[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:06.97,0:00:08.74,Default,,0000,0000,0000,,As your country's top spy,
Dialogue: 0,0:00:08.74,0:00:12.09,Default,,0000,0000,0000,,you must infiltrate the headquarters\Nof the evil syndicate,
Dialogue: 0,0:00:12.09,0:00:13.83,Default,,0000,0000,0000,,find the secret control panel,
Dialogue: 0,0:00:13.83,0:00:16.44,Default,,0000,0000,0000,,and deactivate their death ray.\N
Dialogue: 0,0:00:16.44,0:00:19.20,Default,,0000,0000,0000,,But all you have to go on \Nis the following information
Dialogue: 0,0:00:19.20,0:00:21.33,Default,,0000,0000,0000,,picked up by your surveillance team.
Dialogue: 0,0:00:21.33,0:00:26.48,Default,,0000,0000,0000,,The headquarters is a massive pyramid\Nwith a single room at the top level,
Dialogue: 0,0:00:26.48,0:00:27.99,Default,,0000,0000,0000,,two rooms on the next,
Dialogue: 0,0:00:27.99,0:00:29.70,Default,,0000,0000,0000,,and so on.
Dialogue: 0,0:00:29.70,0:00:32.14,Default,,0000,0000,0000,,The control panel is hidden\Nbehind a painting
Dialogue: 0,0:00:32.14,0:00:36.05,Default,,0000,0000,0000,,on the highest floor that can satisfy\Nthe following conditions:
Dialogue: 0,0:00:36.05,0:00:40.77,Default,,0000,0000,0000,,Each room has exactly three doors\Nto other rooms on that floor,
Dialogue: 0,0:00:40.77,0:00:42.67,Default,,0000,0000,0000,,except the control panel room,
Dialogue: 0,0:00:42.67,0:00:44.59,Default,,0000,0000,0000,,which connects to only one,
Dialogue: 0,0:00:44.59,0:00:45.79,Default,,0000,0000,0000,,there are no hallways,
Dialogue: 0,0:00:45.79,0:00:47.86,Default,,0000,0000,0000,,and you can ignore stairs.
Dialogue: 0,0:00:47.86,0:00:50.46,Default,,0000,0000,0000,,Unfortunately, \Nyou don't have a floor plan,
Dialogue: 0,0:00:50.46,0:00:53.14,Default,,0000,0000,0000,,and you'll only have enough time\Nto search a single floor
Dialogue: 0,0:00:53.14,0:00:56.16,Default,,0000,0000,0000,,before the alarm system reactivates.
Dialogue: 0,0:00:56.16,0:00:58.89,Default,,0000,0000,0000,,Can you figure out which floor\Nthe control room is on?
Dialogue: 0,0:00:58.89,0:01:00.99,Default,,0000,0000,0000,,Pause now to solve the riddle yourself.
Dialogue: 0,0:01:00.99,0:01:01.82,Default,,0000,0000,0000,,Answer in: 3
Dialogue: 0,0:01:01.82,0:01:02.76,Default,,0000,0000,0000,,Answer in: 2
Dialogue: 0,0:01:02.76,0:01:05.13,Default,,0000,0000,0000,,Answer in: 1
Dialogue: 0,0:01:05.13,0:01:08.62,Default,,0000,0000,0000,,To solve this problem, \Nwe need to visualize it.
Dialogue: 0,0:01:08.62,0:01:10.100,Default,,0000,0000,0000,,For starters, we know \Nthat on the correct floor
Dialogue: 0,0:01:10.100,0:01:12.15,Default,,0000,0000,0000,,there's one room,
Dialogue: 0,0:01:12.15,0:01:13.80,Default,,0000,0000,0000,,let's call it room A,
Dialogue: 0,0:01:13.80,0:01:16.02,Default,,0000,0000,0000,,with one door to the control panel room,
Dialogue: 0,0:01:16.02,0:01:17.88,Default,,0000,0000,0000,,plus one door to room B,
Dialogue: 0,0:01:17.88,0:01:19.24,Default,,0000,0000,0000,,and one to C.
Dialogue: 0,0:01:19.24,0:01:21.78,Default,,0000,0000,0000,,So there must be at least four rooms,
Dialogue: 0,0:01:21.78,0:01:23.90,Default,,0000,0000,0000,,which we can represent as circles,
Dialogue: 0,0:01:23.90,0:01:26.58,Default,,0000,0000,0000,,drawing lines between them\Nfor the doorways.
Dialogue: 0,0:01:26.58,0:01:28.76,Default,,0000,0000,0000,,But once we connect rooms B and C,
Dialogue: 0,0:01:28.76,0:01:30.76,Default,,0000,0000,0000,,there are no other connections possible,
Dialogue: 0,0:01:30.76,0:01:34.56,Default,,0000,0000,0000,,so the fourth floor down \Nfrom the top is out.
Dialogue: 0,0:01:34.56,0:01:37.74,Default,,0000,0000,0000,,We know the control panel has to be\Nas high up as possible,
Dialogue: 0,0:01:37.74,0:01:40.02,Default,,0000,0000,0000,,so let's make our way down the pyramid.
Dialogue: 0,0:01:40.02,0:01:43.22,Default,,0000,0000,0000,,The fifth highest floor \Ndoesn't work either.
Dialogue: 0,0:01:43.22,0:01:45.40,Default,,0000,0000,0000,,We can figure that out by drawing it,
Dialogue: 0,0:01:45.40,0:01:47.82,Default,,0000,0000,0000,,but to be sure we haven't missed\Nany possibilities,
Dialogue: 0,0:01:47.82,0:01:49.36,Default,,0000,0000,0000,,here's another way.
Dialogue: 0,0:01:49.36,0:01:52.62,Default,,0000,0000,0000,,Every door corresponds to a line\Nin our graph
Dialogue: 0,0:01:52.62,0:01:55.31,Default,,0000,0000,0000,,that makes two rooms into neighbors.
Dialogue: 0,0:01:55.31,0:01:59.31,Default,,0000,0000,0000,,So in the end, there have to be\Nan even number of neighbors
Dialogue: 0,0:01:59.31,0:02:01.76,Default,,0000,0000,0000,,no matter how many connections we make.
Dialogue: 0,0:02:01.76,0:02:05.82,Default,,0000,0000,0000,,On the fifth highest floor,\Nto fulfill our starting conditions,
Dialogue: 0,0:02:05.82,0:02:08.87,Default,,0000,0000,0000,,we'd need four rooms \Nwith three neighbors each,
Dialogue: 0,0:02:08.87,0:02:11.77,Default,,0000,0000,0000,,plus the control panel room\Nwith one neighbor,
Dialogue: 0,0:02:11.77,0:02:14.08,Default,,0000,0000,0000,,which makes 13 total neighbors.
Dialogue: 0,0:02:14.08,0:02:16.34,Default,,0000,0000,0000,,Since that's an odd number,\Nit's not possible,
Dialogue: 0,0:02:16.34,0:02:21.75,Default,,0000,0000,0000,,and in fact, this also rules out every\Nfloor that has an odd number of rooms.
Dialogue: 0,0:02:21.75,0:02:23.98,Default,,0000,0000,0000,,So let's go one more floor down.
Dialogue: 0,0:02:23.98,0:02:25.87,Default,,0000,0000,0000,,When we draw out the rooms,
Dialogue: 0,0:02:25.87,0:02:30.64,Default,,0000,0000,0000,,low and behold, we can find an arrangement\Nthat works like this.
Dialogue: 0,0:02:30.64,0:02:33.82,Default,,0000,0000,0000,,Incidentally, the study \Nof such visual models
Dialogue: 0,0:02:33.82,0:02:37.52,Default,,0000,0000,0000,,that show the connections and\Nrelationships between different objects
Dialogue: 0,0:02:37.52,0:02:39.33,Default,,0000,0000,0000,,is known as graph theory.
Dialogue: 0,0:02:39.33,0:02:44.34,Default,,0000,0000,0000,,In a basic graph, the circles representing\Nthe objects are known as nodes,
Dialogue: 0,0:02:44.34,0:02:47.27,Default,,0000,0000,0000,,while the connecting lines \Nare called edges.
Dialogue: 0,0:02:47.27,0:02:50.69,Default,,0000,0000,0000,,Researchers studying such graphs\Nask questions like,
Dialogue: 0,0:02:50.69,0:02:53.14,Default,,0000,0000,0000,,"How far is this node from that one?"
Dialogue: 0,0:02:53.14,0:02:56.74,Default,,0000,0000,0000,,"How many edges does \Nthe most popular node have?"
Dialogue: 0,0:02:56.74,0:03:01.57,Default,,0000,0000,0000,,"Is there a route between these two nodes,\Nand if so, how long is it?"
Dialogue: 0,0:03:01.57,0:03:05.49,Default,,0000,0000,0000,,Graphs like this are often used\Nto map communication networks,
Dialogue: 0,0:03:05.49,0:03:08.33,Default,,0000,0000,0000,,but they can represent almost\Nany kind of network,
Dialogue: 0,0:03:08.33,0:03:10.32,Default,,0000,0000,0000,,from transport connections within a city
Dialogue: 0,0:03:10.32,0:03:12.35,Default,,0000,0000,0000,,and social relationships among people,
Dialogue: 0,0:03:12.35,0:03:15.12,Default,,0000,0000,0000,,to chemical interactions between proteins
Dialogue: 0,0:03:15.12,0:03:18.54,Default,,0000,0000,0000,,or the spread of an epidemic\Nthrough different locations.
Dialogue: 0,0:03:18.54,0:03:22.36,Default,,0000,0000,0000,,So, armed with these techniques,\Nback to the pyramid.
Dialogue: 0,0:03:22.36,0:03:24.71,Default,,0000,0000,0000,,You avoid the guards and security cameras,
Dialogue: 0,0:03:24.71,0:03:26.77,Default,,0000,0000,0000,,infiltrate the sixth floor from the top,
Dialogue: 0,0:03:26.77,0:03:28.15,Default,,0000,0000,0000,,find the hidden panel,
Dialogue: 0,0:03:28.15,0:03:30.15,Default,,0000,0000,0000,,pull some conspicuous levers,
Dialogue: 0,0:03:30.15,0:03:33.49,Default,,0000,0000,0000,,and send the death ray crashing\Ninto the ocean.
Dialogue: 0,0:03:33.49,0:03:35.27,Default,,0000,0000,0000,,Now, time to solve the mystery
Dialogue: 0,0:03:35.27,0:03:40.33,Default,,0000,0000,0000,,of why your surveillance team\Nalways gives you cryptic information.
Dialogue: 0,0:03:40.33,0:03:41.32,Default,,0000,0000,0000,,Hi everybody.
Dialogue: 0,0:03:41.32,0:03:44.08,Default,,0000,0000,0000,,If you liked this riddle, \Ntry solving these two.