TedTest

From the Ted Talk by Dennis Shasha: Can you solve the control room riddle?

Unscramble the Blue Letters

As your country's top spy, you must infiltrate the headquarters of the evil sytcdinae, find the secret control pnael, and deactivate their death ray. But all you have to go on is the following information picked up by your snualecivrle team. The hreertqaduas is a massive pyramid with a single room at the top level, two rmoos on the next, and so on. The control panel is hidden behind a painting on the highest floor that can sstfiay 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 hyaalwls, and you can ignore stairs. Unfortunately, you don't have a foolr plan, and you'll only have enough time to seacrh a single floor before the alarm system rieattevcas. Can you figure out which floor the control room is on? Pause now to slvoe the riddle yourself. Answer in: 3 Answer in: 2 Answer in: 1 To solve this problem, we need to visualize it. For stetarrs, 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, daiwnrg lnies 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 cootnrl 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 fgirue 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 stiatrng conditions, we'd need four rooms with three neighbors each, plus the control panel room with one nigbheor, which makes 13 taotl 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 vausil models that show the connections and relationships between different objects is known as graph theory. In a basic graph, the circles rnpieesrtneg the objects are known as nodes, while the connecting lines are called edges. Researchers studying such garhps ask questions like, "How far is this node from that one?" "How many edges does the most popular node have?" "Is there a rutoe 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 sperad of an epidemic through different locations. So, amerd 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 levres, and send the death ray cahrsing into the ocean. Now, time to solve the mytresy of why your surveillance team always gives you cryptic information. Hi everybody. If you liked this riddle, try solving these two.

Open Cloze

As your country's top spy, you must infiltrate the headquarters of the evil _________, find the secret control _____, and deactivate their death ray. But all you have to go on is the following information picked up by your ____________ team. The ____________ is a massive pyramid with a single room at the top level, two _____ on the next, and so on. The control panel is hidden behind a painting on the highest floor that can _______ 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 ________, and you can ignore stairs. Unfortunately, you don't have a _____ plan, and you'll only have enough time to ______ a single floor before the alarm system ___________. Can you figure out which floor the control room is on? Pause now to _____ the riddle yourself. Answer in: 3 Answer in: 2 Answer in: 1 To solve this problem, we need to visualize it. For ________, 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, _______ _____ 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 _______ 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 ______ 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 ________ conditions, we'd need four rooms with three neighbors each, plus the control panel room with one ________, which makes 13 _____ 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 ______ models that show the connections and relationships between different objects is known as graph theory. In a basic graph, the circles ____________ the objects are known as nodes, while the connecting lines are called edges. Researchers studying such ______ ask questions like, "How far is this node from that one?" "How many edges does the most popular node have?" "Is there a _____ 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 ______ of an epidemic through different locations. So, _____ 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 ______, and send the death ray ________ into the ocean. Now, time to solve the _______ of why your surveillance team always gives you cryptic information. Hi everybody. If you liked this riddle, try solving these two.

Solution

mystery
total
solve
hallways
floor
starters
visual
lines
neighbor
search
armed
crashing
starting
panel
graphs
surveillance
representing
levers
figure
syndicate
reactivates
control
rooms
satisfy
drawing
headquarters
route
spread

Original Text

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.

Frequently Occurring Word Combinations

ngrams of length 2

collocation	frequency
control panel	5
death ray	2
surveillance team	2
highest floor	2

Important Words

alarm
answer
armed
arrangement
avoid
basic
behold
call
called
cameras
chemical
circles
city
communication
conditions
connect
connecting
connections
connects
conspicuous
control
correct
corresponds
crashing
cryptic
deactivate
death
door
doors
doorways
draw
drawing
edges
epidemic
evil
fact
figure
find
floor
fourth
fulfill
graph
graphs
guards
hallways
headquarters
hidden
high
highest
ignore
incidentally
infiltrate
information
interactions
kind
level
levers
line
lines
locations
long
map
massive
matter
missed
models
mystery
neighbor
neighbors
network
networks
node
nodes
number
objects
ocean
odd
painting
panel
pause
people
picked
plan
popular
possibilities
problem
proteins
pull
pyramid
questions
ray
reactivates
relationships
represent
representing
researchers
riddle
room
rooms
route
rules
satisfy
search
secret
security
send
show
single
sixth
social
solve
solving
spread
spy
stairs
starters
starting
study
studying
surveillance
syndicate
system
team
techniques
theory
time
top
total
transport
visual
visualize
work
works