Can you solve the counterfeit coin riddle? - Jennifer Lu

View full lesson: ed.ted.com/lessons/can-you-sol...
You’re the realm’s greatest mathematician, but ever since you criticized the Emperor’s tax laws, you’ve been locked in the dungeon. Luckily for you, one of the Emperor’s governors has been convicted of paying his taxes with a counterfeit coin, which has made its way into the treasury. Can you earn your freedom by finding the fake? Jennifer Lu shows how.
Lesson by Jennifer Lu, animation by Artrake Studio.

[@GeometryDash8000]

the emperor is an impatient man. *literally lets you think for eternity*

[@realprisec]

@Julious Lucas *doubt*

[@illbeyourmonster1959]

If this whole scenario isn't a huge red flag to how the kingdom is being run, you probably need to stay in the dungeon.

[@Astromaniac8802]

You can just ZA WARUDO apparently but you don’t abuse it

[@elishatheknight]

*wowza*

[@yes9691]

0MemeMan0 r/unexpectedjojo

[@Anonymous71575]

And then the King realized that the marker was permanent and... threw you back to jail...

[@ehnathanael]

my thought exactly lol

[@cyrusjohnson245]

ikr

[@ranabanana3459]

LOL DED

[@katrinathekitchen]

Anonymous71475 Good point, he doesn't want ink on his coins, he would most likely force you back into the dungeon or have you decapitated.

[@xw2560]

lolololo

[@Frimpa-MJEB]

0:52 But the Emperor's not a patient man **Weigh pieces of money one by one in 2 minutes** Emperor : Too slow! **Think in 2 hours of a possibility to only use balance 3 times** Emperor : Fast enough

[@self-proclaimedanimator]

If ask me I came up with an answer a lot faster and I am not even bright So other prolly would come up with an answer faster *Methmatican

[@Idiotc]

I just split the 13 in half twice taking the lighter halves. So I had 12 and turned it into 6, I had 6 and turned it into three. I weighed two and and if equal then the fake is the one that I didn’t weigh but if one was lighter than the lighter one was the fake. Took me like 1 minute to solve

[@iwbmo]

sock man is fast

[@iwbmo]

@@Idiotc 12...? you mean 12 right not 13 because then you would have been splitting a coin in half

[@Diemoth1987]

@@Idiotc yeap, the marker is useless :P

[@NiftyNesty]

The hardest aspect of this and what people are missing is that the counterfeit is either heavier OR lighter, so you need to figure out that detail. You can’t assume the counterfeit is lighter/heavier from the beginning.

[@voin5371]

Of cause but that isn't the lesson of the video if you get what I mean.

[@deleted-something]

Exactly

[@user-nj9ru4ef2w]

no that's the easiest part. The hard part is solving the problem knowing that there's an extra piece of info you need to find out.

[@alonkob2127]

What's fascinating is that by marking the coins with + or - marks, you effectively negate that issue. Having 9 coins, 4 marked with a - and 5 with a +, you can discover the fake one exactly like how you could do so if you knew the fake was heavier/lighter and you had 9 coins. This is why this riddle should be solvable with 14 coins instead of 12, IF you have a "safe" real coin from the beginning.

[@antonioscendrategattico2302]

@@alonkob2127 But the 5 coins will always be heavier. Because there's more of them.

[@ryancallsin]

“Youre the realm’s greatest mathematician.” Ok, youve already lost me.

[@neilfrize6647]

Mohammad King you only have 3 shots.

[@nadian848]

@@mohammadazad8350 you only get 3 shots tho

[@themarshy83]

I have a solution. 1) weigh 6 against 6 2) Take the lighter stack and weigh 3 against 3 3) take the lighter stack and weigh 1 against 1. If they balance, the remaining coin is the fake. If they are unbalanced, take the lighter coin.

[@justsad2F2]

@@themarshy83 it also can be heavier.. you don't know that

[@Ir1sss_]

@@nadian848 lmaoo that’s what I was thinking too

[@dougmcfarlane]

Here's an easier solution. The King can't tell which one is fake, so, pick one at random and tell him that's the fake one. He can't prove you wrong!

[@dougmcfarlane]

Oh, and what country is this? I think I'm paying higher taxes.

[@shasankshakya2]

A mind even greater than of a mathematician. Hats off to you!

[@ProfessorSyndicateFranklai]

But when he has somebody else weigh all 12 coins individually...

[@1ThePowner]

Sir Francis if he were able to get someone to do that wouldn't he just do it in the first place?

[@ProfessorSyndicateFranklai]

Let's say it takes too long to weigh things on the scale and that the maths guy is thinking on the way there, so he could take less time.

[@diegoavesani530]

"But the emperor it's an impatient man" *Also the emperor when he realizes that this procedure takes 10 times the amount of time you would have used if only you were allowed to use the scale however tf you want* "-_-"

[@DespOIcito]

It really wouldn't though

[@dillon8124]

@@DespOIcito it would definitely take less time to balance each coin than draw out and explain 4:09

[@DespOIcito]

@@dillon8124 They wouldn't need to draw out or explain it though, that's only for the viewer to understand how it works. ETA: All they need to actually do is draw the symbols and weigh the coins until they identify the fake. They don't need to explain their reasoning as they go. It's faster this way than using the scale however you want.

[@lisahenry20]

@@DespOIcito but they would have to think of the solution. And if my life was at risk, I'd be double and triple checking my solution before starting.

[@DespOIcito]

@@lisahenry20 which would barely take any time because you're an expert mathematician...

[@izzyb_ella_m5362]

Who else never gets the answer/doesn’t try, but loves the answer because it’s so fascinating?

[@celine4016]

ME-

[@jennydeleon6318]

ME2-

[@jessezheng6692]

hai hai:3

[@yaoselina1374]

Me

[@Lifea16]

Meh

[@Tunade5]

“You’re the realm’s greatest mathematician.” Guys, I think we have a bigger problem here than a counterfeit coin.

[@Neyobe]

😂

[@ContentDeleted10332]

This might’ve been stolen Very similar to another comment but I’ll give you the benefit of the doubt

[@p3achyyp8p16]

@@ContentDeleted10332 it doesn't have to be stolen this comment is a classic for Ted ed videos.

[@GoldChipz]

Well clearly all the other mathematicians didn't know what's addition and subtraction

[@KodakYarr]

Also, this is not a mathematical problem. It's a logical conundrum.

[@rockstarrist-7897]

My Solution: 1) Think for 10 minutes and tell the King you're ready. 2) GO mental with the marker and mark all the coins after randomly weighing them. 3) Pick one coin and tell the King that's the counterfeit. King doesn't know either, so you have survived. Cheers.

[@idanraviv3079]

look at rule 6 at 1:11

[@TheLucarioBaoJunior]

Idan Raviv ignoring rule 6 would work

[@ilikepizza4633]

Idan Raviv didn't say u had to guess right

[@ovaloaf8780]

XD Perfect

[@alexanderringenberg5712]

but the counterfeiter would still counterfeit ,and the king would realize that you made a mistake then throw you in the dungeon (If you don't run away)

[@sciphyskyguy4337]

There’s a dark twist in any of the solutions to this puzzle… There will be one case out of all possible weighings where the scales have always balanced, and you have decided the last coin is counterfeit by elimination…but you haven’t actually weighed that last coin. If you encounter this particular case, you are sending the treasurer to his death without really knowing if that last coin is fake. This is exactly the case you would reach *every time* if this whole scheme is actually a set-up by the king to get rid of the treasurer…

[@karlgunther1176]

Except, if there is no counterfeit, you would have singled out one coin in two steps of weighing and have one left to check it.

[@axolotlyt3241]

Third dark twist: your marker was permanent, you are 😵

[@deleted-something]

Lol

[@demonslime]

This is not true. All three tries will only balance if there is no fake coin. This is because the solution not only allows you to determine the fake coin, but also determine whether it's heavier or lighter. If the first two weightings balance, you would have a single coin left over. You will then use the third attempt to compare this coin with any other coin to determine whether it's heavier or lighter.

[@moseszero3281]

With balanced results it only takes two weighings to identify the fake. The first balanced 4v4 eliminates 8 coins. Then second weighing is 3 good coins vs 3 of the remaining unknown. Since they balance then those three are now good so then you have left the singular unweighed coin as the only possibility. Problem solved. But since you have and extra turn, you could even weigh the bad vs one of the good coins to see if its lighter or heavier.

[@cuchelo1]

I truly admire ppl whose brains can comprehend things like this. Even watching the explanation, though, I resign myself to the fact that I would take the sweet release of death rather than trying to figure it out.

[@gameskyjumper1721]

if we are being honest here, all of these solutions are non practical. they are all made out scenarios to fit the puzzle.

[@sherazkamran642]

@@gameskyjumper1721 its more a game for us, and actually problem solving training which is fun.

[@GurjeetSingh-Gur_Jeet_Ke]

May we share ?

[@kunalkashelani585]

Well, I will tell you. I solved this puzzle a long time ago and the solution still went over my head (even though it was exactly the same). Even if you know the solution, just looking at an explanation doesn't do you any good. In order to fully understand it, you need to pause the video, map out what the commentator is saying and understand it in depth. Else, its just a sleeping pill.

[@cyberdude8088]

I solved it, but when i heard the answer, even if it's same, it sounded much more complex.

[@mysticmushroom_]

“The coins were already in the treasury” Yet, you are presented with only 12. This king is sure rich

[@beepbop6542]

Maybe they saw about where the coin ended up but not exactly where it was?

[@theannoyingsisters6764]

*he is totally so rich*

[@Opal7777]

@@beepbop6542 that is true, not to mention what rich meant in older times

[@SirVelo]

Im a bit late but in ye olde times there were also like ranks of coins I mean by that copper silver and gold it’s just like the normal times Ofcourse but still 100 gold coins there could mean 1000 silver coins and 10000 copper coins

[@ivanleon6164]

so many died to lower the number to 12, each one with only 3 tries to find it. i salute them.

[@resliward4562]

I'M the realm's greatest mathmetician? Well, that's the first problem. edit: woah 8k ya'll? Thanks!

[@SH19922x]

Get me four thrippets of wine!

[@lucasmellor7070]

Hahaha

[@benedictly1571]

LOL

[@ethanliang1836]

Lol

[@leahdigiacomo5463]

Relatable

[@tzimisce1753]

Technically, if one weighing turn is defined as "as long as you haven't finished stacking and haven't finished removing the ongoing stack", you can just add coins one by one on each side until one pair makes an unbalance. Once it does, you weigh one of the previous, real pairs' coin against one of the pair which was unbalanced. If they're equal, then the remaining coin of the unbalanced pair is the fake. If not, then you picked the fake one to test.

[@spenjaminn3846]

The strategy actually works for 13 coins as well, with the only difference being at 2:03, where you have 2 unknown coins left instead of 1, but there’s still one more weighing left which can determine which of the two is fake, by weighing one against a real coin.

[@kunalkashelani585]

No you can't. If you have two unmarked coins and only one chance to go, there's no way you can identify the coin and mark it heavier or lighter.

[@seanstringfellow1163]

With 13 coins, there's a series of weighings that will tell you which coin weighs different but depending on which coin it is you may not be able to tell if it is lighter or heavier-just that it does not weigh the same as the others. The algorithm of the 3 weighings that i'm familiar with is slightly different than what this video shows.@@kunalkashelani585

[@naiko1744]

@@kunalkashelani585 I didn't check what the other person proposed. However, i want to add that the problem, if i'm not wrong, should be theoretically solvable for 13 coins too, by adjusting the procedure, with just 3 weighings still. That is because even with 13 coins, there's a total of 27 possible answers (coin 1 heavier, coin 2 heavier...coin 13 heavier, coin 1 lighter, coin 2 lighter...coin 13 lighter, all coins equal. 13+13+1 = 27) . Now, every time we use the scale we are able to discern between 3 possible scenarios based on if the scale is balanced or unbalanced to the left or right. If we were able to exclude one third of the possible answers every time we used the scale, by equally distributing them among the scale outcomes, we would first go from 27 to 9, then 9 to 3, and then 3 to 1.

[@kunalkashelani585]

@@naiko1744 I get your point, but mathematically it is not possible to identify the faulty coin, if the number of coins are 13.

[@naiko1744]

@@kunalkashelani585 Yeah, i was thinking about it in bed tonight, and I think one would need an extra reference non-counterfeit coin, in addition to the other 13 to check

[@annacollins8999]

the king then says "tis a witch!" and sends you to the gallows

[@hedoeswhathewants5268]

Lmao :') brilliant

[@jeikiu]

Haha, that has a certain probability as well. :D

[@MCVessels]

He'll need larger scales to prove that, though.

[@gurtajsingh4493]

Aidan Collins iiiii

[@KogoGaming]

laugh my fucking ass off

[@hulohyou8536]

If no one can tell the fake... Me: *takes random coin after three random weighs* Also me: THIS IS THE FAKE!

[@alexoraha7034]

lol

[@zxsugt5912]

Hahshaaa

[@peter_parkour]

There's a clever answer.

[@IllyAwesome]

That could work!

[@eadweard2214]

It could work

[@lapislazuli9961]

And as you droned on explaining each step of each process for each possibility, the impatient king began to wish he'd just let you weigh each individually

[@jedi_cat_l4976]

"Bro why are you drawing on my coins???" "Im trying to save my hide."

[@briidanielle_]

“6) There's no bribing the guards or any other trick.” they know our ways.

[@therealveridicalyt497]

Bribe the king

[@-thanawat-8296]

@@therealveridicalyt497 considering there’s atleast 15 people in the kingdom (12 treasures, 2 guards, you), and the treasury having 12 coins, either coins are very valuable or the income tax is just THAT high

[@deleted-something]

Buy a helicopter and scape

[@romanianpatriot3699]

The romanian teacher ways dont work here

[@Abelhawk]

"What are you doing drawing on the coins with a marker?! I said I was an impatient man! GET BACK IN JAIL"

[@bottomtierbigo]

This is a logic puzzle as well. Really TED?

[@huitlang931]

Why are you sitting there confused?!!!!! Back in jail!

[@OzziesMom]

Lol

[@johnalair2000]

Hi dude i watch your vids! They’re awesome

[@ricardomont808]

Maths : the scale won’t carry 9 coins so the counterfeit is an odd 1 out but you don’t know so you takes just hands test them all and the counterfeit coin will weigh different so boom the answer is simple : just weigh the coins and find the counterfeit

[@MisterWhat100]

I'll always have a respect for this video since it was the very first TedEd video I ever found. Back in 2017.

[@moodswingmona7520]

I loved this one! My approach didn't really work, but the solution makes perfect sense! 😁👍🏻

[@KarlMalowned32]

I'm pretty much only subscribed for these riddle videos.

[@WaterMeetsLava]

KarlMalowned32 Like me you can just tap the bell on the playlist.

[@levilevi9155]

KarlMalowned32 I thought I was the only one. I feel bad though, I think I should watch all of their videos for added knowledge.

[@nivdexbram]

Same haha

[@grandchonkulous]

KarlMalowned32 Exactly

[@Ben-jl2rh]

KarlMalowned32 yes, we are all in the same boat here.

[@lexik4603]

If he's so impatient wouldn't he know that just weighing each one separately would be faster than all this fancy math shit

[@unionmapping4129]

Emperors are always portrayed to be little shits.

[@rolan638]

Airam Roque do you have any proof that says otherwise?

[@pallingtontheshrike6374]

Well, you're the master mathematician. Doing this would take around... 5 seconds?

[@supercool37]

Yeah

[@Dragonoid269]

Even if we assume the master mathematician comes up with the problem instantly, it would still take longer to actually fetch the mathematician instead of having a servant brute force search the false coin.

[@mason1775]

It was very neat to get this and its variations in my college's Data Structures and Algorithms course. We got this version, one where there were two counterfeits with the same heavier weight, one where there were two counterfeits with differing heavier weights, and one where there was one counterfeit lighter and one counterfeit equally heavier.

[@isaacjohnsen867]

Alternatively, if you know the counterfeit is lighter, you could split the pile in half, then weigh them. Take the lighter side and then split it in half again, take this batches lighter side and put two of the coins on the scale. If they weigh the same, the third is counterfeit, if one is lighter, there's your counterfeit. This is a lot easier for me to remember than their solution, but obviously it requires you to know about this kingdom's counterfeit coin production.

[@bucketofparts]

This is the solution I came up with, too. Weird that they went the complicated route.

[@seanty1317]

had the same solution, but I think it's because we don't know if the counterfeit coin is heavier or lighter than the real coins which is why it became this complicated.

[@ZurilasZone]

@@seanty1317 nono they stated its lighter

[@lflagr]

@@ZurilasZone 1:12 Wrong, it says the counterfeit coin "is very slightly heavier or lighter"

[@suoun6938]

@@bucketofparts because you don't know if it's heavier or lighter, this solution doesn't work

[@Luchoedge]

figuring all that out would take more time than just dingo all the weighting in rapid succession. Impatient my ass.

[@animeshwakade5939]

Lucho-Core tru dat 😂😂

[@Paul.V.29]

Was just about to say that.

[@Aflay1]

To be fair, most of this would be done in his head, in rapid succession.

[@greenhat8978]

IKR?

[@CoolJoshido212]

Lucho-Core true

[@checkmate5338]

*I solved it without ever using the balance scale.* Since the Emperor has no idea which one the counterfeit coin is, you can just pick any coin and pretend it's counterfeit.

[@checkmate5338]

Check Mate

[@gv5869]

GG you win.. Eatshit king.. haha

[@shilohschwartz8671]

Check Mate lol

[@Pumbear]

Just make up a really complicated explanation. The king won't understand it, he's not the smartest mathematician of the land.

[@rpenguinboy]

Check Mate LOOL so true

[@TheDreamLeaf]

“Youre the realm’s greatest mathematician.” Or the emperor could get any random sod to weigh the coins. Or weigh it himself lol

[@miriamgiacopinelli3119]

It's 4 am, this is the fifth riddle I try to solve in a row. At this point I listen to words but my brain can't translate them into actual useful information 😂 goodnight

[@tommurphy1880]

Of course the emperor lets you draw all over the coins

[@artificialsweetner]

Damn. He would let us draw on his damn golden coins. Wow he sure is an patient man. But he isnt when someone uses counterfit coins to pay his taxes

[@JBC352]

•Mɪʟᴏ ᴀɴᴅ Vɪxɪᴇ • Or when you criticize his tax laws.

[@wizardystaff]

and change the weight of the coin with extra ink on the coin which make it impossible to guess correctly

[@daerdevvyl4314]

wizardystaff Ink isn’t very heavy.

[@iamnolongerexisting]

Ikr

[@tdiaz5555]

I refused to watch the solution when this video came out and I have been thinking about this riddle for years. Today I finally figured it out. I can't express how satisfied I feel.

[@Idisagreethisisnotanon]

That’s insane!

[@siewpinglee2131]

For a moment there I thought u were lying until I saw the release date of the video and not your post

[@barakah4598]

congrats!

[@norukamo]

Nice!

[@stevencarenduff2623]

The king had to wait years lol

[@72seventytwo]

I figured this riddle out on my own. I feel so happy.

[@shreyasvaranasi7629]

The funny thing is that it would take less time to weigh all of the coins in equal piles until you found the one than it would if you marked all of them as you went

[@abermen]

"I've figured it out!" ...Watches solution... "I didn't figure it out." Me with all of these videos, pretty much.

[@SujeetKumar-cd4cc]

Same here, I think of case 1= 4,4 coin, if all balance then fake in left 4 can be find out in 2 more ways; case 2= lets consider 4,4 is not balanced, then again we left with 4 coin so found out in 2 more ways.

[@shalevasor911]

@@SujeetKumar-cd4cc we arent left with 4 coins we are left with 8 since they can be heavier or lighter

[@SujeetKumar-cd4cc]

@@shalevasor911 oh yeah, got it now. thanks

[@abhijeettalukdar5004]

Me too

[@WendyFilmsTheWorld]

Me i just watch them to see how to figure them out i have never solved one the right way NOT ONCE

[@Sam-vn1yl]

When the emperor realizes that it took me longer to figure it out then to balance the scale 11 times

[@alaamhmd1158]

True lol

[@TerenceTeri-xu3jc]

Another elegant solution is to label each of the 12 coins one of the 24 three letter word, each letter being L,R or O (except for the LLL,RRR and OOO) words. Call two words conjugate if one can be the other after swapping L for R and vice versa. Hence LLR and RRL are conjugates. Now label each coin so that no two of them have conjugate words (since each of the 24 words have exactly 1 conjugate, this means that you can use exactly 12 such words which happens to be the number of coins!). So if a coin is labelled LRO then it will be on the Right, Left then Off the scale in the first, second and third weightings respectively. It's easy to see that on each weighting, there are exactly 4 coins on the right, left and off scale. Record the leaning side of the Ballance on each of the 3 weightings record O if it ballances (notice the recordings can't be one of RRR,LLL or OOO as how we labeled the coins). Suppose the recording of the leaning sides are ROL then if there is a coin labeled ROL then it is the Counterfeit coin and it is heavier than the rest. Otherwise there is a coin labeled LOR (a conjugate) this is the counterfeit coin and it is lighter than the rest.

[@robertora6653]

Great explanation. Thank you

[@tristarnova3454]

That’s actually a clean and slick solution.

[@freek520]

This does not work for this riddle, because the counterfeit coin can be either lighter OR heavier

[@RaghavSuresh]

these riddles are so addicting

[@fortunia08]

Me, an intellectual: "So this is how you solve Captain Holt's island riddle..."

[@gauravranjan6237]

ai , a man of quality

[@gavinli1368]

He couldn’t figure out the how the Monty Hall problem worked, of course he couldn’t solve this one.

[@aditimalviya1900]

Monty Hall problem of Captain Holt solved

[@nif4345]

Ooh

[@thereallylargeknome7461]

wait...

[@mastertrey4683]

The emperor is insane. If he gave me an unlimited number of tries, then i would be able to solve this problem faster than i would if he were to only give me three tries. But that’s just my 2 cents.

[@mufin6930]

the point is that u must do it very quickly with only 3 tries, if u require more time than it takes to do 3 quick balance checks then off with ur head

[@elivandrisse]

Actually your 11 cents and a counterfeit coin.

[@tuainajotogotogo7956]

oh yeah yeah

[@theticsnail0831]

TWrecks 2 cents...ba dum tss

[@duckymomo7935]

The scale breaks or becomes unreliable as use increases.

[@deleted-something]

Quite hard, especially deducting everything mentally, I couldn't have solved the case in which the two balances were equal twice by myself, but pretty cool video

[@YamenNazer]

Another cool riddle as always❤❤

[@DeathlyDiJ]

here i thought i was smart since i instantly got a solution. but i didnt take in consideration that the fake could be either heavier or ligther

[@MrOneeyedpete]

DeathlyDiJ same here

[@extrasoggybagel9015]

DeathlyDiJ sameeee

[@bluesteel1389]

DeathlyDiJ same

[@Pritski]

Same here..

[@MohFak]

Same :(

[@JonatasAdoM]

The king is secretly also a genius. He gave him exactly the amount of measurements needed.

[@ZeroIsMany]

Nah, he's just a tyrant who wanted his marker back, and tried to set the mathematician up to fail.

[@nileshtiwari244]

i first heard of this puzzle back in 2010 and thought it was impossible later during my UG me with my friends look up for the solution and were in awe...To this day it was the hardest puzzle i've ever encountered.

[@goodboyshark3379]

This is the only ted-riddles i could solved

[@jesseli662]

So apparently the emperor doesn't have time for you to measure all the coins, but does have time for you to think about how to do it in 3 weighings

[@adantewalker5882]

And explain it on a white board with illustrations

[@vibscraft1069]

Me:*calls a random coin counterfeit since the king wouldn't question the best mathematician's choice*

[@mafiapig9292]

I mean, you're not wrong...

[@arthurdabest8569]

Well ozo, but actually ulu

[@supriyao9517]

What if he asks to prove?

[@arthurdabest8569]

Say that 1+1=2

[@vibscraft1069]

@@arthurdabest8569 1+1=11

[@burgerkingganyu6961]

The emperor is patient enough to go through all this math but isn't patient enough to let me use the scale a couple more times.

[@johnrogers1752]

Saw this puzzle a long time ago in a Piers Anthony book, along with the solution.

[@Di-xp7uc]

I just gave up so quick. And I know I'm not the only one.

[@thanhngo7310]

def not the only one

[@cjceffect8806]

CHeeTah FalconZT yeah me too

[@gsam3]

CHeeTah FalconZT caugth me

[@finnthefrog4354]

me

[@shiweiding9510]

Laaetri same lol

[@lxlxxl6217]

Nah. I have the simpliest solution. All you have to do is mark the coins randomly, pick up literally any coin, and say it's the fake. If the king asked you to do this calculation, that means he DOESN'T KNOW. So simply say whichever one is the counterfeit and get your tush out of jail. He'd never know because he will cease to never know because YOU are some genius and HE is not.

[@SwordBlaze]

Ravioli ravioli, give me the formuoli 😂😂😂😂😂

[@sleepypotato7183]

It's how scammer works lol

[@hsp15]

what if he ask for explaination ?

[@daltoneudy7148]

The Lord has been using fake coins for awhile so he likely wanted the solution to find all the counterfeit coins.

[@Dubious_Arts]

Either the king or one of his servants knows which one is fake, if they didn't then they wouldn't have been able to take the false coin out of the stockpile and put it into the group of 12 coins in the first place.

[@Collacanac3]

"The emperor is not a patient man." Mathematician proceeds to take the time- wise lengthy route to come up with an algorithm to weigh 12 coins using a scale 3x rather than weighing each one

[@cannonsmith-lc7ee]

I think mine would've worked too. Weigh 2 equal amounts of coins. Mark the coins in the coin pile that weighs less or more. Now, weigh the marked ones in 2 equal groups. Mark the coins in the coin pile that weighs less or more (again). Now, weigh 1 marked twice coin and 1 other marked twice coin separately. If their weights are both equal, take the leftover coin not on the scale. Otherwise, take the coin that weighs less or more on the scale.

[@dustinluke4227]

EXACTLY! That's the solution I came up with also. So much easier than this over complicated answer in the video.

[@neelemgoyalgupta7284]

When you measure two piles of 6 , one will be heavier and other one will be lighter . it's not an either or situation . If one thing is heavier the other is lighter .

[@2Pinnz]

The emperor was too impatient to let him weigh them each separately, yet patient enough to hear out the long explanation near the end. Wot???

[@CandiiANDToastii]

i mean, the video is only 4 minutes sooo, even a toddler can wait that long

[@georgiaewington]

what you do is you tell the emperor "look so you want to find the counterfeit coin or not? right. i'll use the scales 12 times then.

[@Jgrace767]

Georgia Ewington 👏🏾👏🏾👏🏾👏🏾

[@sapphiro]

Georgia Ewington ok then I'm The Emperor and say that scale is in bad condition and will break after 3rd use...

[@georgiaewington]

sapphiro buy new scales

[@sapphiro]

Georgia Ewington Precision scale is difficult to make and it will take my finest artisan one month to built. I need result now.

[@georgiaewington]

give me minute to make a call. theres one in the next town. about 10 mins from here

[@777LasVias]

I came up with a little diffrent solution, pls correct me if it doesnt work that way. So lets say, that the first 4 on each side are balanced. Than you can just take 2 of the remaining 4 and compare with 2 of the real coins: If its still balanced you know its one of the other 2 and you can just take 1 and compare to a regular coin and decide which 1 is odd. If it is unbalanced you do the same procedure with this 2. This way you dont need to mark them. Now if the 4 one each side are not balanced, you should mark them with a + and a -, depending if they are on the heavier or lighter side. Now you take away 2 possibly lighter coins and make group the remaining coins into to groups of 2+ and one -. If it is balanced you know 1 of the minus coins not on the scale are odd and you can just compare 1 from them with a normal 1 and see if this is the odd 1 or the other must be. If it is unbalanced you know the odd one is either the minus coin on the lighter side or one of the 2 plus coins one the heavier side. Now you can put the minus coin with one of the plus coins together and compare to 2 regular coins. if its equel the remaining plus coin is the odd one. if it is lighter then the minus coin is the odd one. and if it is heavier than the plus coin on the scale is the odd one. My english is not the best, but I hope y‘all understand my thoughts.

[@ahmedh1896]

OH MY GOD YOU‘RE A GENIUS 😱😱😱 can i have your number papi chulo 🥵

[@nikolaiflensted3571]

This is the first riddle i figured out for myself

[@jjtomecek1623]

i feel like it would be quicker for me to just weigh all the coins against each other rather than take the time to come up with this plan

[@Oheyitsclaudette]

AJ Tomecek it would be easier but impossible since you're only allowed to use the scale 3 times and you have 12 coins.

[@CalliopePony]

Yes, but the reason for the three use limit is the fact that the king is impatient. If he's impatient then he should want it done in the least amount of time rather than the fewest scale uses. He doesn't even need the mathematician, since he could have anybody weigh each coin against the others in less time than it would take to summon the mathematician from the dungeon.

[@jjtomecek1623]

Calliope Pony lol I didn't even think about that. Yeah, he doesn't even need the mathematician, he could just have had anybody to do it

[@jakubpekarek6400]

The point is, that if there were thousand coins (as in real treasury), weighting each individually would take much more time (over an hour) than doing prety much the same thing as here in which case you'd need to use the weights 7 time if you were very clever. So say, 15 times would suffice without doing it in such a complicated way, and figuring out such relaxed solution takes like 5 minutes. Also, if you were looking for the false coin several times, it would be profitable to optimize the process. Welcome to algoritmization and computer science, that's what it's all about.

[@vrabiealexandru2755]

AJ Tomecek but if there were 1000 coins, it would take too much to make piles, and probably no space, a the marker would run out and you would be just stuck

[@boy638]

plot twist, the king lied and you are back in jail

[@stagdragon3978]

Now the next riddle is how to get through bars without being noticed.

[@ryanhamilton5898]

Plot plot twist.... You are the true King and the other one is a counterfeit. Now all you have is a marker and ....

[@kalyanikataki9617]

Plot Twist..your Mom wakes you up saying "Wake up get ready for school, you're not a king". All this was a dream

[@stagdragon3978]

Kalyani Kataki plot twist you never slept you have insomnia, you thought your mom was the king and you stole her jewlery to do the math. You're now grounded for halucinating.

[@kalyanikataki9617]

We should make a movie lol xD

[@jakestolworthy2869]

guys help i cant stop watching these

[@ianw.7897]

Love how it would be quicker for the emperor to let me measure each coin than to do an entire math problem with probability but he would rather me suffer

[@hollydoes.]

The answer: The king gets mad because you draw all over his coins so even if you're right he'll throw you in the dungeon anyway

[@zedaddy3530]

VirtuallyGlace c; *EASY *A-ALI INTO PLAYS*

[@TheLucarioBaoJunior]

Holly does... well if it’s not permanent you might be able to erase it

[@ivanmertadiwangsa9571]

And as punishment the king order you to eat all of the coins

[@bonormayambem7476]

so y'all gonna lock me up for no good reason, then call me to do your homework, and y'all really have the nerve to tell me you're impatient. Please lock me up forever

[@praveenanookala4457]

😂😂😂

[@praveenanookala4457]

😂😂😂

[@enskripticons]

✌️😌 So true

[@CNV71]

In front of him, nobody will say this 😂😂

[@enskripticons]

@@CNV71 Tbh I would say everything they said in Bonor's comment like- Don't call me to do your darn HW 😤🔪

[@jeromedinmawia]

Moral of the story. Pray it balances at the first turn

[@MyLolmom]

This is the only riddle I was ever able to solve

[@LucasPossatti]

"Can you solve the counterfeit coin riddle?" Me: "Well... Back to the dungeon..."

[@roseinabottle]

I'm sure the impatient king wouldn't mind waiting 20 minutes for you to think up a strategy

[@davidjames1684]

A simple definition of time is the measured or measurable period during which an action, process, or condition exists or continues. So just tell the Emporor you are defining "weigh time" as whatever time you need to finish weighing the coins. The terminology is similar to that when people say something like prime time TV, which could be several hours. You only need 1 "weigh time".

[@janng286]

or you could split them into 2 stacks with 6 coins each. the heavier or lighter side contains the imposter coin. (assuming it shows up heavier, meaning the imposter coin is heavier -- this will work if it appears lighter as well) do this again with the side with the imposter coin weighing 3 coins against the other 3. again, the heavier side contains the imposter coin. now you are left with 3 coins and you can just weigh any random 2. the trend of the heavier side being the imposter coin should continue, so if the 2 coins you picked contains the imposter, it will show up on the heavier side of the scale. if both are balanced, the last unweighed coin is the imposter coin.

[@susorzo4342]

this solution only works if you know it's lighter or heavier beforehand, which you don't

[@stuffedcinema7374]

I'm no mathemetician, but I'm pretty sure this method would take longer than weighing the coins individually

[@ritikchawla8298]

Stuffed Cinema He is a mathematician. He solves a problems in minutes or maybe seconds

[@stuffedcinema7374]

Ritik Chawla even if you're a mathemetician, I doubt you'd be able to solve a problem like 4x(1/3)^3=5(1/2)^x in a few seconds.

[@Marscael24]

Stuffed Cinema well it is possible?

[@KingCadmos]

Greatest mathematician in the world

[@stuffedcinema7374]

King Cadmos has not in the world, just the county

[@fentanyl874]

I didn’t know Thanos was so good at math

[@junodisarapong6635]

ROFLMFAOOO

[@hardikrana3529]

@@junodisarapong6635 what even is the full form of that

[@blankname6657]

In the comics actually, Thanos was an exemplary student. He aced every single test and he had a thirst for knowledge

[@Ltdayman1000]

Mr. Anonymous huh interesting

[@christianali5431]

qweryt or looked like that before the gauntlet.

[@davej5096]

My approach looked slightly different. The first weighing was just as explained in the video. Only that in case the counterfeit coin is among the 8 coins used in the first weighing, I would compare weights of 4 vs 4 coins two more times. So the same 8 coins will be weighed 3 ties in total. Each time I would redistribute the coins in a way that for each pair of coins at least once both coins are on the same side and at least once the two coins are on opposing sides of the scale. There should emerge exactly one coin (the counterfeit) that is 3 times on the heavier or 3 times on the lighter side. As a nice side effect we would also know whether the counterfeit coin is heavier or lighter than a real one.

[@ItsDeveloper_]

“The emperor is not a patient man…” **EMPEROR WAITS 4 MINUTES FOR MATHEMATICIAN TO FIND AN ANSWER**

[@luxandhonor5101]

Answer: Step 1) verify that you have green eyes Step 2) The king will give you permission to leave

[@lilchico3066]

What

[@sssamui286]

lil Chico the green eyes riddle

[@soni-switch5270]

This joke never gets old

[@sssamui286]

Aniket Kangutkar a meme

[@Amanda-rn6tw]

THIS JOKE IS SO OLD

[@TakingThisWay]

15% of the comments: Jokes 80% of the comments: People who think they got it but didnt think that they dont know if the fake coin is heavy or light 5% is the rest

[@barneyholt2287]

TakingThisWay you forgot the 0.5% that's people like you 😅

[@Mernom]

I ended up on the 2nd group... My solution only works if the fake coin is KNOWN to be either lighter OR heavier, not unknown.

[@Marscael24]

Barney Holt then you will have 100.5%

[@rajeshsharmajaipur]

me too in the second group :)

[@andrewolivetreemixing]

TakingThisWay haha I'm in the majority, womp womp

[@THETowandAA]

I spent so much time thinking about what was the use of the freaking marker...turns out it was just to make the explanation easier

[@silentgamer112]

I can find the counterfeit in 2 measures with some trickery. First weigh: divide in halves 6:6 Then I will remove 1 coin on each side of the scale as if I was just resetting the scale 😆. Then if the scale balance once I remove a pair of coins, then it means one of them is the counterfeit. Then I weigh 1 of the possible counterfeit with one of the eliminated ones and if balance, the other coin of the pair is the counterfeit and if not then it is the counterfeit. I know it is not a logical solution.

[@diegorey2655]

So the Lord aint got time to wait for twelve measures but he does to wait for the drawing of the probability chart in the board at the end...

[@ItsChiggy]

Diego Rey yeah cuz he’s testing your math skills

[@Max_j9578]

"there is no bribing the guards" with what? the possible counterfeit money in front of you? of course not!

[@jyotsna3617]

Especially when the king is in front of you

[@susamogus8331]

"Hey John, you want this coin? All you have to do is let me go, it's only a 1 in 16 chance to be fake. The king? Nah he can't hear us we're invisible"

[@jyotsna3617]

@@susamogus8331 lol

[@rootypatooty8543]

I like this one it’s not super hard but still challenging

[@t3lis8]

I think this is the hardest one I've seen so far

[@tobblesmash6193]

“Did you just deface my currency? No prison for you you’re going straight to the electric chair”

[@mithmoonwalker]

but its medieveal tomes

[@tobblesmash6193]

deluxe sure then he'll just drop you in the moat infested with crocodiles

[@MAA-kw4ez]

What if... that marker has erasable ink Lol

[@jmjrulz9482]

@@mithmoonwalker If the mathematician has a marker, the electric chair has already been invented.

[@numberjuan5837]

If they already have a scale and the 12 coins .. why did they need a mathematician?

[@Zarrocification]

because the king is not a patient man :D and apparently bringing you up from the prison took less time when simply weighing all of the coins

[@user-zw8wq9zi9t]

The mathematician realised the scale could be used to detect a counterfeit

[@rodrigomoreno9388]

@@Zarrocification also apparently it takes less time to wait for the mathematician to get out of the dungeon, be given orders with several parameters, give him time to think of this whole strategy and also to wait for him to start stacking and re stacking and marking every single coin. Yes that should take less time than just weighing them right there.

[@kiritsolankii6423]

Why is internet full of people who can't get sarcasm 😂 this guy above me

[@duckymomo7935]

The concept of scales wasn’t known to commoners or kings and knights.

[@jaxterthepenguinboy515]

I like to watch these twice so I feel smarter the second time when i know the answer

[@choryllis6646]

I keep getting tricked into thinking these are actual riddles and not the last few questions on a math test.

[@madison9226]

if the emperor doesn't know which coin it is either, couldn't you just give him any coin then write down anything that looks strategical.?

[@arpitnayak]

Madisøn the Tøp! Crybaby You should be the realm's greatest mathematician.

[@tariqsamaien6215]

Madisøn the Tøp! Crybaby he showed us him showing the emporer his work so i guess you need to work it out and not all fat emperors are stupid you know :)

[@alberteinstein2665]

Madisøn the Tøp! Crybaby Maybe the emperor has got some other mathematicians to check if it would actually work.

[@ViliamVadocz]

give them some of the coins to keep their mouths shut xD

[@peanutbutter369]

you will be sending an innocent man to prison then... and letting a guilty one walk!

[@TheMonsterOfTheDeep]

So the King is impatient when it comes to how many times I have to weigh the coins, but not the the million hours I'll be having to figure how to do it with only three trails!

[@thecutecat22]

Superb comment Bro..

[@SnowFaceChamcham]

the trick is, in this situation, it wouldn't take that long. since you are the best mathematician in all the land, it would be very quick. it's still kind of flawed but it's just for the sake of the math.

[@dintill6478]

but it will still take you longer because you have to write on every damn coin

[@berkleyhuffman48]

Al Seraidy Mohammed Took me 2 minutes.

[@jessicazhu9475]

I like how the marker never runs out of ink

[@alonkob2127]

I always liked this riddle. I've seen it first when I was in 3rd grade, it puzzled me for quite a while, but I couldn't solve it and ended up forgetting it for several years until I came by this video, and finally managed to solve it myself. That felt really great. So now I've also tried to delve deeper into the rules of this riddle. Like, this riddle could still be solved with 13 coins instead of 12, but not with 14. However, if you change the rules and give yourself one safe coin, the riddle would become possible with 14 coins. If you have 4 tries instead of 3, The highest amount of coins you could have in order for the riddle to still be solveable is 40, or 41 if you have a safe coin, at least according to my calculations. I kinda want to see how can the rules of this riddle be expande, say, with 2 or more fake coins.

[@justrandom5710]

I didn't understand anything but I watched to the end

[@windrunner1039]

Kathy the Bestest same

[@a.t.t.123alanis2]

The real question is: How did they know he was the one who used the counterfeit

[@AzkaChannelcom]

Xavier Phillips exactly lmao

[@silvermistneoncloud845]

Well your in jail, not knowing what's going on outside.

[@kuldipprashar9499]

@FIRETEAM 2121 I know what you did there.

[@justa_randomfailure6250]

The king check all the coins before hand but then the guy just grabbed it and threw it in with the other coins s9 he could possibly keep going

[@archtansterpg4246]

Whistleblowers.

[@messupmachine9212]

When the pause came up my personal solution was number the coins 1-12 then flip them and give each set of four a symbol, square, X, and triangle. Weight the squares to the triangles and that'll narrow my set to four coins depending on if the scales shift or stay the same. From there weigh the last four coins two at a time and I'll find my counterfeit using the scales 2-3 times.

[@stamatisloukas8544]

We can all agree this method is way more difficult than if we just compared each coin one by one

[@verifiedfangirl6107]

Why does the character who is supposed to be you look like a sock?

[@kaytk1762]

You are a sock puppet

[@aaronthegold]

Bold of you to assume that I don't look like a sock.

[@arthorization]

He looks more like a muppet with the beard if he is drawn

[@tinknal6449]

Clearly the best reply.

[@F1GHTS0NG]

lolololololol

[@user-wm2mx5iv4d]

How does the marker still have its ink through that whole Time he was in jail?

[@potatotomato7750]

mohammed sachit hello

[@EnderPig]

something called Magic

[@Chicken_o7]

It's a good marker :)

[@Tyler-lx2df]

Just mark it and close the cap and yeah. Markers can last for at least th ree months if you put the cap on and use it every ten seconds

[@lilxc_vxlley]

mohammed sachit he got more

[@LaserZman]

Simpler solution: Step 1: confirm you have green eyes Step 2: ask the king to leave

[@yulingzheng8841]

Right answer, wrong equation. My first time solving it!