WEBVTT 00:00:06.771 --> 00:00:09.831 It was a normal Tuesday at the superconductor, 00:00:09.831 --> 00:00:14.161 until a bug in the system created a small situation. 00:00:14.161 --> 00:00:18.900 Now your team is trapped in eleven separate pocket dimensions. 00:00:18.900 --> 00:00:24.380 Luckily for you, there’s a half-finished experimental teleportation robot 00:00:24.380 --> 00:00:26.718 that may be able to get you all home, 00:00:26.718 --> 00:00:30.838 if you can figure out how to work through the quirks of its design. NOTE Paragraph 00:00:30.838 --> 00:00:32.740 Over interdimensional radio, 00:00:32.740 --> 00:00:34.030 your engineers explain 00:00:34.030 --> 00:00:38.160 that the robot can teleport into the alternate universes you’re trapped in, 00:00:38.160 --> 00:00:41.130 but it’ll do so completely at random. 00:00:41.130 --> 00:00:44.770 The robot has two levers and one big button. 00:00:44.770 --> 00:00:45.800 When it appears, 00:00:45.800 --> 00:00:51.010 you just switch the position of one of the levers from A to B or vice versa, 00:00:51.010 --> 00:00:54.090 and then the robot will note your dimensional position 00:00:54.090 --> 00:00:58.910 and teleport to another of the eleven dimensions at random. 00:00:58.910 --> 00:01:03.880 If it shows up again, you’ll have to pull a lever before it’ll teleport away. 00:01:03.880 --> 00:01:06.060 When anyone presses the button, 00:01:06.060 --> 00:01:10.010 the robot will bring everyone who pulled a lever back home. 00:01:10.010 --> 00:01:14.781 Anyone who didn’t will be lost in the multi-verse forever. NOTE Paragraph 00:01:14.781 --> 00:01:18.361 The challenge is to make sure everyone has pulled a lever 00:01:18.361 --> 00:01:20.891 before anyone hits the button. 00:01:20.891 --> 00:01:24.501 While you can talk to each other now over the interdimensional radio 00:01:24.501 --> 00:01:25.921 and agree on a plan, 00:01:25.921 --> 00:01:28.431 the robot’s teleportation technology 00:01:28.431 --> 00:01:32.801 will interfere with all attempts at communication once it arrives. 00:01:32.801 --> 00:01:35.709 You won’t be able to attach messages to the robot 00:01:35.709 --> 00:01:39.759 or scratch notes into its superstrong alloy body. 00:01:39.759 --> 00:01:42.539 Your only way to communicate information 00:01:42.539 --> 00:01:47.189 is to change the position of exactly one lever or hit the button. NOTE Paragraph 00:01:47.189 --> 00:01:50.749 What plan will make sure everyone gets home? NOTE Paragraph 00:01:50.749 --> 00:01:55.024 Pause the video now if you want to figure it out for yourself. NOTE Paragraph 00:01:55.024 --> 00:01:56.026 Answer in 3 NOTE Paragraph 00:01:56.026 --> 00:01:57.817 Answer in 2 NOTE Paragraph 00:01:57.817 --> 00:01:59.349 Answer in 1 NOTE Paragraph 00:01:59.349 --> 00:02:03.029 It would be nice if you could set different combinations of the levers 00:02:03.029 --> 00:02:05.893 to indicate who’s already been visited by the robot. 00:02:05.893 --> 00:02:08.643 But it has only two levers. 00:02:08.643 --> 00:02:10.683 That gives four combinations— 00:02:10.683 --> 00:02:13.673 far too few to communicate about 11 people, 00:02:13.673 --> 00:02:18.763 especially when you’re forced to flip one to send the robot onward. 00:02:18.763 --> 00:02:20.472 There must be another way. NOTE Paragraph 00:02:20.472 --> 00:02:23.492 The critical insight is that not everyone has to know 00:02:23.492 --> 00:02:26.132 when every pocket dimension has been visited. 00:02:26.132 --> 00:02:30.242 If one person accepts responsibility ahead of time for hitting the button, 00:02:30.242 --> 00:02:33.582 then only they need to know who the robot has visited. 00:02:33.582 --> 00:02:37.872 In fact, they don’t even need to know exactly who’s been visited… 00:02:37.872 --> 00:02:39.872 just how many people have been. NOTE Paragraph 00:02:39.872 --> 00:02:43.982 You volunteer to be the person in charge of pressing the button 00:02:43.982 --> 00:02:45.442 when the moment is right, 00:02:45.442 --> 00:02:48.842 and give the following directions to everyone else. 00:02:48.842 --> 00:02:50.392 Your plan is simple: 00:02:50.392 --> 00:02:53.102 you’ll use the left lever to count visits, 00:02:53.102 --> 00:02:55.522 and the right lever will have no meaning, 00:02:55.522 --> 00:02:58.662 so there’s no harm in moving it up or down. 00:02:58.662 --> 00:03:00.892 Each of the others will pull the left lever 00:03:00.892 --> 00:03:05.282 from position A to position B exactly once. 00:03:05.282 --> 00:03:09.160 If the robot appears with the left lever already pulled down, 00:03:09.160 --> 00:03:12.970 or if an individual has previously pulled the left lever down 00:03:12.970 --> 00:03:14.790 at any point in the past, 00:03:14.790 --> 00:03:16.910 then they should move the right lever. 00:03:16.910 --> 00:03:22.400 You, meanwhile, will be the only one who ever resets the left lever from position B 00:03:22.400 --> 00:03:24.152 to position A. 00:03:24.152 --> 00:03:28.392 This gives you a way to count how many people have been visited by the robot. 00:03:28.396 --> 00:03:32.126 Everyone needs to pull the left lever down exactly once, 00:03:32.126 --> 00:03:35.066 and you’re the only one to pull it back up. 00:03:35.066 --> 00:03:38.156 So you know that the tenth time the robot visits you 00:03:38.156 --> 00:03:40.716 with its left lever in the down position, 00:03:40.716 --> 00:03:43.876 it must have visited all ten of the others. 00:03:43.876 --> 00:03:48.766 And that means you’re safe to press the button and teleport everyone home. 00:03:48.766 --> 00:03:49.906 It may take a while– 00:03:49.906 --> 00:03:55.596 most likely the robot will need to teleport around 355 times; 00:03:55.596 --> 00:03:58.595 but better that than leave anyone behind. 00:03:58.595 --> 00:04:02.765 Your teammates phase back into your home dimension one at a time. 00:04:02.765 --> 00:04:05.127 The mission proves a great success. 00:04:05.127 --> 00:04:07.317 Well...mostly.