full transcript

## Unscramble the Blue Letters

As your country's top spy, you must infiltrate the headquarters of the evil syndicate, find the secret control pneal, 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 hisehgt 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 hlaawyls, and you can ignore stairs. Unfortunately, you don't have a floor plan, and you'll only have enough time to search a snglie foolr 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 anwser 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 pimyrad. 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 cdpsonoerrs to a line in our graph that makes two rooms into nhbregois. So in the end, there have to be an even number of neighbors no matetr how many ctocnoeinns we make. On the fifth highest floor, to fulfill our starting coitnndios, we'd need four rooms with three neighbors each, plus the cnoortl panel room with one neighbor, which makes 13 toatl neighbors. Since that's an odd number, it's not possible, and, in fact, this also rlues out every floor that has an odd number of romos. So let's go one more floor down. When we draw out the rooms, low and behold, we can find an arrangement that wrkos 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 gprah, 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 eegds 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 ppoele, to chemical interactions between piortens or the sraped of an epidemic through different locations. So, armed with these techniques, back to the pyramid. You avoid the gaudrs and srtuciey cameras, infiltrate the sixth floor from the top, find the hidden panel, pull some cospocinuus levers, and send the dteah ray crashing into the ocean. Now, time to slvoe the mystery of why your surveillance team always gives you ctrypic irfniomotan. 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 syndicate, find the secret control _____, 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 _______ 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 ________, and you can ignore stairs. Unfortunately, you don't have a floor plan, and you'll only have enough time to search a ______ _____ 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 ______ 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 _______. 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 ___________ to a line in our graph that makes two rooms into _________. So in the end, there have to be an even number of neighbors no ______ how many ___________ we make. On the fifth highest floor, to fulfill our starting __________, we'd need four rooms with three neighbors each, plus the _______ panel room with one neighbor, which makes 13 _____ neighbors. Since that's an odd number, it's not possible, and, in fact, this also _____ out every floor that has an odd number of _____. So let's go one more floor down. When we draw out the rooms, low and behold, we can find an arrangement that _____ 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 _____, 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 _____ 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 ______, to chemical interactions between ________ or the ______ of an epidemic through different locations. So, armed with these techniques, back to the pyramid. You avoid the ______ and ________ cameras, infiltrate the sixth floor from the top, find the hidden panel, pull some ___________ levers, and send the _____ ray crashing into the ocean. Now, time to _____ the mystery of why your surveillance team always gives you _______ ___________. Hi everybody. If you liked this riddle, try solving these two.

## Solution

1. rules
2. single
4. floor
5. works
6. total
7. edges
8. control
9. pyramid
10. death
11. hallways
12. solve
13. conspicuous
14. panel
15. cryptic
16. connections
17. matter
18. information
19. guards
20. proteins
21. security
22. conditions
23. graph
24. corresponds
25. neighbors
27. people
28. highest
29. rooms

## 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

1. alarm
3. armed
4. arrangement
5. avoid
6. basic
7. behold
8. call
9. called
10. cameras
11. chemical
12. circles
13. city
14. communication
15. conditions
16. connect
17. connecting
18. connections
19. connects
20. conspicuous
21. control
22. correct
23. corresponds
24. crashing
25. cryptic
26. deactivate
27. death
28. door
29. doors
30. doorways
31. draw
32. drawing
33. edges
34. epidemic
35. evil
36. fact
37. figure
38. find
39. floor
40. fourth
41. fulfill
42. graph
43. graphs
44. guards
45. hallways
47. hidden
48. high
49. highest
50. ignore
51. incidentally
52. infiltrate
53. information
54. interactions
55. kind
56. level
57. levers
58. line
59. lines
60. locations
61. long
62. map
63. massive
64. matter
65. missed
66. models
67. mystery
68. neighbor
69. neighbors
70. network
71. networks
72. node
73. nodes
74. number
75. objects
76. ocean
77. odd
78. painting
79. panel
80. pause
81. people
82. picked
83. plan
84. popular
85. possibilities
86. problem
87. proteins
88. pull
89. pyramid
90. questions
91. ray
92. reactivates
93. relationships
94. represent
95. representing
96. researchers
97. riddle
98. room
99. rooms
100. route
101. rules
102. satisfy
103. search
104. secret
105. security
106. send
107. show
108. single
109. sixth
110. social
111. solve
112. solving
114. spy
115. stairs
116. starters
117. starting
118. study
119. studying
120. surveillance
121. syndicate
122. system
123. team
124. techniques
125. theory
126. time
127. top
128. total
129. transport
130. visual
131. visualize
132. work
133. works