[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:06.59,0:00:08.25,Default,,0000,0000,0000,,You heard the traveler's tales,
Dialogue: 0,0:00:08.25,0:00:10.03,Default,,0000,0000,0000,,you followed the crumbling maps,
Dialogue: 0,0:00:10.03,0:00:12.90,Default,,0000,0000,0000,,and now, after a long and dangerous quest,
Dialogue: 0,0:00:12.90,0:00:16.02,Default,,0000,0000,0000,,you have some good news and some bad news.
Dialogue: 0,0:00:16.02,0:00:19.47,Default,,0000,0000,0000,,The good news is you've managed to locate\Nthe legendary dungeon
Dialogue: 0,0:00:19.47,0:00:22.66,Default,,0000,0000,0000,,containing the stash \Nof ancient Stygian coins
Dialogue: 0,0:00:22.66,0:00:25.60,Default,,0000,0000,0000,,and the eccentric wizard \Nwho owns the castle
Dialogue: 0,0:00:25.60,0:00:29.24,Default,,0000,0000,0000,,has even generously\Nagreed to let you have them.
Dialogue: 0,0:00:29.24,0:00:31.96,Default,,0000,0000,0000,,The bad news is that he's not\Nquite as generous
Dialogue: 0,0:00:31.96,0:00:37.70,Default,,0000,0000,0000,,about letting you leave the dungeon,\Nunless you solve his puzzle.
Dialogue: 0,0:00:37.70,0:00:39.68,Default,,0000,0000,0000,,The task sounds simple enough.
Dialogue: 0,0:00:39.68,0:00:44.28,Default,,0000,0000,0000,,Both faces of each coin bear\Nthe fearsome scorpion crest,
Dialogue: 0,0:00:44.28,0:00:45.37,Default,,0000,0000,0000,,one in silver,
Dialogue: 0,0:00:45.37,0:00:47.11,Default,,0000,0000,0000,,one in gold.
Dialogue: 0,0:00:47.11,0:00:50.84,Default,,0000,0000,0000,,And all you have to do is separate them\Ninto two piles
Dialogue: 0,0:00:50.84,0:00:56.29,Default,,0000,0000,0000,,so that each has the same number\Nof coins facing silver side up.
Dialogue: 0,0:00:56.29,0:01:00.30,Default,,0000,0000,0000,,You're about to begin when all\Nof the torches suddenly blow out
Dialogue: 0,0:01:00.30,0:01:02.94,Default,,0000,0000,0000,,and you're left in total darkness.
Dialogue: 0,0:01:02.94,0:01:05.02,Default,,0000,0000,0000,,There are hundreds \Nof coins in front of you
Dialogue: 0,0:01:05.02,0:01:08.76,Default,,0000,0000,0000,,and each one feels the same on both sides.
Dialogue: 0,0:01:08.76,0:01:11.60,Default,,0000,0000,0000,,You try to remember \Nwhere the silver-facing coins were,
Dialogue: 0,0:01:11.60,0:01:13.27,Default,,0000,0000,0000,,but it's hopeless.
Dialogue: 0,0:01:13.27,0:01:14.77,Default,,0000,0000,0000,,You've lost track.
Dialogue: 0,0:01:14.77,0:01:17.14,Default,,0000,0000,0000,,But you do know one thing for certain.
Dialogue: 0,0:01:17.14,0:01:18.61,Default,,0000,0000,0000,,When there was still light,
Dialogue: 0,0:01:18.61,0:01:23.38,Default,,0000,0000,0000,,you counted exactly \N20 silver-side-up coins in the pile.
Dialogue: 0,0:01:23.38,0:01:24.84,Default,,0000,0000,0000,,What can you do?
Dialogue: 0,0:01:24.84,0:01:29.44,Default,,0000,0000,0000,,Are you doomed to remain in the dungeon\Nwith your newfound treasure forever?
Dialogue: 0,0:01:29.44,0:01:31.53,Default,,0000,0000,0000,,You're tempted to kick the pile of coins
Dialogue: 0,0:01:31.53,0:01:34.89,Default,,0000,0000,0000,,and curse the curiosity \Nthat brought you here.
Dialogue: 0,0:01:34.89,0:01:37.30,Default,,0000,0000,0000,,But at the last moment, you stop yourself.
Dialogue: 0,0:01:37.30,0:01:41.82,Default,,0000,0000,0000,,You just realized there's \Na surprisingly easy solution.
Dialogue: 0,0:01:41.82,0:01:43.46,Default,,0000,0000,0000,,What is it?
Dialogue: 0,0:01:43.46,0:01:46.76,Default,,0000,0000,0000,,Pause here if you want to figure\Nit out for yourself.
Dialogue: 0,0:01:46.76,0:01:47.79,Default,,0000,0000,0000,,Answer in: 3
Dialogue: 0,0:01:47.79,0:01:49.16,Default,,0000,0000,0000,,Answer in: 2
Dialogue: 0,0:01:49.16,0:01:50.89,Default,,0000,0000,0000,,Answer in: 1
Dialogue: 0,0:01:50.89,0:01:54.18,Default,,0000,0000,0000,,You carefully move aside 20 coins\None by one.
Dialogue: 0,0:01:54.18,0:01:57.78,Default,,0000,0000,0000,,It doesn't matter which ones:\Nany coins will do,
Dialogue: 0,0:01:57.78,0:02:00.32,Default,,0000,0000,0000,,and then flip each one of them over.
Dialogue: 0,0:02:00.32,0:02:02.06,Default,,0000,0000,0000,,That's all there is to it.
Dialogue: 0,0:02:02.06,0:02:04.50,Default,,0000,0000,0000,,Why does such a simple solution work?
Dialogue: 0,0:02:04.50,0:02:08.04,Default,,0000,0000,0000,,Well, it doesn't matter how many\Ncoins there are to start with.
Dialogue: 0,0:02:08.04,0:02:12.92,Default,,0000,0000,0000,,What matters is that only 20\Nof the total are facing silver side up.
Dialogue: 0,0:02:12.92,0:02:15.50,Default,,0000,0000,0000,,When you take 20 coins in the darkness,
Dialogue: 0,0:02:15.50,0:02:19.09,Default,,0000,0000,0000,,you have no way of knowing how many\Nof these silver-facing coins
Dialogue: 0,0:02:19.09,0:02:21.95,Default,,0000,0000,0000,,have ended up in your new pile.
Dialogue: 0,0:02:21.95,0:02:24.27,Default,,0000,0000,0000,,But let's suppose you got seven of them.
Dialogue: 0,0:02:24.27,0:02:27.72,Default,,0000,0000,0000,,This means that there are thirteen\Nsilver-facing coins left
Dialogue: 0,0:02:27.72,0:02:29.61,Default,,0000,0000,0000,,in the original pile.
Dialogue: 0,0:02:29.61,0:02:33.22,Default,,0000,0000,0000,,It also means that the other\Nthirteen coins in your new pile
Dialogue: 0,0:02:33.22,0:02:35.80,Default,,0000,0000,0000,,are facing gold side up.
Dialogue: 0,0:02:35.80,0:02:40.50,Default,,0000,0000,0000,,So what happens when you flip\Nall of the coins in the new pile over?
Dialogue: 0,0:02:40.50,0:02:44.77,Default,,0000,0000,0000,,Seven gold-facing coins and\Nthirteen silver-facing coins
Dialogue: 0,0:02:44.77,0:02:47.100,Default,,0000,0000,0000,,to match the ones in the original pile.
Dialogue: 0,0:02:47.100,0:02:52.93,Default,,0000,0000,0000,,It turns out this works no matter how\Nmany of the silver-facing coins you grab,
Dialogue: 0,0:02:52.93,0:02:54.36,Default,,0000,0000,0000,,whether it's all of them,
Dialogue: 0,0:02:54.36,0:02:54.92,Default,,0000,0000,0000,,a few,
Dialogue: 0,0:02:54.92,0:02:56.52,Default,,0000,0000,0000,,or none at all.
Dialogue: 0,0:02:56.52,0:03:00.52,Default,,0000,0000,0000,,That's because of what's known\Nas complementary events.
Dialogue: 0,0:03:00.52,0:03:04.23,Default,,0000,0000,0000,,We know that each coin only has\Ntwo possible options.
Dialogue: 0,0:03:04.23,0:03:08.48,Default,,0000,0000,0000,,If it's not facing silver side up,\Nit must be gold side up,
Dialogue: 0,0:03:08.48,0:03:09.85,Default,,0000,0000,0000,,and vice versa,
Dialogue: 0,0:03:09.85,0:03:12.12,Default,,0000,0000,0000,,and in any combination of 20 coins,
Dialogue: 0,0:03:12.12,0:03:15.29,Default,,0000,0000,0000,,the number of gold-facing\Nand silver-facing coins
Dialogue: 0,0:03:15.29,0:03:17.78,Default,,0000,0000,0000,,must add up to 20.
Dialogue: 0,0:03:17.78,0:03:20.93,Default,,0000,0000,0000,,We can prove this mathematically\Nusing algebra.
Dialogue: 0,0:03:20.93,0:03:24.50,Default,,0000,0000,0000,,The number of silver-facing coins\Nremaining in the original pile
Dialogue: 0,0:03:24.50,0:03:29.17,Default,,0000,0000,0000,,will always be 20 minus\Nhowever many you moved to the new pile.
Dialogue: 0,0:03:29.17,0:03:32.52,Default,,0000,0000,0000,,And since your new pile also\Nhas a total of 20 coins,
Dialogue: 0,0:03:32.52,0:03:35.26,Default,,0000,0000,0000,,its number of gold-facing coins will be
Dialogue: 0,0:03:35.26,0:03:39.49,Default,,0000,0000,0000,,20 minus the amount of \Nsilver-facing coins you moved.
Dialogue: 0,0:03:39.49,0:03:42.32,Default,,0000,0000,0000,,When all the coins in the new pile\Nare flipped,
Dialogue: 0,0:03:42.32,0:03:45.97,Default,,0000,0000,0000,,these gold-facing coins become\Nsilver-facing coins,
Dialogue: 0,0:03:45.97,0:03:51.54,Default,,0000,0000,0000,,so now the number of silver-facing\Ncoins in both piles is the same.
Dialogue: 0,0:03:51.54,0:03:55.16,Default,,0000,0000,0000,,The gate swings open\Nand you hurry away with your treasure
Dialogue: 0,0:03:55.16,0:03:57.27,Default,,0000,0000,0000,,before the wizard changes his mind.
Dialogue: 0,0:03:57.27,0:04:00.88,Default,,0000,0000,0000,,At the next crossroads, you flip\None of your hard-earned coins
Dialogue: 0,0:04:00.88,0:04:03.80,Default,,0000,0000,0000,,to determine the way \Nto your next adventure.
Dialogue: 0,0:04:03.80,0:04:07.35,Default,,0000,0000,0000,,But before you go, we have another \Nquick coin riddle for you –
Dialogue: 0,0:04:07.35,0:04:11.55,Default,,0000,0000,0000,,one that comes from this video \Nsponsor’s excellent website.
Dialogue: 0,0:04:11.55,0:04:14.01,Default,,0000,0000,0000,,Here we have 8 arrangements of coins.
Dialogue: 0,0:04:14.01,0:04:18.79,Default,,0000,0000,0000,,You can flip over adjacent pairs of coins \Nas many times as you like.
Dialogue: 0,0:04:18.79,0:04:22.92,Default,,0000,0000,0000,,A flip always changes gold to silver, \Nand silver to gold.
Dialogue: 0,0:04:22.92,0:04:26.18,Default,,0000,0000,0000,,Can you figure out how to tell, \Nat a glance,
Dialogue: 0,0:04:26.18,0:04:29.64,Default,,0000,0000,0000,,which arrangements can be made all gold?
Dialogue: 0,0:04:29.64,0:04:33.92,Default,,0000,0000,0000,,You can try an interactive version of \Nthis puzzle and confirm your solution
Dialogue: 0,0:04:33.92,0:04:36.30,Default,,0000,0000,0000,,on Brilliant’s website.
Dialogue: 0,0:04:36.30,0:04:39.39,Default,,0000,0000,0000,,We love Brilliant.org because the site \Ngives you tools
Dialogue: 0,0:04:39.39,0:04:42.92,Default,,0000,0000,0000,,to approach problem-solving in \None of our favorite ways—
Dialogue: 0,0:04:42.92,0:04:47.23,Default,,0000,0000,0000,,by breaking puzzles into smaller pieces \Nor limited cases,
Dialogue: 0,0:04:47.23,0:04:49.65,Default,,0000,0000,0000,,and working your way up from there.
Dialogue: 0,0:04:49.65,0:04:52.93,Default,,0000,0000,0000,,This way, you're building up a \Nframework for problem solving,
Dialogue: 0,0:04:52.93,0:04:55.73,Default,,0000,0000,0000,,instead of just memorizing formulas.
Dialogue: 0,0:04:55.73,0:04:59.31,Default,,0000,0000,0000,,You can sign up for Brilliant for free, \Nand if you like riddles
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Dialogue: 0,0:05:02.78,0:05:05.79,Default,,0000,0000,0000,,to countless more interactive puzzles.
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