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  • 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 all you have to go on is the following information

  • picked up by your surveillance team.

  • The headquarters is a massive pyramid with a single room at the top level,

  • two rooms on the next,

  • and so on.

  • The control panel is hidden behind a painting

  • on the highest floor that can satisfy the following conditions:

  • Each room has exactly three doors to other rooms on that floor,

  • except the control panel room,

  • which connects to only one,

  • there are no hallways,

  • and you can ignore stairs.

  • Unfortunately, you don't have a floor plan,

  • and you'll only have enough time to search a single floor

  • before the alarm system reactivates.

  • Can you figure out which floor the control room is on?

  • Pause now to solve the riddle yourself.

  • Answer in: 3

  • Answer in: 2

  • Answer in: 1

  • To solve this problem, we need to visualize it.

  • For starters, we know that on the correct floor

  • there's one room,

  • let's call it room A,

  • with one door to the control panel room,

  • plus one door to room B,

  • and one to C.

  • So there must be at least four rooms,

  • which we can represent as circles,

  • drawing lines between them for the doorways.

  • But once we connect rooms B and C,

  • there are no other connections possible,

  • so the fourth floor down from the top is out.

  • We know the control panel has to be as high up as possible,

  • so let's make our way down the pyramid.

  • The fifth highest floor doesn't work either.

  • We can figure that out by drawing it,

  • but to be sure we haven't missed any possibilities,

  • here's another way.

  • Every door corresponds to a line in our graph

  • that makes two rooms into neighbors.

  • So in the end, there have to be an even number of neighbors

  • no matter how many connections we make.

  • On the fifth highest floor, to fulfill our starting conditions,

  • we'd need four rooms with three neighbors each,

  • plus the control panel room with one neighbor,

  • which makes 13 total neighbors.

  • Since that's an odd number, it's not possible,

  • and, in fact, this also rules out every floor that has an odd number of rooms.

  • So let's go one more floor down.

  • When we draw out the rooms,

  • low and behold, we can find an arrangement that works like this.

  • Incidentally, the study of such visual models

  • that show the connections and relationships between different objects

  • is known as graph theory.

  • In a basic graph, the circles representing the objects are known as nodes,

  • while the connecting lines are called edges.

  • Researchers studying such graphs ask questions like,

  • "How far is this node from that one?"

  • "How many edges does the most popular node have?"

  • "Is there a route between these two nodes, and if so, how long is it?"

  • Graphs like this are often used to map communication networks,

  • but they can represent almost any kind of network,

  • from transport connections within a city

  • and social relationships among people,

  • to chemical interactions between proteins

  • or the spread of an epidemic through different locations.

  • So, armed with these techniques, back to the pyramid.

  • You avoid the guards and security cameras,

  • infiltrate the sixth floor from the top,

  • find the hidden panel,

  • pull some conspicuous levers,

  • and send the death ray crashing into the ocean.

  • Now, time to solve the mystery

  • of why your surveillance team always gives you cryptic information.

  • Hi everybody.

  • If you liked this riddle, try solving these two.

As your country's top spy,

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B1 TED-Ed floor control panel panel room riddle

【TED-Ed】Can you solve the control room riddle? - Dennis Shasha

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    黃于珍 posted on 2016/06/21
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