Can you solve the dark coin riddle? – Lisa Winer

Can you solve the dark coin riddle? – Lisa Winer


You heard the traveler’s tales, you followed the crumbling maps, and now, after a long and dangerous quest, you have some good news and some bad news. The good news is you’ve managed to locate
the legendary dungeon containing the stash
of ancient Stygian coins and the eccentric wizard
who owns the castle has even generously
agreed to let you have them. The bad news is that he’s not
quite as generous about letting you leave the dungeon,
unless you solve his puzzle. The task sounds simple enough. Both faces of each coin bear
the fearsome scorpion crest, one in silver, one in gold. And all you have to do is separate them
into two piles so that each has the same number
of coins facing silver side up. You’re about to begin when all
of the torches suddenly blow out and you’re left in total darkness. There are hundreds
of coins in front of you and each one feels the same on both sides. You try to remember
where the silver-facing coins were, but it’s hopeless. You’ve lost track. But you do know one thing for certain. When there was still light, you counted exactly
20 silver-side-up coins in the pile. What can you do? Are you doomed to remain in the dungeon
with your newfound treasure forever? You’re tempted to kick the pile of coins and curse the curiosity
that brought you here. But at the last moment, you stop yourself. You just realized there’s
a surprisingly easy solution. What is it? Pause here if you want to figure
it out for yourself. Answer in: 3 Answer in: 2 Answer in: 1 You carefully move aside 20 coins
one by one. It doesn’t matter which ones:
any coins will do, and then flip each one of them over. That’s all there is to it. Why does such a simple solution work? Well, it doesn’t matter how many
coins there are to start with. What matters is that only 20
of the total are facing silver side up. When you take 20 coins in the darkness, you have no way of knowing how many
of these silver-facing coins have ended up in your new pile. But let’s suppose you got 7 of them. This means that there are 13
silver-facing coins left in the original pile. It also means that the other
13 coins in your new pile are facing gold side up. So what happens when you flip
all of the coins in the new pile over? Seven gold-facing coins and
13 silver-facing coins to match the ones in the original pile. It turns out this works no matter how
many of the silver-facing coins you grab, whether it’s all of them,
a few, or none at all. That’s because of what’s known
as complementary events. We know that each coin only has
two possible options. If it’s not facing silver side up,
it must be gold side up, and vice versa, and in any combination of 20 coins, the number of gold-facing
and silver-facing coins must add up to 20. We can prove this mathematically
using algebra. The number of silver-facing coins
remaining in the original pile will always be 20 minus
however many you moved to the new pile. And since your new pile also
has a total of 20 coins, its number of gold-facing coins will be 20 minus the amount of
silver-facing coins you moved. When all the coins in the new pile
are flipped, these gold-facing coins become
silver-facing coins, so now the number of silver-facing
coins in both piles is the same. The gate swings open
and you hurry away with your treasure before the wizard changes his mind. At the next crossroads, you flip
one of your hard-earned coins to determine the way
to your next adventure. But before you go, we have another
quick coin riddle for you – one that comes from this video
sponsor’s excellent website. Here we have 8 arrangements of coins. You can flip over adjacent pairs of coins
as many times as you like. A flip always changes gold to silver,
and silver to gold. Can you figure out how to tell,
at a glance, which arrangements can be made all gold? You can try an interactive version of
this puzzle and confirm your solution on Brilliant’s website. We love Brilliant.org because the site
gives you tools to approach problem-solving in
one of our favorite ways— by breaking puzzles into smaller pieces
or limited cases, and working your way up from there. This way, you’re building up a
framework for problem solving, instead of just memorizing formulas. You can sign up for Brilliant for free,
and if you like riddles a Brilliant.org premium membership
will get you access to countless more interactive puzzles. Try it out today by visiting
brilliant.org/TedEd and use that link so they know
we sent you. The first 833 of you to visit that link will receive 20% off the annual premium
subscription fee.

100 Comments

  1. If you want to practice more problem-solving for free, head to https://brilliant.org/TedEd/. If you want to signup for a "premium" account, hurry! The first 833 of you to visit that link will receive 20% off the annual premium subscription. Thanks to Brilliant.org for supporting this video!

  2. if your can't see the coin surfaces, who is to say you can even see the coins? and what happens if you knock them over?

  3. For the bonus riddle, think about parity! The possible arrangements are those where you have an even number of silver coins!

  4. What if you picked up 20 silver coins? When you flipped it over you would have 20 gold coins, they would all be facing gold

  5. For the final riddle, you have to have an odd # of gold coins to be able to flip them to all gold. Including the #'s 1 and 3. If any of the 3 coin piles start with an odd # of silver coins, it wont be possible. This includes starting with 3 coins facing silver up and 1 coin facing silver up. This means that 4 out of the 8 3-coin piles are able to be turned to all gold solutions

  6. the solution to the bonus riddle:

    if the number of silver coins is even then you can do it every time without fail no matter how many coins there are:
    consider this case:
    S G S G S S
    flip last two
    S G S G G G
    first two
    G S S G G G
    2nd and 3rd
    G G G G G G

  7. It's easy! I know a trick, and I learned it from "Hacking the System"!

    Close 1 (either left or right) eye for at least 30 minutes, after, open that eye and close the opposing eye. You will aquire night vision after this! Then proceed to wreck the so called 'Wizard' with this trick and leave with a glorious win!

  8. There is a way I have found out, but a little more difficult. Stand the coins up on its side. Since gold is more dense than silver, it’s side is more massive, assuming that the silver and gold go right down the middle of the coins in equal volumes. That means when you put the coin up on its side, it will always land gold side down and silver side up.

  9. I knew this from a magic trick using 10 or 20 cards, lets say 10. 5 would be face up and a spectator would shuffle without flipping cards, give it to you without looking, put it behind your back, count out 5 and flip that, now both decks have the same amount of face up and down

  10. The real riddle is: How did I remember seeing 20 silver-up coins, when clearly I was occupied with other studd?

  11. For the ending riddle you don’t even need “brilliant”.org. It’s if it has an odd number of gold side up. (Or an even number of silver side up.)

  12. Alternate simply place coin on edge it falls on the gold now. All coins silver side up it can be assumed as it wasn't in the rules origionally that this method of testing is allowed they simply all can't be in piles on edges but must be decidedly chosen by end
    not mathematical but just as good a solution

  13. Hold up, if you grab 20 of the coins and they all turn out to be gold; then you fillip them and they are all silver, almost definitely there will be at least another silver coin face up still in the pile you did not touch. Can someone please explain?

  14. what if the first 20 coins are all silver….then after he flips,all the coins are showing gold at the top….. please explain

  15. Was bout to say flip all the coins and split the pile but there is a slight chance u will be stuck in the dungeon

  16. If I manage to not pick up any silver facing coins (so there’s still 20 left) then I flip that pile. I would have 40 coins left not 20

  17. Easy, get your phone out a put the flashlight on. You can see with that.

    Edit: If he doesn't have a phone, okay. If someone else did this, we got the same idea.

  18. Wizard: NOW LIGHTS OUT!
    ( torches blow out )
    Wizard: Turn them back on I can’t see anything.
    ( torches light up )
    Wizard: You have to wait until I’m like out of the hallway. It’s a figure of speech.

    Like if you get it. If you don’t it’s from Muppets: Most Wanted, great movie go see it

  19. @Ted_ed what if you happened to pick up all the silver coins facing up and proceeded to flip them over, wouldn’t that leave you with 0 silver coins?

  20. hundreds of coins…all in piles….somehow you know there is EXACTLY 20 silver coins?….not a single one more? this whole riddle needs to be re-written

  21. My solution was, remove all the coins 1 by 1, make sure none is stacked

    Since the number of silver coins is even, when the light comes on, just draw a line separating the piles with 10 silver coins on each side.

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