1 00:00:06,771 --> 00:00:09,831 It was a normal Tuesday at the superconductor, 2 00:00:09,831 --> 00:00:14,161 until a bug in the system created a small situation. 3 00:00:14,161 --> 00:00:18,900 Now your team is trapped in eleven separate pocket dimensions. 4 00:00:18,900 --> 00:00:24,380 Luckily for you, there’s a half-finished experimental teleportation robot 5 00:00:24,380 --> 00:00:26,718 that may be able to get you all home, 6 00:00:26,718 --> 00:00:30,838 if you can figure out how to work through the quirks of its design. 7 00:00:30,838 --> 00:00:32,740 Over interdimensional radio, 8 00:00:32,740 --> 00:00:34,030 your engineers explain 9 00:00:34,030 --> 00:00:38,160 that the robot can teleport into the alternate universes you’re trapped in, 10 00:00:38,160 --> 00:00:41,130 but it’ll do so completely at random. 11 00:00:41,130 --> 00:00:44,770 The robot has two levers and one big button. 12 00:00:44,770 --> 00:00:45,800 When it appears, 13 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, 14 00:00:51,010 --> 00:00:54,090 and then the robot will note your dimensional position 15 00:00:54,090 --> 00:00:58,910 and teleport to another of the eleven dimensions at random. 16 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. 17 00:01:03,880 --> 00:01:06,060 When anyone presses the button, 18 00:01:06,060 --> 00:01:10,010 the robot will bring everyone who pulled a lever back home. 19 00:01:10,010 --> 00:01:14,781 Anyone who didn’t will be lost in the multi-verse forever. 20 00:01:14,781 --> 00:01:18,361 The challenge is to make sure everyone has pulled a lever 21 00:01:18,361 --> 00:01:20,891 before anyone hits the button. 22 00:01:20,891 --> 00:01:24,501 While you can talk to each other now over the interdimensional radio 23 00:01:24,501 --> 00:01:25,921 and agree on a plan, 24 00:01:25,921 --> 00:01:28,431 the robot’s teleportation technology 25 00:01:28,431 --> 00:01:32,801 will interfere with all attempts at communication once it arrives. 26 00:01:32,801 --> 00:01:35,709 You won’t be able to attach messages to the robot 27 00:01:35,709 --> 00:01:39,759 or scratch notes into its superstrong alloy body. 28 00:01:39,759 --> 00:01:42,539 Your only way to communicate information 29 00:01:42,539 --> 00:01:47,189 is to change the position of exactly one lever or hit the button. 30 00:01:47,189 --> 00:01:50,749 What plan will make sure everyone gets home? 31 00:01:50,749 --> 00:01:55,024 Pause the video now if you want to figure it out for yourself. 32 00:01:55,024 --> 00:01:56,026 Answer in 3 33 00:01:56,026 --> 00:01:57,817 Answer in 2 34 00:01:57,817 --> 00:01:59,349 Answer in 1 35 00:01:59,349 --> 00:02:03,029 It would be nice if you could set different combinations of the levers 36 00:02:03,029 --> 00:02:05,893 to indicate who’s already been visited by the robot. 37 00:02:05,893 --> 00:02:08,643 But it has only two levers. 38 00:02:08,643 --> 00:02:10,683 That gives four combinations— 39 00:02:10,683 --> 00:02:13,673 far too few to communicate about 11 people, 40 00:02:13,673 --> 00:02:18,763 especially when you’re forced to flip one to send the robot onward. 41 00:02:18,763 --> 00:02:20,472 There must be another way. 42 00:02:20,472 --> 00:02:23,492 The critical insight is that not everyone has to know 43 00:02:23,492 --> 00:02:26,132 when every pocket dimension has been visited. 44 00:02:26,132 --> 00:02:30,242 If one person accepts responsibility ahead of time for hitting the button, 45 00:02:30,242 --> 00:02:33,582 then only they need to know who the robot has visited. 46 00:02:33,582 --> 00:02:37,872 In fact, they don’t even need to know exactly who’s been visited… 47 00:02:37,872 --> 00:02:39,872 just how many people have been. 48 00:02:39,872 --> 00:02:43,982 You volunteer to be the person in charge of pressing the button 49 00:02:43,982 --> 00:02:45,442 when the moment is right, 50 00:02:45,442 --> 00:02:48,842 and give the following directions to everyone else. 51 00:02:48,842 --> 00:02:50,392 Your plan is simple: 52 00:02:50,392 --> 00:02:53,102 you’ll use the left lever to count visits, 53 00:02:53,102 --> 00:02:55,522 and the right lever will have no meaning, 54 00:02:55,522 --> 00:02:58,662 so there’s no harm in moving it up or down. 55 00:02:58,662 --> 00:03:00,892 Each of the others will pull the left lever 56 00:03:00,892 --> 00:03:05,282 from position A to position B exactly once. 57 00:03:05,282 --> 00:03:09,160 If the robot appears with the left lever already pulled down, 58 00:03:09,160 --> 00:03:12,970 or if an individual has previously pulled the left lever down 59 00:03:12,970 --> 00:03:14,790 at any point in the past, 60 00:03:14,790 --> 00:03:16,910 then they should move the right lever. 61 00:03:16,910 --> 00:03:22,400 You, meanwhile, will be the only one who ever resets the left lever from position B 62 00:03:22,400 --> 00:03:24,152 to position A. 63 00:03:24,152 --> 00:03:28,392 This gives you a way to count how many people have been visited by the robot. 64 00:03:28,396 --> 00:03:32,126 Everyone needs to pull the left lever down exactly once, 65 00:03:32,126 --> 00:03:35,066 and you’re the only one to pull it back up. 66 00:03:35,066 --> 00:03:38,156 So you know that the tenth time the robot visits you 67 00:03:38,156 --> 00:03:40,716 with its left lever in the down position, 68 00:03:40,716 --> 00:03:43,876 it must have visited all ten of the others. 69 00:03:43,876 --> 00:03:48,766 And that means you’re safe to press the button and teleport everyone home. 70 00:03:48,766 --> 00:03:49,906 It may take a while– 71 00:03:49,906 --> 00:03:55,596 most likely the robot will need to teleport around 355 times; 72 00:03:55,596 --> 00:03:58,595 but better that than leave anyone behind. 73 00:03:58,595 --> 00:04:02,765 Your teammates phase back into your home dimension one at a time. 74 00:04:02,765 --> 00:04:05,127 The mission proves a great success. 75 00:04:05,127 --> 00:04:07,317 Well...mostly.