full transcript

From the Ted Talk by Ganesh Pai: Can you solve the passcode riddle?

Unscramble the Blue Letters

In this dystopian world, your resistance group is humanity's last hope. Unfortunately, you've all been creuptad by the tnniycraal rulers and bghurot to the ancient colosseum for their deadly entertainment. Before you're thrown into the dungeon, you see many nmbureed hallways lnadeig outside. But each exit is blocked by an electric barrier with a combination keypad. You learn that one of you will be allowed to try to escape by passing a challenge while everyone else will be fed to the mutant salamanders the next morning. With her peerfct logical reasoning, Zara is the obvious chioce. You hand her a concealed audio transmitter so that the rest of you can listen along. As Zara is led away, you hear her footsteps echo through one of the hallways, then stop. A voice announces that she must enter a code consisting of three psoivite whole numbers in ascending order, so the second number is gtreaer than or equal to the first, and the third is greater than or equal to the second. She may ask for up to three clues, but if she makes a wrong guess, or says anything else, she'll be thrown back into the dungeon. For the first clue, the voice says the product of the three numbers is 36. When Zara asks for the second clue, it tells her the sum of the numbers is the same as the number of the hallway she etenred. There's a long snliece. You're sure Zara rebmremes the hallway number, but there's no way for you to know it, and she can't say it outloud. If Zara could enter the pdosacse at this point, she would, but instead, she asks for the third clue, and the vcoie announces that the largest number appears only once in the combination. Moments later, the buzz of the eictelrc biearrr stops for a few seconds, and you realize that Zara has escaped. Unfortunately, her transmitter is no logenr in range, so that's all the information you get. Can you find the solution? Pause on the next screen to work out the soouiltn. 3 2 1 You're worried about the fact that you don't know Zara's hallway number, but you dedice to satrt from the bniningeg anyways. From the first clue, you work out all of the eight possible combinations that come out to a product of 36. One of these must be right, but which one? Now comes the hard part. Even though you don't know which number you're looking for, you decide to work out the sum of each combination's three numbers. That's when it hits you. All but two of the sums are unique, and if the hllaawy number had matched any of these, Zara would have known the cecrrot combination right then and there without asking for the third clue. Since she did ask for the clue, the hallway number must have matched the only sum that appears more than once in the list: thirteen. But which of the two combinations that add up to thirteen is correct: 1,6,6, or 2,2,9? That's where the third clue comes in. Since it tlles us that the largest number must be uiuqne, 2,2,9 must be the code. When night falls, you and the others escape through hallway thirteen and rejoin Zara outside. You've freed yourselves through math and loigc. Now it's time to free the rest of the world.

Open Cloze

In this dystopian world, your resistance group is humanity's last hope. Unfortunately, you've all been ________ by the __________ rulers and _______ to the ancient colosseum for their deadly entertainment. Before you're thrown into the dungeon, you see many ________ hallways _______ outside. But each exit is blocked by an electric barrier with a combination keypad. You learn that one of you will be allowed to try to escape by passing a challenge while everyone else will be fed to the mutant salamanders the next morning. With her _______ logical reasoning, Zara is the obvious ______. You hand her a concealed audio transmitter so that the rest of you can listen along. As Zara is led away, you hear her footsteps echo through one of the hallways, then stop. A voice announces that she must enter a code consisting of three ________ whole numbers in ascending order, so the second number is _______ than or equal to the first, and the third is greater than or equal to the second. She may ask for up to three clues, but if she makes a wrong guess, or says anything else, she'll be thrown back into the dungeon. For the first clue, the voice says the product of the three numbers is 36. When Zara asks for the second clue, it tells her the sum of the numbers is the same as the number of the hallway she _______. There's a long _______. You're sure Zara _________ the hallway number, but there's no way for you to know it, and she can't say it outloud. If Zara could enter the ________ at this point, she would, but instead, she asks for the third clue, and the _____ announces that the largest number appears only once in the combination. Moments later, the buzz of the ________ _______ stops for a few seconds, and you realize that Zara has escaped. Unfortunately, her transmitter is no ______ in range, so that's all the information you get. Can you find the solution? Pause on the next screen to work out the ________. 3 2 1 You're worried about the fact that you don't know Zara's hallway number, but you ______ to _____ from the _________ anyways. From the first clue, you work out all of the eight possible combinations that come out to a product of 36. One of these must be right, but which one? Now comes the hard part. Even though you don't know which number you're looking for, you decide to work out the sum of each combination's three numbers. That's when it hits you. All but two of the sums are unique, and if the _______ number had matched any of these, Zara would have known the _______ combination right then and there without asking for the third clue. Since she did ask for the clue, the hallway number must have matched the only sum that appears more than once in the list: thirteen. But which of the two combinations that add up to thirteen is correct: 1,6,6, or 2,2,9? That's where the third clue comes in. Since it _____ us that the largest number must be ______, 2,2,9 must be the code. When night falls, you and the others escape through hallway thirteen and rejoin Zara outside. You've freed yourselves through math and _____. Now it's time to free the rest of the world.

Solution

  1. perfect
  2. electric
  3. numbered
  4. tells
  5. silence
  6. voice
  7. positive
  8. unique
  9. remembers
  10. logic
  11. entered
  12. brought
  13. decide
  14. hallway
  15. passcode
  16. choice
  17. solution
  18. longer
  19. greater
  20. beginning
  21. start
  22. captured
  23. tyrannical
  24. leading
  25. barrier
  26. correct

Original Text

In this dystopian world, your resistance group is humanity's last hope. Unfortunately, you've all been captured by the tyrannical rulers and brought to the ancient colosseum for their deadly entertainment. Before you're thrown into the dungeon, you see many numbered hallways leading outside. But each exit is blocked by an electric barrier with a combination keypad. You learn that one of you will be allowed to try to escape by passing a challenge while everyone else will be fed to the mutant salamanders the next morning. With her perfect logical reasoning, Zara is the obvious choice. You hand her a concealed audio transmitter so that the rest of you can listen along. As Zara is led away, you hear her footsteps echo through one of the hallways, then stop. A voice announces that she must enter a code consisting of three positive whole numbers in ascending order, so the second number is greater than or equal to the first, and the third is greater than or equal to the second. She may ask for up to three clues, but if she makes a wrong guess, or says anything else, she'll be thrown back into the dungeon. For the first clue, the voice says the product of the three numbers is 36. When Zara asks for the second clue, it tells her the sum of the numbers is the same as the number of the hallway she entered. There's a long silence. You're sure Zara remembers the hallway number, but there's no way for you to know it, and she can't say it outloud. If Zara could enter the passcode at this point, she would, but instead, she asks for the third clue, and the voice announces that the largest number appears only once in the combination. Moments later, the buzz of the electric barrier stops for a few seconds, and you realize that Zara has escaped. Unfortunately, her transmitter is no longer in range, so that's all the information you get. Can you find the solution? Pause on the next screen to work out the solution. 3 2 1 You're worried about the fact that you don't know Zara's hallway number, but you decide to start from the beginning anyways. From the first clue, you work out all of the eight possible combinations that come out to a product of 36. One of these must be right, but which one? Now comes the hard part. Even though you don't know which number you're looking for, you decide to work out the sum of each combination's three numbers. That's when it hits you. All but two of the sums are unique, and if the hallway number had matched any of these, Zara would have known the correct combination right then and there without asking for the third clue. Since she did ask for the clue, the hallway number must have matched the only sum that appears more than once in the list: thirteen. But which of the two combinations that add up to thirteen is correct: 1,6,6, or 2,2,9? That's where the third clue comes in. Since it tells us that the largest number must be unique, 2,2,9 must be the code. When night falls, you and the others escape through hallway thirteen and rejoin Zara outside. You've freed yourselves through math and logic. Now it's time to free the rest of the world.

Frequently Occurring Word Combinations

ngrams of length 2

collocation frequency
electric barrier 2
voice announces 2
largest number 2
hallway number 2

Important Words

  1. add
  2. allowed
  3. ancient
  4. announces
  5. appears
  6. ascending
  7. asks
  8. audio
  9. barrier
  10. beginning
  11. blocked
  12. brought
  13. buzz
  14. captured
  15. challenge
  16. choice
  17. clue
  18. clues
  19. code
  20. colosseum
  21. combination
  22. combinations
  23. concealed
  24. consisting
  25. correct
  26. deadly
  27. decide
  28. dungeon
  29. dystopian
  30. echo
  31. electric
  32. enter
  33. entered
  34. entertainment
  35. equal
  36. escape
  37. escaped
  38. exit
  39. fact
  40. falls
  41. fed
  42. find
  43. footsteps
  44. free
  45. freed
  46. greater
  47. group
  48. guess
  49. hallway
  50. hallways
  51. hand
  52. hard
  53. hear
  54. hits
  55. hope
  56. information
  57. keypad
  58. largest
  59. leading
  60. learn
  61. led
  62. listen
  63. logic
  64. logical
  65. long
  66. longer
  67. matched
  68. math
  69. moments
  70. morning
  71. mutant
  72. night
  73. number
  74. numbered
  75. numbers
  76. obvious
  77. order
  78. outloud
  79. part
  80. passcode
  81. passing
  82. pause
  83. perfect
  84. point
  85. positive
  86. product
  87. range
  88. realize
  89. reasoning
  90. rejoin
  91. remembers
  92. resistance
  93. rest
  94. rulers
  95. salamanders
  96. screen
  97. seconds
  98. silence
  99. solution
  100. start
  101. stop
  102. stops
  103. sum
  104. sums
  105. tells
  106. thirteen
  107. thrown
  108. time
  109. transmitter
  110. tyrannical
  111. unique
  112. voice
  113. work
  114. world
  115. worried
  116. wrong
  117. zara