Can you solve the control room riddle? - Dennis Shasha
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0:07 - 0:09As your country's top spy,
-
0:09 - 0:12you must infiltrate the headquarters
of the evil syndicate, -
0:12 - 0:14find the secret control panel,
-
0:14 - 0:16and deactivate their death ray.
-
0:16 - 0:19But all you have to go on
is the following information -
0:19 - 0:21picked up by your surveillance team.
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0:21 - 0:26The headquarters is a massive pyramid
with a single room at the top level, -
0:26 - 0:28two rooms on the next,
-
0:28 - 0:30and so on.
-
0:30 - 0:32The control panel is hidden
behind a painting -
0:32 - 0:36on the highest floor that can satisfy
the following conditions: -
0:36 - 0:41Each room has exactly three doors
to other rooms on that floor, -
0:41 - 0:43except the control panel room,
-
0:43 - 0:45which connects to only one,
-
0:45 - 0:46there are no hallways,
-
0:46 - 0:48and you can ignore stairs.
-
0:48 - 0:50Unfortunately,
you don't have a floor plan, -
0:50 - 0:53and you'll only have enough time
to search a single floor -
0:53 - 0:56before the alarm system reactivates.
-
0:56 - 0:59Can you figure out which floor
the control room is on? -
0:59 - 1:01Pause now to solve the riddle yourself.
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1:01 - 1:02Answer in: 3
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1:02 - 1:03Answer in: 2
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1:03 - 1:05Answer in: 1
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1:05 - 1:09To solve this problem,
we need to visualize it. -
1:09 - 1:11For starters, we know
that on the correct floor -
1:11 - 1:12there's one room,
-
1:12 - 1:14let's call it room A,
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1:14 - 1:16with one door to the control panel room,
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1:16 - 1:18plus one door to room B,
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1:18 - 1:19and one to C.
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1:19 - 1:22So there must be at least four rooms,
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1:22 - 1:24which we can represent as circles,
-
1:24 - 1:27drawing lines between them
for the doorways. -
1:27 - 1:29But once we connect rooms B and C,
-
1:29 - 1:31there are no other connections possible,
-
1:31 - 1:35so the fourth floor down
from the top is out. -
1:35 - 1:38We know the control panel has to be
as high up as possible, -
1:38 - 1:40so let's make our way down the pyramid.
-
1:40 - 1:43The fifth highest floor
doesn't work either. -
1:43 - 1:45We can figure that out by drawing it,
-
1:45 - 1:48but to be sure we haven't missed
any possibilities, -
1:48 - 1:49here's another way.
-
1:49 - 1:53Every door corresponds to a line
in our graph -
1:53 - 1:55that makes two rooms into neighbors.
-
1:55 - 1:59So in the end, there have to be
an even number of neighbors -
1:59 - 2:02no matter how many connections we make.
-
2:02 - 2:06On the fifth highest floor,
to fulfill our starting conditions, -
2:06 - 2:09we'd need four rooms
with three neighbors each, -
2:09 - 2:12plus the control panel room
with one neighbor, -
2:12 - 2:14which makes 13 total neighbors.
-
2:14 - 2:16Since that's an odd number,
it's not possible, -
2:16 - 2:22and, in fact, this also rules out every
floor that has an odd number of rooms. -
2:22 - 2:24So let's go one more floor down.
-
2:24 - 2:26When we draw out the rooms,
-
2:26 - 2:31low and behold, we can find an arrangement
that works like this. -
2:31 - 2:34Incidentally, the study
of such visual models -
2:34 - 2:38that show the connections and
relationships between different objects -
2:38 - 2:39is known as graph theory.
-
2:39 - 2:44In a basic graph, the circles representing
the objects are known as nodes, -
2:44 - 2:47while the connecting lines
are called edges. -
2:47 - 2:51Researchers studying such graphs
ask questions like, -
2:51 - 2:53"How far is this node from that one?"
-
2:53 - 2:57"How many edges does
the most popular node have?" -
2:57 - 3:02"Is there a route between these two nodes,
and if so, how long is it?" -
3:02 - 3:05Graphs like this are often used
to map communication networks, -
3:05 - 3:08but they can represent almost
any kind of network, -
3:08 - 3:10from transport connections within a city
-
3:10 - 3:12and social relationships among people,
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3:12 - 3:15to chemical interactions between proteins
-
3:15 - 3:19or the spread of an epidemic
through different locations. -
3:19 - 3:22So, armed with these techniques,
back to the pyramid. -
3:22 - 3:25You avoid the guards and security cameras,
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3:25 - 3:27infiltrate the sixth floor from the top,
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3:27 - 3:28find the hidden panel,
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3:28 - 3:30pull some conspicuous levers,
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3:30 - 3:33and send the death ray crashing
into the ocean. -
3:33 - 3:35Now, time to solve the mystery
-
3:35 - 3:40of why your surveillance team
always gives you cryptic information. -
3:40 - 3:41Hi everybody.
-
3:41 - 3:44If you liked this riddle,
try solving these two.
- Title:
- Can you solve the control room riddle? - Dennis Shasha
- Speaker:
- Dennis Shasha
- Description:
-
View full lesson: http://ed.ted.com/lessons/can-you-solve-the-control-room-riddle-dennis-shasha
As your country's top spy, you must infiltrate the headquarters of the evil syndicate, find the secret control panel, and deactivate their death ray. But your reconnaissance team is spotty, and you have only limited information about the control panel's whereabouts. Can you solve the control room riddle and deactivate their weapon in time? Dennis Shasha shows you how.
Lesson by Dennis Shasha, animation by Zedem Media.
- Video Language:
- English
- Team:
- closed TED
- Project:
- TED-Ed
- Duration:
- 04:01
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