[["X+Y Nathan solves math problem  CLIP","0","mYAahN1G8Y8",6,0,0],[[20,4880,"20 random cards are placed in a row, all faced down.","",""],[5960,10224,"move consists of turning a face-down card face up","",""],[10982,14440,"and turning over the card immediately to the right.","",""],[15320,18420,"Show that no matter what that the choice of cards to turn","",""],[19180,22080,"this sequence of moves must terminate.","",""],[23760,24260,"Nathan!","",""],[25580,27024,"Hiding in the back won't help you.","",""],[27113,28580,"Would you like to come up and show us?","",""],[35459,36780,"Go on, Nathan.","",""],[69080,75777,"Ok, so we need to look at the cards not as cards but as, uh, as numbers.","",""],[77420,81480,"We can call face-down cards...","",""],[83560,84340,"one.","",""],[85000,87820,"face-up cards zero.","",""],[89176,95616,"And initally there would be a sequence of ones as the cards are all face down, but after a while it would look","",""],[95093,98700,"something like that.","",""],[99520,102820,"As we can see that's a binary number.","",""],[103540,110020,"And a move that consists of turning a face-down card face-up and the card immediately to the right of it","",""],[110860,114540,"could be that a one followed by a one","",""],[115080,118040,"will turn into a zero followed by a zero.","",""],[121278,127900,"That would look like that, or it can be a one followed by zero turning into a zero followed by a one.","",""],[129699,135220,"In either case we can see that the number in binary is strictly decreasing.","",""],[137316,138380,"And that means?","",""],[139800,142780,"Which means that the sequence must terminate.","",""],[143600,144380,"Because?","",""],[144339,147940,"Because you can't keep taking away from a positive integer without it turning negative.","",""],[148220,149120,"Now","",""],[149220,151920,"You can. You definitely can.","",""],[151920,155020,"Good work. Everyone, good work!","",""]]]