# 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.

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!

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

Flip the silver coin

You can bite the coins to see if it's the gold side

'There is a surprisingly easy solution' pulls out quantum physics bs

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.)

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

wow finally got one right! woohoo

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?

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

Anyone else's guess was to taste te coins with your tongue? As silver has a defined taste…

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

Real solution: Kick the coins and hope 20 coins flip up.

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

I understood……

Nothing! How can we solve this Riddle??? And, can't I just use a flashlight?

I actually solved the riddle XD

Wait if you’re in total darkness how did you know where the coins were??!!

Let your eyes adjust.

I can almost never solve these Ted riddles without help lol

No

I thought you were supposed to end up with 20 coins. Not so. Well, I want my money back!

Wow I actually got this one

Just say no u then the wizard won’t know what to do so then he will just give up

What if the coins's sides are of the same color?

Or you could bring a match box

Walks

Falls into a horizontal hole

TED-ED physics

Just flip all of the coins.

Top right, middle upper left, and the bottom two can be all gold.

Bonus answer.

Parity(either odd or evenl of gold never change. So we need odd number gold coins.

I got it! The German stole the fish!

Haha! I got this one!

I saw Micheals Math Magic episode before I saw this so ik the answer HAHAHAHAH you cant stop the big mike

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.

Mind o-fish-ally blown

C n me engana tu é brasileiro

Any arrangement with an even amount of silver.

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

3:08

He shouldn’t be interested in gold

He should be interested in magic tricks

If #of gold is odd, can be made all gold

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

B

There’s a simple solution just ask the wizard to light the torches back up and do it

It just needs to be an even number lol

What if they were silver side up to begin with? If you flip them over, then you'd have more gold up.

Next time, bring a flashlight

Lick em

TED-ED: pause the video to figure it out yourself Me: NOPE!! no way am i figuring this out

4:00 I choose Mordor

That’s why take a LED torch at all times in expedition

Left bottom one

1:08

i go back to 0:57 and pause it to memorize the coins

not so smart now eh

Twist : You being a torch

he is ROCKING that unibrow though

Easy, get better memory.

Of course there's a puzzle.

@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?

I say half it so u have tow piles of 50 coins half it again now u have 4 piles worth 25 add 1, 3 and 2, 4

1 use a lantern

2 problem solved

I tought remember where the silver and flip 10 so it's 5

(Never said how many silver coins equal)

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

I would punch all sides of the coins one by one e touched for recognize gold

This guy is an adventurer right he must have a flashlight XD

cut it into two even piles but put all the coins in burrito style roll

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.

I got the answer because I remembered seeing a similar card trick in a Vsauce video, does that count?

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.

This is the only riddle I was able to solve, felt great for a change

I love these

I am terrible at these

You are wrong, TED-ED

I can never realize that there is a surprisingly easy solution

Even with the explanation I still don’t understand

The anwser was 6 in brilliant problem

I fail to see a problem I simply use my lighter to see. You see a problem I see a solution.

all the sudden the torches go outme: pulls out flashlight on phone

Imagine he got all silver coins

I actually got this one, I use it as a magic trick with cards

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

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.

Bonus riddle: every arrangements can be made into all 3 gold coins.

SSS > GGS/SGG > GSG > SSG > GGG

SGS > SSG/GSS > GGG

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.

TedEd: Can you solv-

Me: No but I'll watch

Yeet

Atleast no – think out-of-box or – no we won't give you all rules kind of plot twisting!

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

well travelers always bring flashlights and phones with them so just turn on the light by the phone or flashlight

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

How are you supposed to solve it in a paper if there's no light?You just want us to do mathematics😡

Who walks in a hole

Cant you just bring your phone for light??!?

just get 20 coins and flip them, and make that one of the 2 piles

Me: oh good now ill know what to do when I get into this situation

Why does he look like Bendy when he smiles in the dark

Great cave tedensive

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?

who tf doesnt bring a flashlight while finding treasure

LOL I solved a variant a day before seeing this.

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

Me: (solves riddle)

Wizard: (loses his keys)

Me: FML.

wHAT IF THEY ALL ARE SILVER? THEN THERE WOULD BE ONLY GOLD FACED COINS LEFT, RIGHT?

This was actually easy among other Ted-Ed riddles which I couldn't solve at all. I solved this in 1 min.