full transcript

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 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
  3. spread
  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
  26. answer
  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
  2. answer
  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
  46. headquarters
  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
  113. spread
  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