Can you solve the Billy Bonka riddle? - Edwin F. Meyer — Transcript

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1. 0:06You’re on a tour of the eccentric Billy Bonka’s mysterious candy factory,
2. 0:12when a wrong turn searching for the restroom
3. 0:15lands you in the TOP SECRET candy laboratory.
4. 0:20Enraged at your trespassing,
5. 0:22Bonka explains that the consequences are simple:
6. 0:26you must play his game.
7. 0:28You win, he’ll set you free.
8. 0:30You lose, he’ll throw you into his Chew-O-Meter 3000.
9. 0:34and you’re as good as gum.
10. 0:37Bonka unveils his latest invention:
11. 0:40candies that instantly change your hair color.
12. 0:44He holds seven of these Do-Dye Drops, four red drops, two white, and one blue.
13. 0:51He then summons the magical creatures who maintain his factory,
14. 0:56the Proofa-Boompas, to form a single-file line.
15. 1:01You’re placed at the front with four Proofa-Boompas behind you.
16. 1:05All five of you blindly take one of the seven drops,
17. 1:10and the leftover drops are hidden.
18. 1:12Everyone in line can see the hair transformations of those in front of them,
19. 1:18but not their own hair or that of anyone behind them.
20. 1:23Since you are at the very front of the line, you can’t see anything.
21. 1:28The Proofa-Boompas, who are renowned for logical reasoning,
22. 1:33are polled from back to front, and asked,
23. 1:36“Are you logically certain of your hair color?”
24. 1:39You hear the following replies:
25. 1:42no, yes, yes, yes.
26. 1:46Bonka then slyly turns to you and asks, “what is the color of your hair?”
27. 1:53Pause now to figure it out for yourself. Answer in 3
28. 1:56Answer in 2
29. 1:59Answer in 1
30. 2:03The key to solving a logic problem like this is understanding
31. 2:08that each Proofa-Boompa’s response
32. 2:10depends both on the hair colors they see in front of them,
33. 2:14and what they’ve learned from the responses behind them.
34. 2:19And as we go down the line,
35. 2:21each response will help us further narrow the pool
36. 2:25of possible hair color arrangements.
37. 2:28We’ll start with the first Proofa-Boompa’s “no.”
38. 2:32If all four hairdos in front of them were red,
39. 2:36they still wouldn't be able to tell whether their own hair was blue or white.
40. 2:41In fact, the only situation where they could say “yes”
41. 2:45is if they saw two white and one blue in front of them, in any order.
42. 2:51In that case, they would know that they must be red.
43. 2:54So we can eliminate that hair color combination
44. 2:58and list out all the remaining combinations
45. 3:01Proofa-Boompa 1 might see that would leave him uncertain.
46. 3:06It's important to note that for each scenario,
47. 3:09these colors could appear in any order in positions two through five.
48. 3:14Now let’s move on to Proofa-Boompa 2, who answers “yes.”
49. 3:19We can take what we learned from Proofa-Boompa 1
50. 3:22and work through the remaining possibilities.
51. 3:26Once again, it’s helpful to think in terms of what Proofa-Boompa 2
52. 3:30could see in front of them.
53. 3:32Say they see three red.
54. 3:35Based on the pool of remaining possibilities,
55. 3:37there are scenarios in which Proofa-Boompa 2′s hair
56. 3:41could be red, white, or blue.
57. 3:44So Proofa-Boompa 2 wouldn’t be able to say “yes” with certainty.
58. 3:50If we keep working through cases like this,
59. 3:52we’ll find that most leave ambiguity,
60. 3:55and would therefore lead Proofa-Boompa 2 to say no.
61. 4:00In fact, there are only two scenarios in which the second Proofa-Boompa
62. 4:04could be certain.
63. 4:06They see two white and one red,
64. 4:08or they see one white, one blue, and one red.
65. 4:13In both cases,
66. 4:14the second Proofa-Boompa could confidently conclude that their hair must be red.
67. 4:20If it were blue here, or white here,
68. 4:24then Proofa-Boompa 1 would have said yes.
69. 4:27These two scenarios leave us with nine possible color orders
70. 4:32for positions two through five.
71. 4:34Now on to Proofa-Boompa 3′s “yes.”
72. 4:38How can they be certain?
73. 4:40Looking at this list,
74. 4:42we see multiple rows where the colors in positions four and five are the same,
75. 4:47but Proofa-Boompa 3 is a different color.
76. 4:50Here they see red and white, but could be either white or blue.
77. 4:55The same logic applies here.
78. 4:58Since these would leave Proofa-Boompa 3 uncertain,
79. 5:02we can eliminate them,
80. 5:03leaving us with five possibilities as we move on to Proofa-Boompa 4’s certainty.
81. 5:10Once again, we can apply the same logic to further narrow down our list.
82. 5:16In these two rows, Proofa-Boompa 4 sees white, but could be either white or blue.
83. 5:23And in these two rows they see blue, but could be either white or red.
84. 5:28Since these would lead Proofa-Boompa 4 to say no, we can eliminate them.
85. 5:33We're now left with only one option.
86. 5:36You confidently proclaim that your hair is red.
87. 5:41Bonka is thoroughly impressed.
88. 5:44The Proofa-Boompas are too, who, fed up with Bonka’s antics,
89. 5:49take your advice and begin to unionize.