Can you solve the honeybee riddle? - Dan Finkel
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0:07 - 0:09You’re a biologist on a mission
-
0:09 - 0:14to keep the rare honeybee
Apis Trifecta from going extinct. -
0:14 - 0:19The last 60 bees of the species
are in your terrarium. -
0:19 - 0:24You’ve already constructed wire frames
of the appropriate size and shape. -
0:24 - 0:28Now you need to turn
them into working beehives -
0:28 - 0:32by helping the bees fill
every hex with wax. -
0:32 - 0:35There are two ways to fill a given hex.
-
0:35 - 0:38The first is to place a bee into it.
-
0:38 - 0:43Once placed, a bee cannot
be removed without killing it. -
0:43 - 0:44The second:
-
0:44 - 0:50if at any point an unfilled hex has three
or more neighboring wax-filled hexes, -
0:50 - 0:55the bees already in the hive
will move in and transform it. -
0:55 - 0:59Once the bees have transformed
every hex in a hive, -
0:59 - 1:05you can place an additional bee inside
and it’ll specialize into a queen. -
1:05 - 1:09The hive, if well cared for,
will eventually produce new bees -
1:09 - 1:11and continue the species.
-
1:11 - 1:16If there are no hexes with three or more
transformed neighbors, -
1:16 - 1:19the bees will just sit and wait.
-
1:19 - 1:24And once a bee transforms a hex,
it can never become a queen. -
1:24 - 1:30You could put 59 bees in one wire hive,
wait till they transform all the hexes, -
1:30 - 1:32and then create a queen.
-
1:32 - 1:36But then just one collapse
would end the species. -
1:36 - 1:41The more viable hives
you can make now, the better. -
1:41 - 1:44So how many can you make with 60 bees?
-
1:44 - 1:46Pause the video to figure
it out yourself -
1:46 - 1:46Answer in 3
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1:46 - 1:49Answer in 2
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1:49 - 1:51Answer in 1
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1:51 - 1:52Answer in 0
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1:52 - 1:57What you're looking for here is some
kind of self-sustaining chain reaction, -
1:57 - 2:01where a small number of bees
will transform an entire hive. -
2:01 - 2:05The lower the number of bees needed,
the better. -
2:05 - 2:12So how low can we go,
and how can we engineer a chain reaction? -
2:12 - 2:14Let’s start with the first question.
-
2:14 - 2:16There's a really clever approach to this,
-
2:16 - 2:20which involves counting the sides
of the filled-in hexes, -
2:20 - 2:22and examining their total perimeter.
-
2:22 - 2:26Let’s suppose we put bees
in these three hexes. -
2:26 - 2:30The total transformed
perimeter has 18 sides. -
2:30 - 2:33But the middle hex
has three transformed neighbors, -
2:33 - 2:36so the bees will transform it too.
-
2:36 - 2:38What happens to the perimeter?
-
2:38 - 2:40It’s still 18!
-
2:40 - 2:45And even after the bees transform the next
sets of hexes with three neighbors, -
2:45 - 2:47it still won’t change.
-
2:47 - 2:49What’s going on here?
-
2:49 - 2:54Each hex that has at least three sides
touching the bee-friendly space -
2:54 - 2:59will remove those sides from the perimeter
when it transforms. -
2:59 - 3:03Then it adds at most three new sides
to the perimeter. -
3:03 - 3:09So the perimeter of the transformed hexes
will either stay the same or shrink. -
3:09 - 3:13The final perimeter
of the entire hive is 54, -
3:13 - 3:17so the total perimeter of the hexes
we place bees in at the start -
3:17 - 3:21must be at least 54 as well.
-
3:21 - 3:26Dividing that 54 by the six sides
on each non-adjacent hex -
3:26 - 3:31tells us it’ll take at least 9 bees
to transform the entire hive. -
3:31 - 3:33That’s a great start,
-
3:33 - 3:38but we still have the tough question
of where the nine bees should go, -
3:38 - 3:40and if we’ll need more.
-
3:40 - 3:42Let’s think smaller.
-
3:42 - 3:48We already know that three bees could
completely transform a hive this big. -
3:48 - 3:50What about a slightly bigger one?
-
3:50 - 3:52The perimeter of this hive is 30,
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3:52 - 3:55which means we’ll need
at least 5 bees to fill it in. -
3:55 - 3:57With 6 it’d be easy.
-
3:57 - 4:02Placing them like this would fill out
the whole hive in just three steps. -
4:05 - 4:06But we can do better!
-
4:06 - 4:10We don’t actually need to place
a bee on this hex, -
4:10 - 4:14since the other bees will transform
that spot on their own. -
4:19 - 4:22It looks like we have
the beginning of a pattern. -
4:22 - 4:25Can we extend it to our full hive?
-
4:25 - 4:28That would mean placing
our 9 bees like so. -
4:28 - 4:32Once they get to work,
they’ll create a chain reaction -
4:32 - 4:36that fills in the center of the hive
and extend it to its edges. -
4:39 - 4:44Add a 10th bee to the completed hive
and it becomes a queen. -
4:44 - 4:47Repeat that process five more times
-
4:47 - 4:51and you’ve helped the last 60 members
of Apis trifecta -
4:51 - 4:54create 6 producing hives.
-
4:54 - 4:57All in all,
it’s a pretty good bee-ginning.
- Title:
- Can you solve the honeybee riddle? - Dan Finkel
- Speaker:
- Dan Finkel
- Description:
-
View full lesson: https://ed.ted.com/lessons/can-you-solve-the-honeybee-riddle-dan-finkel
You're a biologist on a mission to keep the rare honeybee Apis Trifecta from going extinct. The last 60 bees of the species are in your terrarium. You've already constructed wire frames of the appropriate size and shape. Now you need to turn them into working beehives by filling every hex with wax. Can you help the bees create producing hives? Dan Finkel shows how.
Lesson by Dan Finkel, directed by Charlotte Arene.
- Video Language:
- English
- Team:
- closed TED
- Project:
- TED-Ed
- Duration:
- 04:58
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