full transcript

From the Ted Talk by Lisa Winer: Can you solve the locker riddle?

Unscramble the Blue Letters

Your rich, eicetrncc uncle just passed away, and you and your 99 nasty relatives have been invited to the rnadieg of his will. He wanted to laeve all of his money to you, but he knew that if he did, your relatives would pester you forever. So he is banking on the fact that he taught you everything you need to know about riddles. Your ulnce left the following note in his will: "I have certaed a puzzle. If all 100 of you answer it together, you will sahre the money evenly. However, if you are the first to find the prtaetn and solve the problem without going through all of the leg work, you will get the etrine itcenianhre all to yourself. Good luck." The lawyer takes you and your 99 relatives to a secret room in the mansion that contains 100 lockers, each hiding a single word. He explains: Every relative is assigned a neubmr from 1 to 100. Heir 1 will open every locker. Heir 2 will then close every second locker. Heir 3 will change the sttuas of every third locker, specifically if it's open, she'll clsoe it, but if it's closed, she'll open it. This pattern will continue until all 100 of you have gone. The words in the lockers that remain open at the end will help you cacrk the code for the safe. Before csuion Thaddeus can even start down the line, you step forward and tell the lawyer you know which lockers will remain open. But how? Pause the vdieo now if you want to figure it out for yourself! Answer in: 3 Answer in: 2 aesnwr in: 1 The key is realizing that the number of times a locker is touched is the same as the number of factors in the locker number. For example, in lekocr #6, Person 1 will open it, Person 2 will close it, Person 3 will open it, and Person 6 will close it. The numbers 1, 2, 3, and 6 are the factors of 6. So when a locker has an even number of factors it will remain closed, and when it has an odd number of factors, it will remain open. Most of the lockers have an even number of factors, which makes sense because factors naturally pair up. In fact, the only locreks that have an odd number of factors are pfreect squares because those have one foactr that when multiplied by itself equals the number. For Locker 9, 1 will open it, 3 will close, and 9 will open it. 3 x 3 = 9, but the 3 can only be counted once. Therefore, every locker that is a perfect square will remain open. You know that these ten lockers are the solution, so you open them immediately and read the wrods inside: "The code is the first five lockers touched only twice." You rleziae that the only lockers touched twice have to be pmrie numbers since each only has two factors: 1 and itself. So the code is 2-3-5-7-11. The lawyer brings you to the safe, and you claim your inheritance. Too bad your relatives were always too busy being nasty to each other to pay attention to your eccentric uncle's riddles.

Open Cloze

Your rich, _________ uncle just passed away, and you and your 99 nasty relatives have been invited to the _______ of his will. He wanted to _____ all of his money to you, but he knew that if he did, your relatives would pester you forever. So he is banking on the fact that he taught you everything you need to know about riddles. Your _____ left the following note in his will: "I have _______ a puzzle. If all 100 of you answer it together, you will _____ the money evenly. However, if you are the first to find the _______ and solve the problem without going through all of the leg work, you will get the ______ ___________ all to yourself. Good luck." The lawyer takes you and your 99 relatives to a secret room in the mansion that contains 100 lockers, each hiding a single word. He explains: Every relative is assigned a ______ from 1 to 100. Heir 1 will open every locker. Heir 2 will then close every second locker. Heir 3 will change the ______ of every third locker, specifically if it's open, she'll _____ it, but if it's closed, she'll open it. This pattern will continue until all 100 of you have gone. The words in the lockers that remain open at the end will help you _____ the code for the safe. Before ______ Thaddeus can even start down the line, you step forward and tell the lawyer you know which lockers will remain open. But how? Pause the _____ now if you want to figure it out for yourself! Answer in: 3 Answer in: 2 ______ in: 1 The key is realizing that the number of times a locker is touched is the same as the number of factors in the locker number. For example, in ______ #6, Person 1 will open it, Person 2 will close it, Person 3 will open it, and Person 6 will close it. The numbers 1, 2, 3, and 6 are the factors of 6. So when a locker has an even number of factors it will remain closed, and when it has an odd number of factors, it will remain open. Most of the lockers have an even number of factors, which makes sense because factors naturally pair up. In fact, the only _______ that have an odd number of factors are _______ squares because those have one ______ that when multiplied by itself equals the number. For Locker 9, 1 will open it, 3 will close, and 9 will open it. 3 x 3 = 9, but the 3 can only be counted once. Therefore, every locker that is a perfect square will remain open. You know that these ten lockers are the solution, so you open them immediately and read the _____ inside: "The code is the first five lockers touched only twice." You _______ that the only lockers touched twice have to be _____ numbers since each only has two factors: 1 and itself. So the code is 2-3-5-7-11. The lawyer brings you to the safe, and you claim your inheritance. Too bad your relatives were always too busy being nasty to each other to pay attention to your eccentric uncle's riddles.

Solution

  1. number
  2. cousin
  3. answer
  4. status
  5. words
  6. uncle
  7. crack
  8. lockers
  9. created
  10. perfect
  11. video
  12. entire
  13. prime
  14. eccentric
  15. inheritance
  16. pattern
  17. leave
  18. reading
  19. factor
  20. close
  21. locker
  22. share
  23. realize

Original Text

Your rich, eccentric uncle just passed away, and you and your 99 nasty relatives have been invited to the reading of his will. He wanted to leave all of his money to you, but he knew that if he did, your relatives would pester you forever. So he is banking on the fact that he taught you everything you need to know about riddles. Your uncle left the following note in his will: "I have created a puzzle. If all 100 of you answer it together, you will share the money evenly. However, if you are the first to find the pattern and solve the problem without going through all of the leg work, you will get the entire inheritance all to yourself. Good luck." The lawyer takes you and your 99 relatives to a secret room in the mansion that contains 100 lockers, each hiding a single word. He explains: Every relative is assigned a number from 1 to 100. Heir 1 will open every locker. Heir 2 will then close every second locker. Heir 3 will change the status of every third locker, specifically if it's open, she'll close it, but if it's closed, she'll open it. This pattern will continue until all 100 of you have gone. The words in the lockers that remain open at the end will help you crack the code for the safe. Before cousin Thaddeus can even start down the line, you step forward and tell the lawyer you know which lockers will remain open. But how? Pause the video now if you want to figure it out for yourself! Answer in: 3 Answer in: 2 Answer in: 1 The key is realizing that the number of times a locker is touched is the same as the number of factors in the locker number. For example, in locker #6, Person 1 will open it, Person 2 will close it, Person 3 will open it, and Person 6 will close it. The numbers 1, 2, 3, and 6 are the factors of 6. So when a locker has an even number of factors it will remain closed, and when it has an odd number of factors, it will remain open. Most of the lockers have an even number of factors, which makes sense because factors naturally pair up. In fact, the only lockers that have an odd number of factors are perfect squares because those have one factor that when multiplied by itself equals the number. For Locker 9, 1 will open it, 3 will close, and 9 will open it. 3 x 3 = 9, but the 3 can only be counted once. Therefore, every locker that is a perfect square will remain open. You know that these ten lockers are the solution, so you open them immediately and read the words inside: "The code is the first five lockers touched only twice." You realize that the only lockers touched twice have to be prime numbers since each only has two factors: 1 and itself. So the code is 2-3-5-7-11. The lawyer brings you to the safe, and you claim your inheritance. Too bad your relatives were always too busy being nasty to each other to pay attention to your eccentric uncle's riddles.

Frequently Occurring Word Combinations

ngrams of length 2

collocation frequency
remain open 4
locker heir 2
odd number 2
lockers touched 2

Important Words

  1. answer
  2. assigned
  3. attention
  4. bad
  5. banking
  6. brings
  7. busy
  8. change
  9. claim
  10. close
  11. closed
  12. code
  13. continue
  14. counted
  15. cousin
  16. crack
  17. created
  18. eccentric
  19. entire
  20. equals
  21. evenly
  22. fact
  23. factor
  24. factors
  25. figure
  26. find
  27. good
  28. heir
  29. hiding
  30. immediately
  31. inheritance
  32. invited
  33. key
  34. knew
  35. lawyer
  36. leave
  37. left
  38. leg
  39. line
  40. locker
  41. lockers
  42. luck
  43. mansion
  44. money
  45. multiplied
  46. nasty
  47. naturally
  48. note
  49. number
  50. numbers
  51. odd
  52. open
  53. pair
  54. passed
  55. pattern
  56. pause
  57. pay
  58. perfect
  59. person
  60. pester
  61. prime
  62. problem
  63. puzzle
  64. read
  65. reading
  66. realize
  67. realizing
  68. relative
  69. relatives
  70. remain
  71. rich
  72. riddles
  73. room
  74. safe
  75. secret
  76. sense
  77. share
  78. single
  79. solution
  80. solve
  81. specifically
  82. square
  83. squares
  84. start
  85. status
  86. step
  87. takes
  88. taught
  89. ten
  90. thaddeus
  91. times
  92. touched
  93. uncle
  94. video
  95. wanted
  96. word
  97. words
  98. work