Never thought I'd see TED-ed have a video titled like a Buzzfeed article

@LuMe.Garage

Жыл бұрын

True that 😂

@LovesAlchemist

Жыл бұрын

I literally said this must be click bait cuz ain't no way the powers that be want us to have access to free gold

@yuuji3795

Жыл бұрын

here before this blows up

@TheOnlyName

Жыл бұрын

Ikr

@sanjanaakotyada4753

Жыл бұрын

😂

Clicked for the curiosity of gold. But I got trapped with a math problem. Touche.

@aditisk99

Жыл бұрын

Same

@daredemptionn

Жыл бұрын

sameeee i thought it would be about alchemy ahahah

@ebenezeryeboah7090

Жыл бұрын

same😀

@asiaattia2773

Жыл бұрын

Me too, 😅

@marckiezeender

Жыл бұрын

Me signing up for college

1:11 that's the first time EVER I heared the TED narrator change his tone in any way.

@debadityanath4398

Жыл бұрын

a casual one at 4:14 as well

@youjustgotgooped

Жыл бұрын

watch a history on trial video you'll see him in three different accents at once

For anyone wondering, I found a closed form function for the bag that you could graph on a calculator: f(x) = 2(x-2*3^floor(log_3(x)))+|x-2*3^floor(log_3(x))|+3^(floor(log_3(x))+1). It could probably simplified, but this works for all positive x where f(f(x)) = 3x.

@iika_a

Жыл бұрын

how did you do this

@alasdairsinclair916

Жыл бұрын

This guy maths

@danielkellett6981

Жыл бұрын

Disappointed that there's not a nice way to put it but: When N can be written as 3^x+y where y is less than or equal to 3^x, N transforms to 2*3^x+y Otherwise N transforms to 3y So any N such that N= 3^x+y becomes 2*3^x+y = 3^x+(3^x+y) becomes 3*(3^x+y) = 3N

@janparkki5704

Жыл бұрын

I got as far as doing all the steps indicated in the solution except extending the table far enough. I tried to force the general solution out of my brain thinking it had to be something simple and probably do with divisibility by three and modulus. I gave up 15 mins later and am happy now to notice that the proper general form isn't pretty nor totally trivial.

@MutantChicken7397

Жыл бұрын

Ulu

I really appreciate the time effort the animator(s) put into this. As someone who animates casually for fun this is really impressive.

@t3li5

Жыл бұрын

It makes sense since it's their job. But of course they are really talented!

@fruitpl7615

6 ай бұрын

fr

"Also, it's on the back of your shirt." 💀

@axolotlo2

Жыл бұрын

bro was flabbergasted 💀

@jhunelmullanida6852

Жыл бұрын

😂😂 made me laugh

@ashwindongre5918

2 ай бұрын

🤣🤣🤣

@JoshRendall

29 күн бұрын

@@ashwindongre5918 I know! That was funny!

For once I have thought too hard in an attempt to solve a ted-ed puzzle instead of throwing up my hands in confusion. Thank you VSauce for teaching me about Banarch-Tarski

@mewmew8932

Жыл бұрын

Same here

@metal_pipe9764

Жыл бұрын

Meanwhile i just went to shooting them

@djdog120

Жыл бұрын

@@metal_pipe9764 dawg waht

@metal_pipe9764

Жыл бұрын

@@djdog120 they can't steal if they're dead

@lycrowkurato

Жыл бұрын

It'll probably be easier if he asked what colour were his eyes

The way she just DROPPED HER BABY

@aditisk99

Жыл бұрын

Yeah 😂

@asheep7797

Жыл бұрын

0:59 here

@GunNNife

Жыл бұрын

Yeet the baby!

@raymundolancealfreds1050

Жыл бұрын

"Were you dropped in the head as a baby" Yes

@netherite9051

Жыл бұрын

HAHAHAHAHAHAHHAHAHAHAHAHAHAHHAH 🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣

If only all math tests could be like this; I'd be way more invested if they were like this

@carealoo744

Жыл бұрын

Still didnt know how to solve it though.

@K__kelly

Жыл бұрын

@@carealoo744 me too

@kompatybilijny9348

Жыл бұрын

You would get 5% enjoying them and the rest getting frustrated and depressed.

@amberwerwolfschool8927

Жыл бұрын

Ikr! The answer should be on the back of the paper! >:( Oh that's waht u meant-

@erikaz1590

Жыл бұрын

Yes, if only all math tests had the teacher wearing all the answers on their clothing, so you just need to figure out where to plug everything in

I hope whoever animated this get jobs at big studios, because I found it so pleasing to watch.

@nawel991

Жыл бұрын

yes! it was a mixture of a fairy tale and riddles I used to do when I was a child, it took me back in time, we live for this kind of moments 🤩

@Airton2

Жыл бұрын

btu if they get jobs at big studios, we won't have as much ted-ed animations as we have today.....

@IEatDirtForFun

Жыл бұрын

It’s like Netflix level animation, which isn’t that good. I mean the animation is alright, not my favorite at all

@jehadal-kourdy3129

Жыл бұрын

1:42 two ez that's twenty to

@Stickman_Productions

8 ай бұрын

All I could find was Movult Website

Trying to figure out the general formula, and finding out the answer is "you have a set number, just brute force it until you get to it" is incredibly dissapointing, but, incredibly on theme for riddles, where misdirection and unusual ways of thinking are common tools. Cool.

@imperator9343

Жыл бұрын

I actually like this more than just "write the problem as equations and solve with algebra". My issue with most of these riddles is they're just math problems with a thin aesthetic veneer of a puzzle. This one actually requires you to use more basic logic than just "use what you learned in 5th grade" or whatever.

@subhajitsarkar2272

Жыл бұрын

Exactly ! I am in depression now..haha

@Gamesaucer

Жыл бұрын

There has to be a general formula. Just because it's not easily described in purely mathematical form doesn't mean it doesn't exist. Just like in Fibonacci where "each number is the sum of the previous two numbers" doesn't let you create a formula going from one number to the next, nor can you easily find the Nth number without calculating all the ones before it. If you write down everything in the form A -> B, you just get an index on the left where you can say "the Ath magic bag number is B", and so this is just a series of numbers like any other, just one with a somewhat complicated ruleset. The only remaining question is whether it's infinite or not.

@imperator9343

Жыл бұрын

@@Gamesaucer I'm not sure that this completely makes sense. It is entirely possible to create a sequence like this that has no "general" formula, and saying that it might not be infinite (depending on what you mean) contradicts the existence of a general formula. This puzzle was solved using the constraints of a finite band of possibilities. I actually don't think that there is a generalizable f(x) for all x formula to this solution. If the strange man had made this request using, say, 20 coins, I don't think that there is a singular logical answer that can be derived from this premise alone. The constraint that all results must be whole numbers (coins) means that any sort of consistent linear or exponential solution can't be generalized for all numbers. It would require either: a) specific rules for specific sets of inputs, and those rules would necessarily require a number of conditions on the order of the number of inputs (i.e. countably infinite), or b) an initial scheme followed by a "simpler" formula for the rest of the inputs. (a) is not a "general" solution, and both (a) and (b) would not be unique, you would be able to come up with multiple valid ways of constructing it (assuming (b) is even possible, which I'm pretty sure it isn't having played around with the algebra myself).

@vaxjoaberg

Жыл бұрын

@@Gamesaucer You might find "Binet's Formula" interesting.

Interesting facts about this puzzle 1) There is an OEIS entry where a(n) is the dollar amount that comes out when used once on n 2) In 1992, British Math Olympiad tasked students to find the number of coins that came out when 1992 coins were put in. This was Q5. 3) There is a really elegant (IMO) way to get the answer for any n: Convert n to base-3, (ternary). It either starts with 1 or 2. If it started with 1, then the answer is the same number but the lead digit is 2 instead. Example, 13 is 111 in base 3, so the answer is 211 in base 3 which is 22 in base 10 If it started with 2, change the lead digit to 1 and add a zero at the end. So 1992, which is 2201210 in base 3 becomes 12012100 which is 3789 in base 10(and is the solution to BMO Q5) Proving this is pretty fun, but I'm not good at articulating it as a YT Comment, so i leave that as a challenge to you!

@NaHBrO733

Жыл бұрын

I proved the function f(x) Let n=floor(log_3_(x)) If x

@ammonwolfert

10 ай бұрын

I just worked through this too and came up with the same piecewise function f(x) = (x >= 2n) ? 3x - 3n : x +n where n is the largest power of three that is less than or equal to x. It seemed strange at first but after reading this and understanding those operations in base three it makes so much more sense now. Thanks for posting.

@MTGandP

8 ай бұрын

Another way to formulate (3): Let k be the greatest power of 3 that's less than n. if n then f(n) = n + k else f(n) = 3(n - k)

@mwolfe99

8 ай бұрын

Just fantastic information - thanks for posting this. The OEIS entry is A003605. The Q5 on the BMO was: "Let f be a function mapping the positive integers into positive integers. Suppose that f(n + 1) > f(n) and f(f(n)) = 3n for all positive integers n. Determine f(1992)."

@TheAgentAPM

2 ай бұрын

I was hoping there is an elegant solution that uses ternary, alike to the elegant solution to Josephus problem, that uses binary.

New lore for the riddleverse? Yay. Clearly she figured it out because he has green eyes which means if he saw two frogs and one said ozo the fuddly must have used the tri source to make the bag for him.

@pingpong2563

Жыл бұрын

its always quite unfortunate when your crew of five pirates need to take turns crossing a bridge with only a single lamp to get fuel for your aircraft :(

@MichaelDarrow-tr1mn

Жыл бұрын

wow 5 riddles in one sentence

@redthefoxisWritingUpAStorm

Жыл бұрын

Wha?

@MichaelDarrow-tr1mn

Жыл бұрын

@@uncreative127 6 riddles wow

@kingvideogames

Жыл бұрын

Also, it was all on the his nametag

I’m a huge fan of the art style of this video! Please have this animation team back!

@ag-13studios51

Жыл бұрын

Same. I'm glad I'm not the only one who enjoyed the art style and the animation; very cartoony but also very unique and fun (and other descriptions I can't figure out)

This was the most creative way of presenting Banach-Tarsky.

*Me who clicked hoping to make infinite gold:* I've been tricked, I've been backstabbed and I've been quite possibly, bamboozled. My disappointment is immeasurable, and my day is ruined. 💀

@carlosgutierrez6970

Жыл бұрын

You know if u actually looked at the thumbnail you know it was a riddle

The tone of this one was soo completely different from the usual riddles! So many quick jokes and character breaks, it was very funny

Extending the video solution to larger numbers reveals what might be an infinite stack of interleaved sequences, that in total fill the space of all positive integers. Each sequence begins with two values. The pairs of values for starting the first eleven sequences are: (0 0) (1 2) (4 7) (5 8) (10 19) (11 20) (13 22) (14 23) (16 25) (17 26) (28 55) (29 56). To generate the next terms in each sequence you take the last but one number and multiply by three. So for example the sequence starting (4 7) continues as 4, 7, 12, 21, 36, 63, 108, 189, 324 .... The puzzle as posed, for 13 coins, is the start of the seventh sequence 13, 22, 39, 66 etc. This all feels rather Fibonacci. Another presentation of the results is to list in sequence the numbers of coins that come out of the magic bag if you put into the bag 0, 1, 2, 3, 4, etc coins. That sequence starts 0 2 3 6 7 8 9 12 15 ... and (at least) the first 28 terms match "The On-line Encyclopedia Of Integer Sequences" - sequence number A003605.

@isaacnebula9508

Жыл бұрын

In the Encyclopedia it says "Unique monotonic sequence of nonnegative integers satisfying a(a(n)) = 3n." -- Which is exactly what this is. I also generated the sequence, and found a web page displaying the first 10,000 terms of the sequence, such a curio.

@karthikeyan020

Жыл бұрын

And a new sequence is generated by taking a number that doesn't exist in any existing sequence and adding nearest lower power of 3. For e.g. 3^0 for less than 3, 3^1 for less than 9 and so on.

For those who are wondering how to calculate the function without using computation table, here's the function looks like: Lets say k is the largest integer that satisfy 3^k

@willnewman9783

Жыл бұрын

For completion, one should also show that there is a unique function satisfying f(f(x))=3x. I do not think this is clear.

@lennyarms4476

Жыл бұрын

can you explain the thought process like how did you come up with this

@ricofilberto404

Жыл бұрын

@@lennyarms4476 I used a program to generate the computation for the first 1000 value, and then I notice some pattern in f(x)-x, there's a lot of 3^k term showing up.

@ricofilberto404

Жыл бұрын

@@willnewman9783 It's easy to compute f(x), for x = 3^k or 2 * 3^k, for example: f(1) = 2 f(2) = 3 f(3) = 6 f(6) = 9 f(9) = 18 f(18) = 27 f(27) = 54 f(54) = 81 f(81) = 162 And now we want to fill in the gap for the value that hasn't be computed, lets see at the gap between f(3^k) to f(2 * 3^k), for example f(9) to f(18), we can uniquely find value for f(10) to f(17) since we know that f(x) must be increasing and produce integer value (for x is positive integer). So f(10) = 19, f(11) = 20, ..., f(17) = 26. Since know we have a function that result in f(x) = 19 to 26, we know can also compute f(x), with x = 19 to 26, since f(f(x)) = 3x. So f(19) = 30, f(20) = 33, ..., f(26) = 51. With this it's can be easily seen that the function f(f(x))=3x can be computed uniquely (with the rule that it's must be increasing and produce integer value).

@KeithDePew

Жыл бұрын

@@ricofilberto404 Why is the solution not 26? This would also fit the riddle as far as I can tell if the progression is: Y goes in and the magic adds Y, then 2 Y comes out, when 2Y goes back in, the magic adds Y again, and 3Y comes out...done. As far as I can tell, the riddle only stipulates the rule for two uses of the magic, and not a continuing progression, so this would work for all cases and satisfy that more comes out when more is put it. What am I missing?

you guys should sell pedagogic courses to the schools of the world, because if we were introduced to science and math like this, so many more people would love learning

@hakimdiwan5101

Жыл бұрын

Won't be enough for me

@eBrunoro

9 ай бұрын

But they do, it's the video's sponsor

Bruh, can't y'all just put the baby in the bag and get like, 2 or 3 babies? Then the Tarski guy can take the other two away, and everything would be fine!z

@nawel991

Жыл бұрын

im not sure I got this right are you speaking bunny dialect?

@mick4563

Жыл бұрын

That probably wouldn't be ethical to the babies though.

@luxtempestas

Жыл бұрын

The bad part is that you would have ended up with one more baby too! 😂

@bowboi

Жыл бұрын

@@nawel991 ah yes sry it's ohio dialect so i was saying just duping the baby would work if the guy wants it

@bowboi

Жыл бұрын

@@luxtempestas you'd have to use the magic twice to do that, the 1 coin was turned into 3 after the magic was used twice.

Thought it was a hack, then thought it was a fairytale animation. It turned out to be functions chasing me to the internet 😂

The explanation went above my head lol.

The summary pause screen lacks the fact that you have to put all the coins in the bag in order to make the "always tripled" rule work. With that left out, "using it twice" is still unclear if in the second round you put all the coins or only the initial ones (in which case is trivial since it would be x2)

@pragyabiswas1562

Жыл бұрын

Exactly

@Akronox

Жыл бұрын

Agreed that I had to rewatch the part before the summary to confirm this.

@kwaddell

7 ай бұрын

Ok yeah, I was confused because I got stuck thinking I’m just putting the initial amount back in, which then simply lets you double, then triple that initial number, so I settled on 26

I'm getting Infinite 1-Ups from jumping on a Koopa Shell vibes from this 😂

@NOTZeroBlank

Жыл бұрын

3D world was amazing

@ChaosZTC

Жыл бұрын

@@NOTZeroBlank fr

0:57 did she drop the baby?

@malininatarajan7948

Жыл бұрын

Yeah lol

@getthedunkon9347

2 ай бұрын

Nah, you crazy.

I love ted-ed riddles... never stop

@kingwolf3044

Жыл бұрын

Agreed. What’s your favorite

@catoctober8005

Жыл бұрын

Agreed

I love this puzzle, it also reminds me of one thing I've always questioned about the what number comes next riddles. At the end of the day you can always make more complicated formulas that will go through all those points. What's more as in this case technically there doesn't have to be a formula at all, a function can simply be looked up from a table. Implicitly they're asking for the simplest continuous function in most cases. But they should say it explicitly to teach the kids what's going on.

4:19 my man got drafted for squid game 💀

Banarch-Tarski: Has a bag that gives him infinite gold. Also Banarch-Tarski: Can't afford to forgive your debt.

@waiyisit

Жыл бұрын

He just wants to make people suffer.

I can't believe that this is the first puzzle I haven't failed!

@kingwolf3044

Жыл бұрын

Congratulations

@Cora.T

Жыл бұрын

Mind explaining me how it works? Because I can for the life of me not figure it out, like it feels like the explanation makes even less sense

@andrejors9501

Жыл бұрын

@@Cora.T the explanation is really clear tho.. you don't have to use any mathematical formula, its just pure logic.. you simply just start from 1-2-3 and keep on doing that until you got 13

@Cora.T

Жыл бұрын

@@andrejors9501 how though?? Why is it 3,6,9 and not 3,4,9? Or 3,5,9?

@Aagames_

Жыл бұрын

@@Cora.T 1 goes to 2, which goes to 3. 2 goes to X, which goes to 6. Based on the first sentence, X equals 3. Because of this, 3 goes to 6, and since the outcome is triple, 3 goes to 6 goes to 9. The same logic can apply to the rest.

I love TED-ed riddle series, I am not able to solve these but I do always like watching them. It fascinates me😂

My answer was 26, and also seems to satisfy the wording of the riddle. 13-26-39, and as the third time is always triple, and more coins yield more out, then 1-2-3, 2-4-6, etc still hold true to the wording of the riddle.

@tacohouse01

Ай бұрын

same

@diedoktor

Ай бұрын

does 2 become 3 or does 2 become 4?

@MCTrapsandTutorials

Ай бұрын

Your solution doesn't follow the consistent rule stipulation. If 1-2-3 works then 2-4-6 does not, because for the first one you put in 2 and got 3 and for the second you got 4.

@shadowmancy9183

Ай бұрын

@@MCTrapsandTutorials 3 is triple of 1, 4 is double of 2. It's consistent.

@tacohouse01

Ай бұрын

@@diedoktor well we didnt understand that part had to be considered

I can't be the only one who realized the riddle's backstory references Rumpelstiltkin, even all the way up to the lady promising the little man his firstborn and the little man riddling her to guess his name.

@pasta_eeee

Жыл бұрын

proud to say i noticed this too:D

@irishmanfromengland25

Жыл бұрын

it's only one of my the most famous fairy tales in the world, of course you aren't the only one who noticed. I hope... or maybe I'm just one of very few people who read Grimm's Fairy Tales...

@Inkyminkyzizwoz

11 ай бұрын

Must admit I didn't remember the bit about the baby

@elfpiesomeanotherword

7 ай бұрын

I only watch the video show I will try to get Grimm Fairy Tales though to read @@irishmanfromengland25

How dare they trick me to doing math at 6:00 in the morning

I thought I had a different solution, but it turned out to be wrong. My idea was to multiply odd numbers by 2 and multiply even numbers by 1.5, and in two uses that does triple most numbers you put into it, but it turns out that it fails when you start with a multiple of four.

@christiannielsen725

Жыл бұрын

Got the same “solution”. How does it fail again?

@Pyrogecko08

Жыл бұрын

@@christiannielsen725 because two uses only triples most numbers, but it is supposed to triple any number you start with. Starting with four, or any multiple of four doesn't work the way it's supposed to.

@christiannielsen725

Жыл бұрын

@@Pyrogecko08 yeah ok, ty

@dwaraganathanrengasamy6169

Жыл бұрын

​@Pyrogecko08 mate, I thought the same and worked around it. Let's say we are currently having x gold coins. 1) If x is odd, we double the coins. 2) If x is divisible by 2 but not 4, multiply x by 3/2. Following these 2 steps, we will have almost all numbers in its distinct loop. Note that if number x already lies in a loop, next number is found by tripling the number at previous step of the loop. Initially, we might have left a few numbers that are divisible by 4. Form loops of 2 with such nearby numbers and continue the loop by tripling the previous element. Doing this, we are able to uniquely map each element in its distinct loop such that the number is always tripled 2 steps ahead. Loops for first few numbers are, 1 - 2 - 3 - 6 - 9 - 18 - 27 -... 4 - 8 - 12 - 24 -... 5 - 10 - 15 - 30 -... 7 - 14 - 21 -... 11 - 22 - 33 -... 13 - 26 - 39 -... 17 - 34 - 51 -... 19 - 38 - 57 -... This logic too works. So, it makes me wonder, are there infinitely many such possible functions on whole numbers which when applied twice, triples a number. So the next number looped with 13 is 26 AM I WRONG ANYWHERE..?!

@pianoplayer1262

Жыл бұрын

The issue with this strategy is 7->14 but 8->12 which is less. This is due to using two different multipliers, as two adjacent numbers will get mapped non-monotonically (fail to satisfy the condition that the more you put in, the more you get out).

.... But... 13 times 2 is 26....

At first I thought it was some myth story. But it was my favorite riddle video again. Thanks!

So if I understand correctly, this is a function defined by induction, meaning f(x) is defined in terms of f(y) where y

I watched all TED-Ed riddles and loved them :)

i think they already patched it, doesn't work

It's honestly really satisfying having our character have a line in 1 of these let alone 3-5

x is the starting value of the coins, y is the multiplier used in every action we start with the base X and multiply it with Y (First action) afterwards, we multiply it again with the same multiplier as in First action (Second action) -> with that said we can create the formula y^2 * x = 3x with easy access to y we can solve that the multiplier is 1.732, which answers the question and saves the baby.

@rioc2802

Ай бұрын

Doesn't work. 6 * 1.732 = 10.392. 10 * 1.732 = 17.32 Your formula says that 6 * 1.732^2 should equal 18, therefore putting 10 coins in the big should get you 18 coins back. However, your formula also says that 10 coins put in the bag also returns 17 coins, which contradicts the first rule saying the bag works consistently.

I love the animation! It looks so refined and animated compared to the old style 😀

I love the art style in this one! The animation is stellar

I'm like half sure this riddle has slight nods to Rumpelstiltskin. Could just be me being a literature nerd though.

@kingwolf3044

Жыл бұрын

Pretty sure it’s the inspiration. There’s a lot of obvious inspiration in the riddleverse

@timeme5460

Жыл бұрын

it definitely is

@chashubokchoy8999

Жыл бұрын

not even inspiration, it’s literally a rendition of it

@thenovicenovelist

Жыл бұрын

I thought of Rumplestiltskin too. Maybe they're related 😉

@mrosskne

Жыл бұрын

only a literature nerd would know the very obscure tale of ... Rumpelstiltskin

"I'm thinking of a number between 1 and 3, not including 1 or 3." "M!"

The sequence f(x) where f(f(x)) = 3x, can also be described as the list of numbers who's base 3 representations begin with a 2 or end in a 0 (starting from 2). Proving the equivalency is left as an exercise to the reader.

“Sometimes an enigmatic man is going to pose you a riddle, that’s life” Who do you think I am Ted-Ed, Professor Layton?

I thought this is gonna be a story time and end up letting my guard down

1:44 everyone else: what a good riddle. Me: bros name tag went to the backrooms

@ManicDymanic

5 күн бұрын

fr i just saw that 💀

Okay wow, I got that wrong. I thought it was 26, since if it triples at 2, maybe it only double at 1. But then they brought out the 1-2-3 into 2-3-6, so I started writing that out and went 'oh, okay maybe it's a 'if,then' computer function, where if your starting number is odd, you add itself, but if it's even, you add half of itself. But that doesn't work for anything not in the 3's family. tldr, I would definitely have needed the 3 guesses....or knowing that this guy keeps using his answer keys as his clothing fabric.

@sahasrakondapalli50

Жыл бұрын

Ya, I thought you would multiply by root 3 until the no bits rule came up, then I tried to associate it to sets since in those relations, you don't need to know the function itself and this is how they get the answer, but my mind drew a blank and went: 26, even though you initially disproved it.

@user-py3kd6pw7y

Жыл бұрын

I had a similar idea, I thought that if you put in some gold then you get that gold doubled but if you put that same gold in again you only get that initial amount doubled so in this example it would go 13, 26, 39, 52 and so on. But doesn't make much sense so yeah

@cavox5205

Жыл бұрын

I got the same idea but then realized any number divisible by 4 wouldnt work lol

@dwaraganathanrengasamy6169

Жыл бұрын

Guys, I thought of the same idea and worked around it. Let's say we are currently having x gold coins. 1) If x is odd, we double the coins. 2) If x is divisible by 2 but not 4, multiply x by 3/2. Following these 2 steps, we will have almost all numbers in its distinct loop. Note that if number x already lies in a loop, next number is found by tripling the number at previous step of the loop. Initially, we might have left a few numbers that are divisible by 4. Form loops of 2 with such nearby numbers and continue the loop by tripling the previous element. Doing this, we are able to uniquely map each element in its distinct loop such that the number is always tripled 2 steps ahead. Loops for first few numbers are, 1 - 2 - 3 - 6 - 9 - 18 - 27 -... 4 - 8 - 12 - 24 -... 5 - 10 - 15 - 30 -... 7 - 14 - 21 -... 11 - 22 - 33 -... 13 - 26 - 39 -... 17 - 34 - 51 -... 19 - 38 - 57 -... This logic too works. So, it makes me wonder, are there infinitely many such possible functions on whole numbers which when applied twice, triples a number. So the next number looped with 13 is 26 AM I WRONG ANYWHERE..?!

@ilyakam

Ай бұрын

@dwaraganathanrengasamy6169 I came up with the exact same logic as you. Weird to find it this deep in the comments. It works for all cases as far as I can tell.

what's even more exciting about this function is that it is describes it's value for every integer, as big as we want, with those few simple rules. also, it's easy to notice it is altering from jumping 1 step at a time to 3 steps at a time in increasing lengths. One can explain this last phenomenon geometrically by looking at it between the graphs of f(x)=x and g(x)=3x. When drawing a line from the x axis at one point (n,0) to it's value obtained by the said function to (n,h(n)) and then taking a perpendicular to (h(n),h(n)) you can always close continue it by taking it to (h(n),h(h(n)) and the great surprise is that the alternating behaviour of the function leads it to return back to (n,3n)=(h(h(n))/3,h(h(n)) by going back horizontally to g(x)=3x! this is much better explained visually so I highly encourage anyone who wants to understand how this function behaves

@sussykanyeballs176

Жыл бұрын

what function are you referring to when you say h?

@laincoubert7236

Жыл бұрын

yeah, i was surprised there's only one function f: N -> N that satisfies those rules

@Muhahahahaz

9 ай бұрын

@@sussykanyeballs176f and g refer to 2 simpler related functions, and h refers to the function from the video h(n) = #coins after using the magic bag on n coins (once)

@bradensorensen966

9 ай бұрын

@@sussykanyeballs176 it’s logarithmic. If the number of starting coins (n) is between 3 and 8 you add somewhere between 3 and 7 coins. If n is between 9 and 26 you add somewhere between 9 and 25 coins. The number you add is based on how close to the next power of 3 you are. The power of 3 becomes 1 at n = 3, then it becomes 2 at n = 9, 3 at n = 27… it’s basically floor(log3(n)) where floor means round down to the nearest whole number. If n divided by the current power of 3 is 2 or less you just add that power. n = 6 power of 3 is 1 6/3^1 = 2 Just add 3 6 + 3 = 9 n = 13 power of 3 is 2 13/3^2 Just add 9 13 + 9 = 22 If n divided by the current power of 3 is greater than 2, you have to add 2 times the difference n = 25 power of 3 is 2 25/3^2 > 2 Add 9 and 2*(25-18) 25 + 23 = 48 You have to add this number because as n passes a power of 3 you add that power until n becomes double the power of 3. So 3-6, 9-18, 27-54, 81-162… Whenever you have one of the above numbers you add a power of 3. So 3, 9, 27, 81… You add this number whether you are using the starting number of coins or you are doing the second step. Therefor, for the other numbers: 7-8, 19-26, 55-80, 163-242 You have to add the power and 2 for each number you are past the double of the power Hence 13 is +9 but 25 is + 23. 13 +9 14 +9 15 +9 16 +9 17 +9 18 +9 (note: 18 = 9*2) 19 +9 +2 20 +9 +4 21 +9 +6 22 +9 +8 23 +9 +10 24 +9 +12 25 +9 +14 26 +9 +16 27 +27 (the next power of 3) Looking at the above pattern also shows that 27 is +9 +18 which makes sense following +9 +16 just above it! Ain’t math cool!

I love that his name is Banach-Tarsky, after the mathematical paradox that theoretically allows you to split a sphere into 2 spheres which are perfectly identical to the original.

I loved this riddle here! I want more of this characther.

Haven’t watched the solution, but if you put in n coins, one possible (but not necessarily the only) rule could be that you get back (7n-cos(πn))/4 coins. n=13 evaluates to 26. Edit: I did not see that the function must be strictly increasing.

The secret to the bag is that there's a mini universe inside of it and he's giving the little people in there loans at a 200% interest rate

One of the few ones I managed to solve. At first I tried to figure out the logic behind the function but couldn't so I just ended up doing it exactly the same way showed in the video. Genuinely can't believe they did it the same way. Never felt smarter 🙈🙈🙈😍😍😍

"Also, it was written on the back of your shirt," killed me. This is the worst-prepared magical baby snatcher I've ever heard of

@mathguy37

Жыл бұрын

Never thought I’d see “worst prepared magical baby snatcher” in my life but here we are

1: Read the back of the little man's shirt. 2: Confirm you have green eyes 3: Ask the guard if you can leave 4: Steal the secret sauce recipe 5: Lick the male frog 6: Pick the Churrozard disk 7: Cheat death 8: Get your guitar from the drumset box 9: drop the worthless egg from story 34 10: Separate the Fire dragons from the Ice dragons 11: Write down the jousting tournament scores 12: Ask "If I had a burrito for lunch, would you say Ozo"? 13: Light all of the giant's birthday candles 14: Keep the Keystone 15: Put in the charged batteries in the giant iron 16: Cut the werewolf antidote into five squares 17: Make the Professor and the Janitor cross the bridge together 18: Program the multiverse teleportation robot 19: Stop going on youtube because you watch WAY too much Ted-Ed riddles 20: Have a nice day!

Can you solve the infinite gold riddle? would be a better title.

I enjoy these riddle videos for not just the riddles, but also the scenarios that come with them. My guess for this riddle was 26 coins, well I was close.

@Muhahahahaz

9 ай бұрын

Unfortunately, that doesn’t work because the bag has no way to “know” you started with 13 coins before the doubled magic (rather than 26 being your starting point) You want 13 -> 26 to yield 39, but if you apply the same reasoning when starting with 26, then you would be wanting to triple it via 26 -> 52 -> 78 This is inconsistent, since 26 cannot yield both 39 and 52 at the same time

Glad to see another riddle!

I did this one! I've learned after watching a lot of these, that most can be solved by making a sudoku-esque table and using the rules they give you to solve it

How would 1-2-3 work if they said more gold in will mean more comes out? If you put 1 in, you get 2 out. Meaning you get a gain of 1 coin. So if you put in 2 coins, you must need greater than 1 coin to come back out which must be greater than 3? That’s how I interpreted the problem

@kohwenxu

Жыл бұрын

They provided an example. (In 1:54, when they showed the rules.) Basically the number of coins you get back putting 3 coins in the bag has to be greater than the number of coins you get back putting 2 coins in the bag.

@johnwhinston4626

Жыл бұрын

@@kohwenxu but it should work the same for 2 coins vs 1 coin and 3 coins vs 6 coins but in both cases you get the same amount of additional coins as the previous term in the series which breaks the rule

@personalanonymous3172

Жыл бұрын

@@johnwhinston4626 The rule doesn't care about "additional coins", it only cares about number of coins. Putting 1 coin in gives you 2 coins out. Simple as that. The rule doesn't talk about coin generation (or marginal coins or the derivative of coins or however you want to say it). So 2 has to give you more than 2, because 1 gives you 2.

@johnwhinston4626

Жыл бұрын

@@personalanonymous3172 1:58 rule #2 at best it's bad wording at worst it's straight up false

can someone explain the part at 3:49? I don't understand how it gives the answer of the next 2 blanks shown.

@GreenMeansGOF

Жыл бұрын

Notice how we have 4,7,12. That means 7 goes to 12. Now we have 7,12,21 so 12 goes to 21. By the same reasoning, that’s how we get 15 and 24.

@felixliao5801

Жыл бұрын

@@GreenMeansGOF oh I see. Got it

1:44 dude's nametag just nopes out of there

Well I thought this was a clever puzzle - even though I didn't figure it out. The rule about putting in a given amount always producing the same result threw me because I didn't consider a -> b -> c implies b -> c, even though obvious in hindsight. That and the cardinal rule of always start with a simpler case.

Tell me What is your accent?

Great riddle. After a while, it became the first riddle that I was actually able to solve without cheating, so yay I guess🥳🤭

actually root of 3 does work, if you assume its around 1.7, it comes out to 22.1 coins, which rounds up to 22.

I love how casually the whole sold my baby for my life thing was said. I really had to get that over my head before I continued to the riddle

@anthonyjames696

7 ай бұрын

Have you never heard of the German fairy tale Rumpilstilskin :o?

Who chose that opening quote?! Lol.

I would really like if they brought back the demon of reason

Proud of myself for figuring this one out. Took a moment to realize an equation wouldn't work, but then I got it!

Just give him your first born child, Like you're not attached yet and you can just make another one.

These such theories of wonders that matchs with physics is really auspicious within the interconnection of the fictional magical world to sense making practical world. Awesome right!

The title sounds like a video game hack Edit: I actually came really close this time

@nawel991

Жыл бұрын

▶

I solved it differently and got something else: if you make a long chain starting with 1, you get: 1 --> 2 --> 3-->6-->9-->18-->27-->54-->81 etc. so then you see the patern: if the number is odd, then you add the previous two, if even, then the previous three numbers. So 13 must go to 39, which is odd, so 39 = x + 13, giving us 26. ( im pretty sure i messed up with rule number 2, can't spot it tho)

How have they had channel for over a decade and still have new art styles every video.

Glad the baby is ok after she drop it 😂

This one is fun because it tricks you into thinking it's a math puzzle. But it isn't math, it's just logic!

@zmaj12321

Жыл бұрын

People often say that, but IMO math and logic are too similar to make a clear distinction. For example, even though the function given in the video was never completely defined, you can use math to figure out the exact nature of the function (indeed, many people have done this in the comments).

@jonathanlevy9635

Жыл бұрын

well, this is math

@Muhahahahaz

9 ай бұрын

Can it be solved with basic algebra? No But it’s still math. Not everything can be solved with a simple formula (though there is a rather simple algorithm to solve the puzzle for any number of coins, it’s just not a closed algebraic formula like some might assume)

This video was a bit different from the rest of the riddle videos, but I still loved it! Actually, I think it might have been even better.

I started out the same, but then noticed a pattern of: 2x-0, 2x-1, 2x-0, 2x-1, 2x-2, 2x-3, 2x-2, 2x-1, 2x So I extrapolated the next loop down from 2x-0 to 2x-5 and back again, making 13 land at 2x-4, or 22.

His name is Rumpelstielzschen.

Print dollars and use the dollars to buy the world's gold, it's a neat trick.

1:07 oh that took me a moment. That’s very clever. Naming a person who can triple gold after the guy that figured out how to rearrange things to make more of them.

"also its on the back of your shirt" got me rolling on the floor

Smart how you chose a name for the guy based on a paradox based on duplicating things. That led me down quite the rabbit hole… Now if only I can figure out where the heck his name tag magically disappeared to at 1:45….probably on the side of his shirt.

If bag works as a function what would be the equation of that function

@sieevansetiawan4792

Жыл бұрын

A function does not necesarrily have an equation.

@XCM666

Жыл бұрын

That is also how I approached the problem and I got stumped. There has to be some internal logic to that bag, a function that for input x returns output y. The solution suggests that it's just a lookup table and solves the problem through deduction. It works for solving the riddle, but I suspect the approach will fail for higher numbers.

@vladislav_sidorenko

Жыл бұрын

@@XCM666 A function is essentially defined as a lookup table tbh, assigning exactly one value of the output set to each value within the input set.

@ForteGX

Жыл бұрын

@@XCM666 I found that you can define a sort of piecewise recursive formula that covers all natural numbers in this function. f(x+1)=f(x)+1 or f(x+1)=f(x)+3. The first case is followed if 3^k

@kohwenxu

Жыл бұрын

Had one I did (piecewise function) f(x) = x + 3^[floor(log_3(x))] if x = 3x - 3^[floor(log_3(x))] otherwise.

So glad the riddles are back!😄

I thought I had it by defining a piece-wise function: f(x) = 2x, if x is odd; 3x/2 if x is even That function meets all the requirements except for the second one ("the more gold comes in, the more comes out"). In my system, f(5) = 10, but f(6) = 9. Since 9 I'm a little disappointed that the answer wasn't a nice, elegant closed-form expression but rather merely a set of arbitrary mappings. I guess that's why I'm more interested in mathematics than magics.

@MichaelDarrow-tr1mn

Жыл бұрын

it is closed-form, it's just piecewise

@spacefun101

Жыл бұрын

This also wouldn’t work for multiples of 4 because you would end up multiplying by 1.5 twice

Wait, this is a riddle?

@kingwolf3044

Жыл бұрын

Yes. It’s riddleverse canon now

Me: Just take my child-

@newthrill4027

Жыл бұрын

Me literally...

These riddles are always awesome

There are multiple solutions to this problem. The first time in the bag could be x2 and the second time x1.5 the riddle states: 'if you use the magic twice' which could be read as 'if you apply the function to the same set twice'. This solution doesn't require that only multiples of three have commutative multiplication.

@rioc2802

29 күн бұрын

The first rule is clear on the fact that putting in a given amount of coins AT ANY POINT will always produce the same result. In other words, if you have F(1) = 2 and F(2) = 3, F(2) can't also equal 4, as these results are occurring at different points (i.e. previous consecutive uses of the magic) yet produce different results. So you're breaking the first rule.

I definitely didn’t get this right on my first try (I had to finish the video to find my error), but I eventually found a piecewise definition for the bag function, f(x) f(0) = 0 f(3ᵃ + b) = 2•3ᵃ + b, 0 ≤ b ≤ 3ᵃ f(2•3ᵃ + b) = 3ᵃ⁺¹ + 3•b, 0 ≤ b ≤ 3ᵃ Note that the piecewise definition is consistent on the overlapping cases where b = 3ᵃ as f(3ᵃ⁺¹) = 2•3ᵃ⁺¹ = 3ᵃ⁺¹ + 3•3ᵃ = f(2•3ᵃ + 3ᵃ), and f(2•3ᵃ) = 3ᵃ⁺¹ = 2•3ᵃ + 3ᵃ = f(3ᵃ + 3ᵃ). It’s easy to see from the definition that f(x) > x for all x > 0. It’s less obvious that f(x) is monotonically increasing (that is, f(x + 1) > f(x) for all x, or “the more coins you put in, the more you get out”). The overlapping cases of f(x) make proving this easier, though. If x = 3ᵃ + b, 0 ≤ b f(x) = f(3ᵃ + b) = 2•3ᵃ + b f(x + 1) = f(3ᵃ + (b + 1)) = 2•3ᵃ + (b + 1) since 0 so f(x+1) - f(x) = 1 > 0. If x = 2•3ᵃ + b , 0 ≤ b f(x) = f(2•3ᵃ + b) = 3ᵃ⁺¹ + 3•b f(x + 1) = f(2•3ᵃ + (b + 1)) = 3ᵃ⁺¹ + 3•(b + 1) since 0 so f(x+1) - f(x) = 3 > 0. Finally, to prove f(f(x)) = 3•x, it suffices to examine it by cases. If x = 0, then f(f(x)) = f(f(0)) = f(0) = 0 = 3•0 = 3•x. If x = 3ᵃ + b with 0 ≤ b ≤ 3ᵃ, then f(f(x)) = f(f(3ᵃ + b)) = f(2•3ᵃ + b) = 3ᵃ⁺¹ + 3•b = 3•(3ᵃ + b) = 3•x. If x = 2•3ᵃ + b with 0 ≤ b ≤ 3ᵃ, then we know 0 ≤ 3•b ≤ 3ᵃ⁺¹, so f(f(x)) = f(f(2•3ᵃ + b)) = f(3ᵃ⁺¹ + 3•b) = 2•3ᵃ⁺¹ + 3•b = 3•(2•3ᵃ + b) = 3•x.

@mathguy37

Жыл бұрын

and then you realize to do 1 2 3 and then go from there

@rampion

Жыл бұрын

@mathguy37 The nice thing about having a formulaic representation of the function rather than a linear algorithm is that we can calculate f(x) without first calculating f(y) for y For example, consider f(1,000,000,000). One billion = 2·3¹⁸ + 225,159,022 So f(1,000,000,000) = 3¹⁹ + 3·225,159,022 = 1,837,738,533.

Society if this was the story instead of rumpletiltskin...

Why isn’t the answer f(x) = { 3/2x for x even, 2x for x odd } where x is the number of coins put in the bag? In the even case, x (even) -> 3/2x (odd) -> 3x. In the odd case, x (odd) -> 2x (even) -> 3x. This is a strictly increasing function that will always triple after 2 uses. The answer according to this would be 26.

@syphon5899

9 ай бұрын

Exactly my thoughts, and because of such, I have become confused as to why the answer was 22 instead of 26 As a arithmetic series

@Hendrik_F

8 ай бұрын

With those rules you also get 4 -> 6 -> 9, which doesn't triple the initial number@@syphon5899

I think the function is f(x) = { 2x if x is even, otherwise x + x/2 }, not 100% certain though since I haven't had time to thoroughly check it.

@CtrlZGabi

Жыл бұрын

I think you meant f(x) = { 2x if x is *odd*, 1.5x if x is *even* }. In your case x + x/2 will result in a fraction. I think it doesn't work because of this: If x is odd it works fine, if x is even it may result in 4x after applying the function twice, consider x = 4. f(4) = 8, f(8) = 16. Multiplying an even number by 2 doesn't guarantee an odd result.