงื• ื•ืœืจืื•ืช ืื—ื“,
02:50
stand in the middle and see two,
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ืœืขืžื•ื“ ื‘ืืžืฆืข ื•ืœืจืื•ืช ืฉื ื™ื™ื,
02:52
or stand anywhere else and see all six.
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ืื• ืœืขืžื•ื“ ื‘ื›ืœ ืžืงื•ื ืื—ืจ ื•ืœืจืื•ืช ืืช ื›ืœ ื”ืฉื™ืฉื”.
02:56
But thereโ€™s no place from which you can see only three,
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ืื‘ืœ ืื™ืŸ ืืฃ ืžืงื•ื ืžืžื ื• ืชื•ื›ืœื• ืœืจืื•ืช ืจืง ืฉืœื•ืฉื”,
02:59
four,
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02:59
or five,
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ืืจื‘ืขื”,
ืื• ื—ืžื™ืฉื”,
03:00
so one straight line of trees is out.
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ืื– ืงื• ืื—ื“ ื™ืฉืจ ืฉืœ ืขืฆื™ื ืœื ืžืชืื™ื.
03:04
So what about two lines of trees?
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ืื– ืžื” ืขื ืฉื ื™ ืงื•ื™ื ืฉืœ ืขืฆื™ื?
03:06
So long as the lines arenโ€™t parallel and they intersect over land,
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ื›ืœ ืขื•ื“ ื”ืงื•ื™ื ืœื ืžืงื‘ื™ืœื™ื ื•ื”ื ื ืคื’ืฉื™ื ืžืขืœ ื”ืื“ืžื”,
03:10
thereโ€™ll always be a position where the two lines converge
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ืชืžื™ื“ ื™ื”ื™ื• ืžื™ืงื•ื ื‘ื• ืฉื ื™ ืงื•ื™ื ื ืคื’ืฉื™ื
03:14
from which you could see exactly two trees.
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ืฉืžืžื ื• ืืคืฉืจ ืœืจืื•ืช ื‘ื“ื™ื•ืง ืฉื ื™ ืขืฆื™ื.
03:17
And if theyโ€™re grouped two and four,
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ื•ืื ื”ื ืžืงื•ื‘ืฆื™ื ืฉื ื™ื™ื ื•ืืจื‘ืขื”,
03:19
or three and three,
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ืื• ืฉืœื•ืฉื” ื•ืฉืœื•ืฉื”,
03:21
there are many arrangements in which you could also see three,
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ื™ืฉ ื”ืจื‘ื” ืกื™ื“ื•ืจื™ื ื‘ื”ื ืชื•ื›ืœื• ืœืจืื•ืช ื’ื ืฉืœื•ืฉื”,
03:24
four,
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ืืจื‘ืขื”,
03:25
five,
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ื—ืžื™ืฉื”,
03:27
and six trees.
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ื•ืฉื™ืฉื” ืขืฆื™ื.
03:29
Fortunately for us, thereโ€™s only one island in the archipelago
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ืœืžืจื‘ื” ื”ืžื–ืœ ื‘ืฉื‘ื™ืœื ื•, ื™ืฉ ืจืง ืื™ ืื—ื“ ื‘ืืจื›ื™ืคืœื’
03:33
with two non-parallel lines of trees,
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ืขื ืฉื ื™ ืงื•ื™ื ืœื ืžืงื‘ื™ืœื™ื ืฉืœ ืขืฆื™ื,
03:36
and itโ€™ll be buried at the intersection of the two lines.
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ื•ื”ืžื˜ืžื•ืŸ ื™ื”ื™ื” ืงื‘ื•ืจ ื‘ื”ืฆื˜ืœื‘ื•ืช ืฉืœ ืฉื ื™ ื”ืงื•ื™ื.
03:41
You land on this island and dig up a chest containing a massive pile of tree seeds,
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ืืชื ื ื•ื—ืชื™ื ืขืœ ื”ืื™ ื”ื–ื” ื•ื—ื•ืคืจื™ื ืืช ื”ืืจื’ื– ืฉืžื›ื™ืœ ืขืจืžื” ืžืกื™ื‘ื™ืช ืฉืœ ื–ืจืขื™ ืขืฆื™ื,
03:47
ready for planting.
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ืžื•ื›ื ื™ื ืœืฉืชื™ืœื”.
03:49
Was this treasure really worth all that trouble?
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ื”ืื ื”ืื•ืฆืจ ื”ื–ื” ื”ื™ื” ื‘ืืžืช ืฉื•ื•ื” ืืช ื”ืžืืžืฅ?
03:51
Thatโ€™s a matter of perspective.
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ื–ื” ืขื ื™ื™ืŸ ืฉืœ ืคืจืกืคืงื˜ื™ื‘ื”.
ืขืœ ืืชืจ ื–ื”

ืืชืจ ื–ื” ื™ืฆื™ื’ ื‘ืคื ื™ื›ื ืกืจื˜ื•ื ื™ YouTube ื”ืžื•ืขื™ืœื™ื ืœืœื™ืžื•ื“ ืื ื’ืœื™ืช. ืชื•ื›ืœื• ืœืจืื•ืช ืฉื™ืขื•ืจื™ ืื ื’ืœื™ืช ื”ืžื•ืขื‘ืจื™ื ืขืœ ื™ื“ื™ ืžื•ืจื™ื ืžื”ืฉื•ืจื” ื”ืจืืฉื•ื ื” ืžืจื—ื‘ื™ ื”ืขื•ืœื. ืœื—ืฅ ืคืขืžื™ื™ื ืขืœ ื”ื›ืชื•ื‘ื™ื•ืช ื‘ืื ื’ืœื™ืช ื”ืžื•ืฆื’ื•ืช ื‘ื›ืœ ื“ืฃ ื•ื™ื“ืื• ื›ื“ื™ ืœื”ืคืขื™ืœ ืืช ื”ืกืจื˜ื•ืŸ ืžืฉื. ื”ื›ืชื•ื‘ื™ื•ืช ื’ื•ืœืœื•ืช ื‘ืกื ื›ืจื•ืŸ ืขื ื”ืคืขืœืช ื”ื•ื•ื™ื“ืื•. ืื ื™ืฉ ืœืš ื”ืขืจื•ืช ืื• ื‘ืงืฉื•ืช, ืื ื ืฆื•ืจ ืื™ืชื ื• ืงืฉืจ ื‘ืืžืฆืขื•ืช ื˜ื•ืคืก ื™ืฆื™ืจืช ืงืฉืจ ื–ื”.

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