full transcript

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

Unscramble the Blue Letters

As a wiflrdie rgeas through the grasslands, three lions and three wildebeest flee for their lives. To escape the inrnefo, they must cross over to the left bank of a crocodile-infested river. Fortunately, there happens to be a raft nearby. It can carry up to two almains at a time, and needs as least one lion or wildebeest on board to row it across the river. There's just one problem. If the lions ever outnumber the wsdbeeilet on either side of the rievr, even for a moment, their instincts will kick in, and the rltuess won't be pretty. That includes the animals in the boat when it's on a given side of the river. What's the fastest way for all six animals to get across without the lions sniotppg for dinner? Pause here if you want to frigue it out for yourself. Answer in: 3 awensr in: 2 Answer in: 1 If you feel stuck on a problem like this, try linitsg all the deosicins you can make at each ponit, and the consequences each choice leads to. For instance, there are five options for who goes across first: one wildebeest, one lion, two wildebeest, two lions, or one of each. If one animal goes alone, it'll just have to come straight back. And if two wildebeest cross first, the remaining one will immediately get eaten. So those options are all out. Sending two lions, or one of each animal, can actually both lead to solutions in the same number of moves. For the sake of time, we'll focus on the second one. One of each animal crsoses. Now, if the wildebeest stays and the lion returns, there will be three lions on the right bank. Bad news for the two remaining wildebeest. So we need to have the lion stay on the left bank and the wildebeest go back to the right. Now we have the same five options, but with one lion already on the left bank. If two wildebeest go, the one that stays will get eaten, and if one of each aiamnl goes, the wildebeest on the raft will be outnumbered as soon as it reaches the other side. So that's a dead end, which means that at the third crossing, only the two lions can go. One gets dpepord off, leaving two lnois on the left bank. The third lion takes the raft back to the right bank where the wildebeest are waiting. What now? Well, since we've got two lions waiting on the left bank, the only otpoin is for two wildebeest to cross. Next, there's no sense in two wildebeest going back, since that just reverses the last step. And if two lions go back, they'll outnumber the wildebeest on the right bank. So one lion and one wildebeest take the raft back leaving us with one of each animal on the left bank and two of each on the right. Again, there's no point in sdneing the lion-wildebeest pair back, so the next trip should be either a pair of lions or a pair of wildebeest. If the lions go, they'd eat the wildebeest on the left, so they stay, and the two wildebeest cross instead. Now we're quite close because the wildebeest are all where they need to be with safety in numbers. All that's left is for that one lion to raft back and bnrig his fellow lions over one by one. That makes eleven trips ttoal, the seslmalt number needed to get everyone across safely. The slituoon that involves sending both lions on the first step works similarly, and also takes eleven crossings. The six animals escape unharmed from the fire just in time and begin their new lives across the river. Of course, now that the danger's psased, it remains to be seen how long their unlikely anlcilae will last.

Open Cloze

As a ________ _____ through the grasslands, three lions and three wildebeest flee for their lives. To escape the _______, they must cross over to the left bank of a crocodile-infested river. Fortunately, there happens to be a raft nearby. It can carry up to two _______ at a time, and needs as least one lion or wildebeest on board to row it across the river. There's just one problem. If the lions ever outnumber the __________ on either side of the _____, even for a moment, their instincts will kick in, and the _______ won't be pretty. That includes the animals in the boat when it's on a given side of the river. What's the fastest way for all six animals to get across without the lions ________ for dinner? Pause here if you want to ______ it out for yourself. Answer in: 3 ______ in: 2 Answer in: 1 If you feel stuck on a problem like this, try _______ all the _________ you can make at each _____, and the consequences each choice leads to. For instance, there are five options for who goes across first: one wildebeest, one lion, two wildebeest, two lions, or one of each. If one animal goes alone, it'll just have to come straight back. And if two wildebeest cross first, the remaining one will immediately get eaten. So those options are all out. Sending two lions, or one of each animal, can actually both lead to solutions in the same number of moves. For the sake of time, we'll focus on the second one. One of each animal _______. Now, if the wildebeest stays and the lion returns, there will be three lions on the right bank. Bad news for the two remaining wildebeest. So we need to have the lion stay on the left bank and the wildebeest go back to the right. Now we have the same five options, but with one lion already on the left bank. If two wildebeest go, the one that stays will get eaten, and if one of each ______ goes, the wildebeest on the raft will be outnumbered as soon as it reaches the other side. So that's a dead end, which means that at the third crossing, only the two lions can go. One gets _______ off, leaving two _____ on the left bank. The third lion takes the raft back to the right bank where the wildebeest are waiting. What now? Well, since we've got two lions waiting on the left bank, the only ______ is for two wildebeest to cross. Next, there's no sense in two wildebeest going back, since that just reverses the last step. And if two lions go back, they'll outnumber the wildebeest on the right bank. So one lion and one wildebeest take the raft back leaving us with one of each animal on the left bank and two of each on the right. Again, there's no point in _______ the lion-wildebeest pair back, so the next trip should be either a pair of lions or a pair of wildebeest. If the lions go, they'd eat the wildebeest on the left, so they stay, and the two wildebeest cross instead. Now we're quite close because the wildebeest are all where they need to be with safety in numbers. All that's left is for that one lion to raft back and _____ his fellow lions over one by one. That makes eleven trips _____, the ________ number needed to get everyone across safely. The ________ that involves sending both lions on the first step works similarly, and also takes eleven crossings. The six animals escape unharmed from the fire just in time and begin their new lives across the river. Of course, now that the danger's ______, it remains to be seen how long their unlikely ________ will last.

Solution

  1. sending
  2. alliance
  3. answer
  4. passed
  5. listing
  6. inferno
  7. decisions
  8. bring
  9. results
  10. dropped
  11. wildebeest
  12. rages
  13. option
  14. animals
  15. solution
  16. crosses
  17. total
  18. smallest
  19. point
  20. stopping
  21. animal
  22. river
  23. figure
  24. wildfire
  25. lions

Original Text

As a wildfire rages through the grasslands, three lions and three wildebeest flee for their lives. To escape the inferno, they must cross over to the left bank of a crocodile-infested river. Fortunately, there happens to be a raft nearby. It can carry up to two animals at a time, and needs as least one lion or wildebeest on board to row it across the river. There's just one problem. If the lions ever outnumber the wildebeest on either side of the river, even for a moment, their instincts will kick in, and the results won't be pretty. That includes the animals in the boat when it's on a given side of the river. What's the fastest way for all six animals to get across without the lions stopping for dinner? Pause here if you want to figure it out for yourself. Answer in: 3 Answer in: 2 Answer in: 1 If you feel stuck on a problem like this, try listing all the decisions you can make at each point, and the consequences each choice leads to. For instance, there are five options for who goes across first: one wildebeest, one lion, two wildebeest, two lions, or one of each. If one animal goes alone, it'll just have to come straight back. And if two wildebeest cross first, the remaining one will immediately get eaten. So those options are all out. Sending two lions, or one of each animal, can actually both lead to solutions in the same number of moves. For the sake of time, we'll focus on the second one. One of each animal crosses. Now, if the wildebeest stays and the lion returns, there will be three lions on the right bank. Bad news for the two remaining wildebeest. So we need to have the lion stay on the left bank and the wildebeest go back to the right. Now we have the same five options, but with one lion already on the left bank. If two wildebeest go, the one that stays will get eaten, and if one of each animal goes, the wildebeest on the raft will be outnumbered as soon as it reaches the other side. So that's a dead end, which means that at the third crossing, only the two lions can go. One gets dropped off, leaving two lions on the left bank. The third lion takes the raft back to the right bank where the wildebeest are waiting. What now? Well, since we've got two lions waiting on the left bank, the only option is for two wildebeest to cross. Next, there's no sense in two wildebeest going back, since that just reverses the last step. And if two lions go back, they'll outnumber the wildebeest on the right bank. So one lion and one wildebeest take the raft back leaving us with one of each animal on the left bank and two of each on the right. Again, there's no point in sending the lion-wildebeest pair back, so the next trip should be either a pair of lions or a pair of wildebeest. If the lions go, they'd eat the wildebeest on the left, so they stay, and the two wildebeest cross instead. Now we're quite close because the wildebeest are all where they need to be with safety in numbers. All that's left is for that one lion to raft back and bring his fellow lions over one by one. That makes eleven trips total, the smallest number needed to get everyone across safely. The solution that involves sending both lions on the first step works similarly, and also takes eleven crossings. The six animals escape unharmed from the fire just in time and begin their new lives across the river. Of course, now that the danger's passed, it remains to be seen how long their unlikely alliance will last.

Frequently Occurring Word Combinations

ngrams of length 2

collocation frequency
left bank 5
wildebeest cross 2

Important Words

  1. alliance
  2. animal
  3. animals
  4. answer
  5. bad
  6. bank
  7. board
  8. boat
  9. bring
  10. carry
  11. choice
  12. close
  13. consequences
  14. cross
  15. crosses
  16. crossing
  17. crossings
  18. dead
  19. decisions
  20. dinner
  21. dropped
  22. eat
  23. eaten
  24. eleven
  25. escape
  26. fastest
  27. feel
  28. fellow
  29. figure
  30. fire
  31. flee
  32. focus
  33. fortunately
  34. grasslands
  35. immediately
  36. includes
  37. inferno
  38. instance
  39. instincts
  40. involves
  41. kick
  42. lead
  43. leads
  44. leaving
  45. left
  46. lion
  47. lions
  48. listing
  49. lives
  50. long
  51. means
  52. moment
  53. moves
  54. nearby
  55. needed
  56. news
  57. number
  58. numbers
  59. option
  60. options
  61. outnumber
  62. outnumbered
  63. pair
  64. passed
  65. pause
  66. point
  67. pretty
  68. problem
  69. raft
  70. rages
  71. reaches
  72. remaining
  73. remains
  74. results
  75. returns
  76. reverses
  77. river
  78. row
  79. safely
  80. safety
  81. sake
  82. sending
  83. sense
  84. side
  85. similarly
  86. smallest
  87. solution
  88. solutions
  89. stay
  90. stays
  91. step
  92. stopping
  93. straight
  94. stuck
  95. takes
  96. time
  97. total
  98. trip
  99. trips
  100. unharmed
  101. waiting
  102. wildebeest
  103. wildfire
  104. works