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

  3. 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.)

  4. 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

  5. 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?

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

  7. 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

  8. 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

  9. 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.

  10. 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

  11. There could be a 100 coins in the cave and 99 won’t save you, you just need 1 to believe in you

  12. @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?

  13. 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

  14. 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.

  15. The coins with all gold sides facing up or only 1 side of gold facing up of all 3 coins can be made into all sides facing up as gold.In this case (From Up to Down)Column 1 -1st and 4th and Column 2-2nd and 4th.

  16. Wow I actually understand the solution. I wouldn't have figured it out, but I really understand it for the first time
    Edit: dont think about the algebra. Think about what would happen if you selected 20 gold facing coins and turned them over. Then it starts to make sense

  17. With hundreds of coins at disposal a reasonable solution could have been to flip in air randomly all the coins, because the 50% chanche to be or silver or gold the result, and then dividing all of them in 2 pile hoping that the initial number of coins was even to have the piles match in number. Statistically speaking it could work, especially with a large number of tries.

  18. I open the link to the quiz of the coins so I say it is 4 of 8 possible because it is possible to flip all the three coins to gold if there are two silver and one gold while two of them are already gold side those that are not possible can be turned into all silver side up half where silver half where gold.

  19. Why don't you just bring what I'm about to say in a list:

    1: Flashlight

    2: Matchbox

    3: Cellphone

    4: Literally anything that can create light

  20. oh i understand now its easy before I was thinking that is only possible if you had 7 but now I understand

    well 1 sliver in the pile
    19 in the big pile
    pile flips and 19 19

  21. You guys obviously haven’t played Jenga or stacked anything in your life. How in the world are you supposed to grab a stack of coins and flip them in the dark without the wizard laughing at your stack scattering across the dungeon like a dunce? How are you even supposed to reach over and actually grab the stack without knocking it over with your hand?

  22. I was stuck at the thinking screen with the exact thought of taking 20 coins and flipping them over. I thought that it wouldn't have worked so i gave up, continued watchig and… well

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