How To Solve The 6s Challenge

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Thanks to Tyler Cenko, and Caio Cerqueira from Brazil, for suggesting this wonderful number puzzle! I had a lot of fun solving this. Can you make 6 from 3 copies of the same number, where the number ranges from 0 to 10? You can use common mathematical operations, but you cannot introduce any new digits (so the cube root is not allowed), and you must have an equality (this is not a trick question with the "not equal" sign). This is a great exercise for building mathematical number sense! See the video for the many solutions.
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5 окт 2024

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Комментарии : 15 тыс.

@MindYourDecisions 5 лет назад

Nearly 2 million views in one year! Thank you!

@panginoonn 5 лет назад

Hi, Love your videos!

@luisalcocer5095 5 лет назад

Does 8-(8/8)!= 6 work? I just learned what factorial means from the video so im not sure

@Lara-fg9vq 5 лет назад

you deserve it

@prabeshgautam4112 5 лет назад

I was thinking factorial can't be applied cause factorial uses other no... Like 3! = 3*2*1 . Why??

@davidpatterson9770 5 лет назад

You cant use sqrt() either. That's the same as 2root.

@BluecoreG 3 года назад

If cube root is not allowed, square root should not be either, as it introduces a 2.

@Stubbari 3 года назад

No it doesn't.

@DarthBil1 3 года назад

@@Stubbari yes it does

@DarthBil1 3 года назад

@@Stubbari Just because the 2 isn't written out, doesn't mean it isn't there. What do you think "square" means in "square root".

@Stubbari 3 года назад

@@DarthBil1 So if there is no written digit then there's no digit. What's so confusing about that?

@DarthBil1 3 года назад

Inverse isn't the right word, but it's late and I can't remember the right word for what I'm thinking. I'll get back to it later.

@okramra 3 года назад

I got the 2, 2, 2 thing in under a second maybe I am a prodigy

@wahabbayor9090 3 года назад

Lol!

@reidarkollstrm5218 3 года назад

Dude your going to get the nobel prize in mathematics

@okramra 3 года назад

@@reidarkollstrm5218 let me finish college without failing math first

@spartalives 3 года назад

🤣🤣🤣

@-rheto-7837 3 года назад

i also did the 6 6 6 in 5 seconds

@JM-po5hu 6 лет назад

i smart 2+2+2 = 6

@JM-po5hu 6 лет назад

said it before he started working them out

@pedromendz 6 лет назад

dang dude, b-b-but how? is it even possible?

@tumeric3988 5 лет назад

J4M13 b -but, how? This g - guy is hackin!

@iamhappythingy9258 5 лет назад

did stephen hawking wake up

@giovannizottola106 5 лет назад

@@morveoteki2719 2×2+2

@jingusflorpus4274 Год назад

I was messed up when you said that we weren’t allowed to use cube roots, because in my head that meant I wasn’t allowed to use square roots either. As soon as I realized I was allowed to use square roots I figured out the ones I was missing pretty quickly.

@aproplayer8581 Год назад

We can use cube and square roots but of the same number for you are solving.

@king_of_the_sun4897 Год назад

Then how did he use a square root for 3s?

@redaipo Год назад

@@king_of_the_sun4897 he may use a square root because the operation is square by default, but no other root because that would require introducing a new number

@awesomeleozejia8098 Год назад

@@redaipo the operation is the second root of 3*3

@MrEscape314 Год назад

Could do the cubed root of 3 cubed. That uses only threes and all three of them to get 3.. never mind I'll be going... Wait, I meant the 6th root of 6 to the 6th power! Yea! that's what I meant...

@jakobf6165 2 года назад

I found a pretty solution for 10 10 10. You can calculate 10 × 10 + 10 = 110, which is 6 in binary representation!

@ethanpatch6840 2 года назад

that is a nice answer but i don’t think that actually counts as a proper solution

@txtp 2 года назад

well- 10 + 10 + 10 2 + 2 + 2

@txtp 2 года назад

another binary one

@BigMikeECV 2 года назад

There are 10 types of people in the world: those that understand binary and those that don't.

@Serai3 2 года назад

I don't think mixing bases would count.

@imonsanyal 5 лет назад

If you can't use "³√", using "√" should also be against the rules because it is just the short form of "²√".

@Stubbari 5 лет назад

And 4 is a short form of 1+1+1+1. With your locig the whole problem is impossible.

@imonsanyal 5 лет назад

@@Stubbari you're not making any sense.

@Stubbari 5 лет назад

@@imonsanyal Radical symbol doesn't have a digit "2" in it. N:th root is written with a corresponding digit. This js enough "√" you don't need to add a digit "2" to make it square root. With your logic 2+2+2=6 is just a shorter version of 1+1+1+1+1+1=6 which includes 6 new digits.

@imonsanyal 5 лет назад

@@Stubbari I know... but it is the short form of *²√* and the rule clearly states that you can't introduce any new digits. *√* and *²√* are the same thing and hence cannot be used.

@jhndvdvdd 5 лет назад

The thing is sqrt can be used without using any digits, so even though they have the same method like finding the nth root, you did not necessarily used a new number on the square root ,got me?

@connormorton665 3 года назад

Alternate title: how make three numbers equal 3 and then apply a factorial operation

@Nightmare_Developer 3 года назад

yes i solved almost all that didnt include ! except 8 that was hard one tho, don't mind coz im newbie in math...

@SorakuteeYT 3 года назад

@@Nightmare_Developer How did u solve 1 withouts factorial. Would u mind sharing

@Nightmare_Developer 3 года назад

@@SorakuteeYT umm no i said i solved all that didn't include !(factorial) except 8 coz i dont even know what ! is

@SorakuteeYT 3 года назад

@@Nightmare_Developer i mean the one with 1. 1 1 1=6 I cant solve it without factorial

@arcanev4 3 года назад

@@SorakuteeYT he's saying he did all of the equations that DON'T require factorial. 1 1 1 requires a factorial, meaning he didn't do 1.

@MrTacoLama Год назад

In the first case I've actually used Cos(0) instead of 0! My other solutions were similar to yours. That was some really pleasant math here ;) Thanks for the video!

@Hugh.G.Rectionx Год назад

Cos(0) isn't a common mathematical operation

@therealmaster9686 Год назад

@@Hugh.G.Rectionx tbh i've used the cosine function much more that factorials

@msncat Год назад

@@Hugh.G.Rectionx i think it is because he didn't restrictions in detail on this

@rayaanansari4834 Год назад

@@Hugh.G.Rectionxprove it

@swedishpsychopath8795 11 месяцев назад

@@Hugh.G.Rectionx Ask Mathologer, I guess it is super-common to him?

@saxenababita 4 года назад

I figured out 6 6 6 = 6 We cannot use not equal symbol But can use = since not any rule for this 6 = 6= 6= 6 😂😂😂🤭🤭🤭🤣🤣🤣

@fahad5593 4 года назад

Cheesy

@aravinthsrisivasritharan4098 4 года назад

Cheeky

@Coolkid245 4 года назад

Cheesy

@hellohumans9721 4 года назад

Cheeky

@saxenababita 4 года назад

What does it mean Cheeky ckeesy whatever

@kumarsaurav8885 5 лет назад

(0!+0!+0!)!=6 For all the rest: (sgn(x)+sgn(x)+sgn(x))!=6

@asgarrahmani939 5 лет назад

It is not true

@dorondaniel318 5 лет назад

@@asgarrahmani939 it is true + we can say for every one of them including zero: (sgn(x)!+sgn(x)!+sgn(x)!)!=6 If your unfamiliar with the sign function you should jnow it returns one if x is positive and minus one if x is negative (and zero if zero)

@trabadix 5 лет назад

@@dorondaniel318 interesante!

@bruhbruh1580 5 лет назад

Kumar Saurav or for 6 6 +6 =12 12-6=6

@mikel4879 5 лет назад

Kumar S / Because Presh doesn't ask for only natural numbers and you use a function that you have to explain ( you make a new "logic rule" ) then we can make another explanation ( rule, requirement, etc ) : let's define de novo the following : 0=1, 1=2, 2=3....., (n=n+1) where n={ 0,1,2,3,4...n+1 } and then your solution is a general solution.

@Kriegter 2 года назад

Damn the maths developers really need to nerf this new "factorial" boost

@gjproductions9337 2 года назад

They said they will in update 3.14

@CrazyAsians123 2 года назад

@@gjproductions9337 finally

@slaughterhouse5585 2 года назад

@@gjproductions9337 Mmmm! Pumpkin 3.1416.

@benr77 2 года назад

noooo! now I can magically make almost any equation just work

@gorgonix2264 2 года назад

I actually used multifactorials for 2 of the solutions. Surprising that that was the first thing that came to mind for me. And yet I still used cosine for the 0s.

@eddeh0772 Год назад

I followed the same path and worked out the first six pretty easily, but it never occurred to me to use the factorial before giving up and watching the solution. I think I could have got there eventually, but I’m not sure I ever would have thought how to work out the 888 one. That’s some Inception level stuff! Kudos to those who worked them all out Edit: first seven, not six… got stumped by the use of factorials. Should have questioned why the answer was always 6!

@Vicandiers Год назад

so what was your solution to 000 and 111?

@eddeh0772 Год назад

No I mean the first 7 he solved, because I followed the same path, not the first 7 sets in numerical order. So like, 222, 333, 444, 555, 666, 777 and 999 I could work out, but I got stumped by 000, 111, 888 and 101010, because I never thought to use factorial

@Vicandiers Год назад

Got it

@bragesrensen9889 Год назад

The answer wasn't always 720

@smaransure2234 Год назад

i got all of them except 10 10 10

@marvelstark3797 4 года назад

the only part i got confused was at the dont's rule. it says it doesnt allow the introduction specific to ³√ but it still using the √ which in my understanding is the same as 2√

@Stubbari 4 года назад

@Ro Bert Yeah because CR introduces a new digit "3" while SR doesn't.

@videopoetic7101 4 года назад

@@Stubbari You don't have to write it but in SR is number 2 so it's a problem in rules.

@Stubbari 4 года назад

@@videopoetic7101 If you don't write it then it doesn't get introduced. Simple as that. Or do you know what digits I introduce here: " "?

@loganxavier 4 года назад

It said digit, not number. So it is allowed since he wrote the square root. If that rule applied to everything, then multiplication wouldn’t be allowed either because that technically counts as this example: 2 x 2 x 2 = 8 (2 + 2 + 2 + 2 = 8) And that does add another number, but the rules said digits so it is allowed.

@bachlamtung5131 4 года назад

point is, it’s literally the same, the 2’s implied thus you dont have to actually write a number

@gregatherton4688 3 года назад

Fun fact: You can do this for arbitrary n, using ONLY addition, division, and trig identities. That's right, without using square root OR factorial. All you need is patience. And possibly a mental disorder. Thankfully, I have both! One of the trig identities you all likely learned in High School, nestled in with the arcus functions (acos, asin, and atan) is: cos(atan(x)) = 1/√(1+x²) Therefore, using sec(x) = 1/cos(x), we get: sec(atan(x)) = √(1+x²) You may see where I'm going with this. We know, for any n, that (n+n)/n = 2 Therefore, sec(atan((n+n)/n)) = √(1+2²) = √(5) and sec(atan(sec(atan((n+n)/n))) = √(1+5) = √(6) We could continue this until we hit √(9) = 3 and use a factorial to get to 6. But if we've gone this far, do we *really* need to use a factorial? After all, √(36) is right there. Therefore, for arbitrary n, I propose the solution that: sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(sec(atan( (n+n)/n )))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = 6 Plug it into Wolfram|Alpha. You'll see it works. And pedants like me can avoid using √ :)

@andreaq6529 3 года назад

Bro 🤯👍

@static3479 3 года назад

You’re the type of guy that does his homework on time

@sajamily2404 3 года назад

😳😳

@YSFmemories 3 года назад

can someone tell me if this guy is legit or trolling?

@isjosh8064 3 года назад

Who tf even are you?

@kay710 5 лет назад

*888 is hardest* Me : 6 CIRCLES!!!

@dhanajon5528 5 лет назад

😂😂😂

@zirconescalus 5 лет назад

😂

@Lililili0170 5 лет назад

Keerthi Mahesh genius👍👍👍

@walterfischer456 5 лет назад

Ehm.... Yes?

@Broody90 5 лет назад

888 was easy 1. third root of 8 is 2 2. add them up 3. .... 4. profit!

@robertp9297 Год назад

Hi Presh. Even though this video is five years old, it is my first view. Again, you've created high-quality, educational content. I'm a senior citizen, and I STILL enjoy your videos. Thank you.

@mjorozco3786 Год назад

this is a high quality good viewer that we need to protect at all costs

@Tasarran 2 года назад

I never even thought of factorial as one of the operations I could use, but I'm happy to say as soon as you brought it up, the ones I was struggling with fell into place in my brain!

@Numerixx Год назад

As soon as I saw this, I thought 0 0 0 would be (0!+0!+0!)! bruh

@friedfries8432 3 года назад

Theoretically, you could find the derivative of every single number, which gets you to 0 0 0, and then factorial each of them to get 1 1 1, then add them together to get 3 and factorial it to get 6. This could work for all of the problems. For example, 4 4 4 = 6 (d/dx 4) (d/dx 4) (d/dx 4) = 6 0 0 0 = 6 0! 0! 0! = 6 1 1 1 = 6 (1+1+1)! = 6 3! = 6 Since the derivative of any constant is always 0, we can use this approach on any number to get 6, hence we could have solved all of the problems in the same exact way.

@clavio3082 2 года назад

haaaaaaaaa, this is the equivalent to the infinite money glitch hahhahah

@anshsharma2652 2 года назад

Bravo!

@СвободныйУголок 2 года назад

невероятно, я восхищен

@darkdesmond6706 2 года назад

Big Brain Time

@ronaldanderson4995 2 года назад

I resorted to something like this to solve 8. I used delta function to convert each number to zero. Then I realized it works for all but 0.

@AlbertWang1 3 года назад

Square root is controversial for all these kind of quest, as it's square 2.

@ojojojojojoje 3 года назад

my thoughts exactly - I threw it out the window right off the bat, silly me :D And I am not nearly confident enough to toy around with goniometry to get there that way

@thebanditterra2917 3 года назад

Agrees I too thought it was out of bounds and despite having the solutions using it still believe thusly

@diablo6250 3 года назад

@@JossWainwright bruh, do you scan this comment section for this one question? if so- *i shall follow you kid*

@JLvatron 3 года назад

The rule should clarify you can't introduce other numbers, but numberless symbols are allowed. Like √ .

@JLvatron 3 года назад

@@JossWainwright Good point.

@MarcusPereiraRJ Год назад

This challenge is a classic one in Brazil we learn as younglings. Nice to see it here!

@SteveSharps 6 лет назад

lol nice try. square root is technically a short hand for 2√ ... and the suggestion of simple math operation is also quite misleading. Most of people would exclude factorial.

@ellanvanninalde 6 лет назад

And logarithms, since (log10+log10+log10)!=6

@MajaxPlop 6 лет назад

Steven Song take ln0 so I know for e ;)

@ArcticFoxWaffles 6 лет назад

Most people wouldn't know about factorials

@xzZZZ799 6 лет назад

so what do we call a root symbol alone and how does it work

@user-ob5hj5vn8c 6 лет назад

Yah Root 2 is basically X ^ (1/2)

@mrchoon2010 3 года назад

He said the word "factorial" and I knew I was in over my head, haha

@is1hair 3 года назад

Don’t be intimidated! Factorial is *extremely* easy to understand. It’s literally just the multiplication of every whole number before x as well as x itself. Ex: 6! = 6 x 5 x 4 x 3 x 2. That’s it lmao, you’ll grasp it quickly.

@mrchoon2010 3 года назад

@@is1hair Yeh, I went and googled it, thanks

@ayushgangwaropz1088 3 года назад

@@is1hair thank u bro .. it help me a lot.. and prevent to Google it?!!!

@NERONRR 3 года назад

in my opinion i dont think he factorial should have been alowed as it is not deemed as a common mathematical concept. No one is going to be like "oh yeah I have 6 factorial dollars"

@mrchoon2010 3 года назад

@@NERONRR Can you solve them without factorials?

@horsesh8e 4 года назад

The whole is about solving to 3 and taking its factorial.

@swarnavabiswas425 4 года назад

@@leinfare Wow!

@asmitoghosh2193 4 года назад

@@leinfare Yup

@CT-pi2gl Год назад

Some people might say sqrt symbol should not be allowed, as it is really introducing ²√ or ^0.5. And by extension as shown in the "8" example you are allowing all root powers of 2. I wonder if some of these would be solvable in that case?

@jachpi1080 3 года назад

6:16 can you use (cos(0) + cos(0) + cos(0))! = 6 ? I´m not adding any digits, but I don´t know if in this case you can do it...

@m_th_m_t_cs 3 года назад

good idea!

@preyunknown1820 3 года назад

cos is not operation it is FUNCTION

@jachpi1080 3 года назад

@@preyunknown1820 oh sugar lumps yur right. However, it was a nice try.

@jachpi1080 3 года назад

I think it should count, but, welp, rules are... rules I guess? (I think it should count xd)

@preyunknown1820 3 года назад

@@jachpi1080 yeah nt tho

@CorghVosc 6 лет назад

square rooting introduces a 2 into the equation. sqrt shouldn't be allowed

@lepassant478 6 лет назад

True

@wyn2118 6 лет назад

But when you write the symbol of a square root you dont really write the digit 2 down, so technically it still works

@MataMaticas 6 лет назад

Well, it is a little tricky because I can not see any "two" in the square root symbol. Quite clever, indeed.

@michaelmullin106 6 лет назад

I don’t think you could do it with numbers 8, 9, or 10 without the sqrt

@rgazsy8366 6 лет назад

Mike Disney if it can not be done with out it then it can not be done. The floor method someone else mentioned is beyond my comprehension

@hamraj7231 5 лет назад

for 999 just flip the nines upside down

@conanchan9033 5 лет назад

the 6 on the right also get up side down

@dystopia-user181 5 лет назад

Nein nein nein, that won't work.

@ogjrap6928 5 лет назад

Enin Enin Enin Nothing worked

@Iiorem 5 лет назад

(9+9)/√ 9

@myguy4w164 5 лет назад

Whoaaaaaaaaa there brother maybe we can relax

@UrSweetPumpkin 2 года назад

at first it was like impossible, but after you start explaining it, it was like new ideas ware automatically coming into my mind, and I was getting the trick. Awesome video!!!

@kiancroxall2099 5 лет назад

Literally the only two I’m smart enough for: 2+2+2=6 And 6+6-6=6 😂🤣😂

@crazybox9424 4 года назад

Same

@pikachu-dr1vs 4 года назад

wow same lmao

@rajakanijes 4 года назад

5/5+5=6

@melkor991 4 года назад

kingmaker (5^2 + 5)/5

@stefanmichaelsenzegarra5688 4 года назад

Me too lmao

@rogeronslow1498 5 лет назад

You never explained in detail what was allowed or gave an example. I had no idea what I could do.

@SkullDraker 5 лет назад

funny enough you can't use cubic root of a number but can use the square? under what logic? lul

@prenomenomine9355 5 лет назад

@@SkullDraker he said it. You can't involve new numbers. You don't need numbers to do a square root since you don't write the 2.

@danieljared2307 5 лет назад

@@prenomenomine9355 but square root is power to 1/2.. basically new number is there.

@SkullDraker 5 лет назад

@@prenomenomine9355 yes cause it's implicite, you don't NEED to write cause it is known, like that the sun is hot...

@prenomenomine9355 5 лет назад

@@SkullDraker any operation can be expressed with more digits. +3 is just like +1+1+1

@OliviaAndreoli Год назад

For the 8's, I did (8!!)/(8 * 8), because 8!! = 8*6*4*2 = 384, and 384/64 = 6. I definitely brute-forced the 10's with some somewhat dubious logic, doing (10!!!!!!! + 10!!!!!!!)/10 to get (30 + 30)/10 = 6 XD

@yehor_ivanov Год назад

just another one for 8 8 8, for a sample: (square(8 + 8)) = 4; 4! = 24 24/8 = 6) seems pretty easy, once come up with, and effective here) though, the ones in t' video r too, surely) Cheers

@rs5256 Год назад

@@yehor_ivanov 24/8 = 3 not 6. You'd have to say: square(8+8) = 4 -> 4! = 24 -> 24/8 = 3 -> 3! = 6.

@cythism8106 Год назад

@@yehor_ivanov say sqrt(x) not square(x). It almost makes it look like you're saying (x)^2.

@324_Sli Год назад

Just this, 8+8=16 aight? 16 root=4 4 root=2 8-2=6

@los-lobos Год назад

You used 4 10’s

@minafawzy5086 4 года назад

To use 10 10 10 there is another solution (log(10*10*10))!

@Sid37612 4 года назад

Awesome dude! That's an innovative solution!

@ExploitRX 4 года назад

@20 Subs Before Tomorrow? I think, he mean lg (log with base 10)

@andsalomoni 4 года назад

@20 Subs Before Tomorrow? A piece of trunk.

@manuelmontana2827 4 года назад

What is log? Baby don't hurt me~

@daapdary 4 года назад

For 10 10 10 = 6, I did: ( log(10) + log(10) + log(10) ) ! = 6

@maxbrandt1324 5 лет назад

3:29 (9 + 9)/ sqr(9)

@AwesomeCreatorBen 4 года назад

I did that too. Sorry im late to the comment section

@nicolasrozenberg5209 4 года назад

You cannot use sqr(9)

@faradaykhaleesi877 4 года назад

@@nicolasrozenberg5209 do you even know what sqr() is?

@30IYouTube 4 года назад

Of course that equals six, because sqr(9) = 3, and (9 + 9) = 18, and 18 / 3 = 6, and square root doesn’t require a number.

@nicolasrozenberg5209 4 года назад

@@faradaykhaleesi877 Sorry, I didn't watch the video. It shouldn't have been used though, because sqr() is not an operator, it is a function that represents the root of index 2 of a certain number. And that involves implicitly using number 2. The task is not explained correctly

@derekchase5462 3 года назад

Reading that first equation very excitedly “Zero! Plus zero! Plus zero! (!!!)”

@TheIvasyl 2 года назад

@@user-SG717 what's 230 - 220 x 0.5? You probably wouldn't believe me, but the answer is 5!

@TheIvasyl 2 года назад

@@user-SG717 just because you're right doesn't mean I'm wrong

@TheIvasyl 2 года назад

@@user-SG717 it's 5!

@TheIvasyl 2 года назад

@@user-SG717 5! = 120

@moetocafe Год назад

Very interesting. Initially I was able to figure out the answer only to the easier ones. But when you explain it, I can calculate it , as you do and understand it, because of the good way you explain it. Thanks!

@deedeeen 4 года назад

Um, you banned the use of the “not equal” sign, so let’s use < and >. 0=0=0

@mattzekamashi4463 4 года назад

The answer needs to be in =6 form which was stated in prerequisites.

@deedeeen 4 года назад

@@mattzekamashi4463 Oh, sorry, my bad.

@doanthichdocsach 4 года назад

< or > is also "not equal" btw :))

@deedeeen 4 года назад

@Dodo Jan But they aren’t actually not equal. Mathematics, you know?

@doanthichdocsach 4 года назад

@@deedeeen yah ok. I haven't do math for a long time :)))

@JianJiaHe 6 лет назад

I have a neat solution for every positive integer N of the N N N = 6 problem. My solution is (log(sqrt(N), N*sqrt(N)))! = 6, where log is the logarithm, for example log(10, 1000) = 3. Took me 10 minutes to come up with this, amusing puzzle by the way.

@RGP_Maths 6 лет назад

That's brilliant and deserves more attention than it's got so far!

@NestorAbad 6 лет назад

What an awesome and elegant solution!

@donaldasayers 6 лет назад

I love it when someone just kills a puzzle.

@boggless2771 6 лет назад

I hope this counts!

@pentaxian7455 6 лет назад

brilliant: it gives allways 3! (log(sqrt(N), N*sqrt(N)))! = log(N*sgrt(N))/log(sgrt(N)=(log(N)+log(sgrt(N))/(log(sgrt(N)=(log(N)/log(sgrt(N)+1)! =(2*log(N)/log(N)+1)!=3! . You are jenius men!

@Santhosh22NA 5 лет назад

You always have solution in mathematics when u stuck. "Let's assume 0 0 0 = 6"

@wholesomehoorpari1971 5 лет назад

Hahah xd

@arnavverma7308 5 лет назад

😂😂😂

@vivek.r4832 5 лет назад

You are Savage until I am thug bro

@kaderen8461 Год назад

challenge: do the ones with square roots without them, as square roots technically involve other numbers like cube roots do

@Jamesdavey358 Год назад

@@JossWainwright huh? If Cube root isn't allowed then square root shouldn't be. Just because you can get away without writing the " ² " dosent mean it isn't there, you just don't write it because it's implied

@H0uxdubxston Год назад

@@JossWainwright when we first learned square root we would write the 2. At some point in math they dropped the two. It is there, you just can't see it. It is still introducing a new digit

@falling_banana Год назад

@kaderen8461 👍 finally, someone's thinking what i'm thinking

@falling_banana Год назад

@@H0uxdubxston exactly

@projectmoonsleeperagent Год назад

@@JossWainwright So I can write a square root, but say it’s implied as a cube root and then cube root now counts?

@LasTCursE69 5 лет назад

Wait isn't common operations just "+" "-" "/" "x" ? What's with the square roots and factorials? xD

@ThumbsTup 5 лет назад

Have you ever been to school?

@kaladin6199 5 лет назад

i partially agree i think that square roots are ok but i don't think that factorials count as simple common operations

@LasTCursE69 5 лет назад

@@ThumbsTup Yeah.. have you??

@ThumbsTup 5 лет назад

@@LasTCursE69 sorry, I misunderstood the question for a sec, my mistake. And, yes, I have

@LasTCursE69 5 лет назад

@@JossWainwright It isn't about the solution of the puzzle.. It's about how they phrase the rules and the question..

@Rinneganpein389295 5 лет назад

|{x,x,x}|! = 6 for all integers x between 0 and 10. Fight me.

@Anastasia___. 5 лет назад

Actually x can be any number :D Smart! :)

@duffy_io 5 лет назад

Underrated comment. This is the best solution.

@restablex 5 лет назад

So... Is " |{....}| " The math notation for counting an array?... Please correct me if I'm wrong...

@duffy_io 5 лет назад

@@restablex Braces { } denote a set. Elements in a set are separated by commas, so {1, 2, 3} is the set containing the elements 1, 2, and 3. The absolute value sign | | here is called the cardinality in set theory, and evaluates to the number of elements in a set. So |{3, 5, 27}| = 3. And then lastly we take the factorial of 3 which gives 6. The coolest part about this solution is that the elements can be absolutely anything. They don't even have to be numbers! |{duck, chicken, goose}|! = 6. Edit: As mina86 pointed out, technically a set cannot have duplicates of the same element. However I believe we could consider the numbers to be a sequence, which allows duplicates.

@restablex 5 лет назад

@@duffy_io thanks. So, cardinality is 3 even when the element is repeated? Just want to be sure that |{a,a,a}| is 3 and not 1.

@samhecht1492 5 лет назад

In the future please try to be a bit more specific in ur directions because it was unclear which mathematical symbols were allowed

@sondesobbaia1886 5 лет назад

he said all common mathematical operations which do not explicitly introduce a new number is valid... I used logarithm to solve 10 10 10 = 6 as log (10) = 1

@thunderbolto7611 5 лет назад

@@sondesobbaia1886 But why choose a base 10 logarithm? This is just a completely arbitrary base to choose.

@Nuclearburrit0 5 лет назад

Thunderbolt O because it is the only base that doesn’t require a number to be written in order to represent

@sanhakim1335 5 лет назад

@@sondesobbaia1886 log is not a common mathematical operation. The only ones are +×÷-. Square root is ambiguous because it's ^1/2, and there is no way that factorial is common. You will never use that outside of high school-college level math or above.

@J7Handle 5 лет назад

@@sondesobbaia1886 log(10) = 2.302... using the natural logarithm.

@roblatour3511 Год назад

0 0 0 = 6 ; put the first zero on top of the 2nd zero; 8 0 = 6; move the remaining zero to the other side of the equals sign; 8 = 0 6; move the zero one last time so that overlays the six; 8 = 8

@bro_vega_1412 5 лет назад

According to rule 1,you can use d/dx,and d/dx will make any constant 0,then you know what to do.

@Nathan-tg4gu 4 года назад

Favorite comment on this video

@suraj5957 4 года назад

Good one bro😝😝😝

@the_username_is_taken 4 года назад

_Rice_

@hedgehogmind3186 4 года назад

I don’t think calculus is allowed

@phrog7193 4 года назад

wow thats kinda boring.

@gamejunk2707 6 лет назад

3:30 NEIN NEIN NEIN

@einfachben0399 6 лет назад

@gamejunk2707 6 лет назад

Michael Foley kein Problem

@tirthrajmahajan2508 6 лет назад

😂 Guter Witz!

@andererletsplay8139 6 лет назад

geil

@zwischendurundmoll3968 6 лет назад

GameJunk geiler typ 😬😁

@1ups_15 3 года назад

each time you showed the solution I was like "how didn't I think of that?!!" haha

@NikhilTheGreatest 3 года назад

Same with me😂😂

@aubreyundi 2 года назад

In the instructions you said you cannot introduce any new digit, but can you explain how the factorial is not an introduction of new digits.. cause 3!= 3×2×1

@huyxiun2085 2 года назад

@@aubreyundi Sure, both introducing ! and square root are actually introducing new digits. But since there is a code for those which does not imply WRITING the digit, it's considered valid. It annoyed me too at first, but then, i realized there probably was no other way and that the problem needed that "trick". I fully understand you, the problem lies in the phrase "do not introduce new digit". Many people would immediately understand that "code without explicit digit, even if implicit, are fine". Others, like you and me, would immediately consider "implicit digits aren't allowed either, thus square root and factorial can't be allowed". I'm actually pretty sure most of the people are in the second situation. However most of those still are able to switch back to the first, by realizing the problem is impossible without this assumption. Don't be too extreme on implicit vs. explicit. There is not good solution. Both are always possible, and can always be extreme (go too far). If you assume implicit should be always the rule, then you can never solve anything. Because if you keep pushing in that direction, you never have a satisfying "proof". Nothing can be proved expect "cogito ergo sum", and stricly applying implicit rules means everything else is irrelevant. They you can just go back to bed and die. It's true with the other exageration. Explicit is ALWAYS possible, you can invent a new way of writing, a new code, which would make the exercice always super easy. But then everything becomes irrelevant too. Sure playing around the definition and the limits of a problem is fine... but first you need to accept the limits and definition, solve the problem WITHIN this conditions, and ONLY THEN you can play around with the rules and try to bend them. The big problem here isn't mathematics. It's understand what (most of) people would agree too. Not being able to understand what most of the others do or think is actually very frequent. It's also unfuriating, frustrating, because everybody around think you are odd while you did nothing wrong. Your interpretation is just different. It's fine being different, keep at it. But keep in mind that human beings progress A LOT by sharing knowledge and understandings. Thus what you need to do is to work on that too (and probably first). Then you can be different AND able to understand others, play with them, and learn from them.

@TheRenegade... 2 года назад

@@aubreyundi Technically multiplication is adding new digits because it's repeated addition

@memebaltan Год назад

@@aubreyundi a*b=a*a*a... b times ah yes, maeth

@gtaserisiturkiye Год назад

If the floor function is used, it will be valid for all positive integers. If the absolute value function is also used, it will also be valid for negative integers. Since we are using the floor function, it will be valid for all real numbers. It will even work with complex numbers. Here are some examples: floor(sqrt(11))*floor(sqrt(11))-floor(sqrt(11))=6 (|-1|+|-1|+|-1|)!=6 floor(pi)*floor(pi)-floor(pi)=6 (|i|+|i|+|i|)!=6

@Jan_Heckmann Год назад

Or you use the Cardinality, and it does not even have to be Numbers at all. Like (|{X}|+|{X}|+|{X}|)!=6 for all complex Numbers or anything else.

@M3lodicDeathmetal 11 месяцев назад

Actually that's true, repeatedly take the square root and floor in the end to reduce the problem to 1+1+1 and solved for any number.

@Ah-wz6nn 6 лет назад

I don't understand the "you cannot introduce new numbers" How is cube root introducing new numbers? Why can you use sqrt but not cube root?

@sebastien5048 6 лет назад

you don't have to write the number "2" when you write the square root symbol, while you do have to write the number "3" when writing the cubic root symbol

@matthewwilson8292 6 лет назад

But the square root is akin to raising the number to the power of (1/2)...

@acertainbastard5579 6 лет назад

Matthew Wilson Its technically a trick cuz u dont write the number

@Tehom1 6 лет назад

That's why I say that this is more of a text puzzle than a math puzzle. sqrt is canonically written without a number superscript, while cube root is canonically written with one. That's all.

@hunghinsun2123 6 лет назад

It is really strange that we can use sqrt but not cube root.

@danzirulez 3 года назад

nice, although one could argue that sq root 'theoretically' introduces the digit 2 into the equations. it is a defined symbol of sq root. Same way the 3rd root is not necessarily an introduction of the digit 3, it's a mere symbol, but a good puzzle nonetheless :)

@XariksBeatbox 3 года назад

Actually this argument wins, since sq root of any number is that number raised to the power 1/2

@manawer720 2 года назад

You could say the same with the factorial symbol, you are adding numbers and multiplying them even though you don't see them. I think that the puzzle's goal is to only have 3 visible numbers, and make a 6 out of it

@Dark_Voice 2 года назад

@@JossWainwright Tbh, it is totally "I wanna catch you with the rules" BUT the 2 is simply there as much as 3 is in the cubic one. The cubic sign and the square sign are just 2 signs that indicate 2 different functions. Either both or none. Otherwise, you are just being a ahole as the puzzle giver and trying to be a smartass. (Which I think is still wrong because square root still means 2 whether you write it or not - you included another integer.)

@Dark_Voice 2 года назад

@@JossWainwright I read milions of posts in the chain above. You're incorrect. Its simply that. You dont write it because of redundancy but its there whether you like it or not. Also, by proving you mean you will say to me that its exactly how you think it is.

@Dark_Voice 2 года назад

@@JossWainwright Whatever you say. The number 2 is assumed always there if you dont write it. It becomes invisible 2. The fact the video rules out 3√x which is x^(1/3) [the number 3 you can take like a part of the sign, not as an integer because the whole 3√x is a number, not just the 3] but leaves √x which is x^(1/2) is just trying to be a smartass and not working. The 2 is there just you dont write it to save time because everyone understands what you mean. End of story.

@chaincat33 4 года назад

"common mathematical functions that don't introduce new digits" >Uses factorial, extremely uncommon, albeit simple function >Uses square root but cube root and exponents are not allowed

@Simplifier123 4 года назад

By saying "common" I think he referred to "known".. And about the factorial being legal but exponents not, I think its because when you exponent a number you can manipulate the exponent itself (for ex: 2,3 etc.) but when using the factorial you cant do that because its a fixed function which only depends on the number you put factorial on and in this problem the numbers are fixed. For the root being legal and not the cube, I think thats because of the root being a basic function and using cube or anything else is just manipulating the basic function to be a different one. Thats my opinion though..

@3possumsinatrenchcoat 4 года назад

Exactly my thoughts, and seems I'm far from the only one.

@jaakezzz_G 4 года назад

John Jose cube root is not a manipulation of square root. Rooting a number requires a digit. It’s like saying that exponent 2 is a manipulation of exponent 1, it’s not, it’s just a different power exponent.

@Simplifier123 4 года назад

@@jaakezzz_G you didnt get my point.. my point is that factorial us a fixed function, just like adding or substracting or multiplying. In this example you need to use functions that you cant change them. Exponents however, you can change the exponent however you like.. 2,3,5 etc. Same for root you can do sqrt, cube or anything else but factorial depends on the number you do factorial on, you cant change the factroial function to work in a different way as you desire.

@archeosm8606 4 года назад

The one that stood out to me was taking a square root of the square root, that’s basically what he said was against the rules

@ItsJustEthan1 4 года назад

Ayyy best solution for 0 ( cos(0) + cos(0) + cos(0) )! Edit: Somebody already did this solution :(

@MaxMathGames 4 года назад

👍👍👍awesome solution dude, perfect .

@ck3908 4 года назад

0 to the 0 power added three times then factorial.... = 6

@snirpleinad8592 4 года назад

Your incorrect. cos (0) = 1, so ( cos (0) + cos (0) + cos (0) ) = 3

@lAlexLunl 4 года назад

@@snirpleinad8592 he wrote "!" in the end. So its (1 + 1 + 1)! = 3*2*1 = 6.

@rohankorale6381 4 года назад

@@ck3908 ahh, not exactly as 0^0 is indeterminate form 🤷‍♂️

@lebecccomputer287 5 лет назад

The 8’s one is actually really easy once you realize that if you can make it equal to nine you’re good: 8+8/8=9. Square root and factorial

@rperm834 2 года назад

So it is {√[8+(8/8)]}!

@ari998 3 года назад

For 8, I use the following equation: ((square root (8+8))!/8)! =6 explanation: 8+8 equal 16, square root of 16 is 4, factorial of 4 is 24, divided by 8 equal 3, and then factorial of 3 is 6

@-.a 2 года назад

you can't use cube root, which means you shouldn't be able to use square root either

@zaqcarson2875 2 года назад

@@-.a No, dude. That would be the fourth root of x. You can only build (power of 2) roots out of square roots.

@alexkelley8342 2 года назад

just use (8/8 + 8/8 + 8/8)! = 6

@1987Videolover 2 года назад

@@alexkelley8342 cant... because it only allow to use 3 digit not 6 like yours

@MarcoOS05 2 года назад

8 is as easy as number 10, but in 8 you add instead of subtract (square root ( 8 + ( 8 / 8))! =6

@mariusvr Год назад

There is a neat solution for the 8 8 8 using thermial. N thermial, noted n?, is defined to be 1+2+3+...+n, analogously to the factorial definition, but for sums instead of multiplication. Then 8? = 36 and one can easily do sqrt ((8+8-8)?) = 6

@priyenswiss2002 4 года назад

3:29 Adolf Hitler joined the room.

@jaydani1996 4 года назад

How?

@АязВалеев-ъ7з 4 года назад

Nain! Nain! Naaaain!!!

@heorgegarrison5554 4 года назад

N E I N N E I N N E I N

@user-fo4ue9mo4z 4 года назад

Heorge Garrison nine*

@heorgegarrison5554 4 года назад

ঊᴄᴏᴏʟ ᴘʀᴏ idk if you’re joking or not but 9 in English sounds like nein which is german for no, and Adolf Hitler spoke some form of german and who doesnt love a sprinkle of dark humour :)

@freewing3964 3 года назад

for 10 10 10, i just took the log of 10 which =1, then added them up and took a factorial.

@eriklagergren7124 2 года назад

"Clever girl"

@createyourownfuture5410 2 года назад

But log 10 (10) introduces a new number

@davisatdavis1 2 года назад

@@createyourownfuture5410 not if you use natural logarithm.

@freewing3964 2 года назад

@@createyourownfuture5410 Log base 10 is implied, same as the two in a square root. If you can use one, you can use the other.

@createyourownfuture5410 2 года назад

@@freewing3964 I see. Log base ten can be written as lg in the same way as log base e can be written as ln.

@doczero1296 5 лет назад

This comment section is full of nerds. I've never felt more at home.

@user-fo4ue9mo4z 5 лет назад

I only know about square roots but not factorials but factory is like saying 5! = 5x4x3x2x1 = which is 120

@ArtisticScratch 5 лет назад

@@user-fo4ue9mo4z Factorials are easy to understand but this video made me think factorials were addition rather than multiplication: 3+2+1 = 6 = 3x2x1

@AdithyaShankaran 4 года назад

@@user-fo4ue9mo4z so

@user-fo4ue9mo4z 4 года назад

ADITHYA SHANKARAN just explaining how factorials world, because most people don’t know about it!

@orngng 4 года назад

ঊᴄᴏᴏʟ ᴘʀᴏ also written out as n! = n x (n-1) x (n-2) ... x 3 x 2 x 1 As n is a member of a natural number

@sophomoremd 26 дней назад

I've solved the 6s challenge. Drink more and they become 7s.

@1q5 5 лет назад

Anyone else get 2+2+2 and then feel really proud of themselves?

@ElectroGaming5 4 года назад

Seb most of the comments are nerds lol

@JamesCPotter13 4 года назад

I got 2 × 2 + 2 and overcomplicated things.

@extremenugget3658 4 года назад

Shut up, using bad language is prohibited. Please refrain from such use of language, as it may result in ban (SOORY UTUBE ME SMOLL)

@ofcrgry 4 года назад

2! ^ 2! + 2!

@rudyorre 6 лет назад

So square root doesn’t count as adding a digit because you don’t have to write the 2?

@AssistoTudo 6 лет назад

yes

@MrGAS-pu3qs 6 лет назад

it should because it’s implied

@emadkhatri 6 лет назад

@@MrGAS-pu3qs then factorials shouldnt count because it implies multiplying other numbers, point is the notation using a digit, not if it implies the use of a digit

@dystopia-user181 5 лет назад

No it doesnt.

@sondesobbaia1886 5 лет назад

it is implicit.. as long as you don't write the number, then it is valid...

@nathanisbored 6 лет назад

why is square root allowed? is it because the index isnt shown? would log or ln be allowed for simliar reasons?

@SomeGuy712x 6 лет назад

I'm okay with allowing square root since that's the default for that symbol without a digit added to it. Also, I did end up using log for the 10 10 10 = 6 problem myself, coming up with log(10 x √(10^10)) = 6.

@paulkennedy8701 6 лет назад

Yes. Log and ln would be allowed if it's the natural log, since they are written without using an extra digit. Logs to any other base, where a digit needs to be written, would not.

@JohnDixon 6 лет назад

This problem is a test of our current mathematical symbols, so anything that doesn't explicitly use a digit in its symbol is fair game. The only non-numerical symbols that are usually excluded from problems like this are ones that would make the problems too easy or give some sort of "universal solution" that works for all numbers (e.g. the floor and ceiling functions).

@connorhorman 6 лет назад

It has been noted that floor(x) and ceil(x) are fair game. Also hi nathanisbored

@luisaguinaga9563 6 лет назад

Agree I did not use the squares. but I did not solve for 8, 9 or 10. I also tougth that the square root was not allowed

@С-8КОМ Год назад

For 10, i did [Log( 10 ) + Log ( 10 ) + Log ( 10 ) ] ! = 6. Usually log is base 10, so no new digits

@Able89535 11 месяцев назад

Nice, or we can use use ln or even sqrt directly if we introduce ceiling or flooring

@С-8КОМ 10 месяцев назад

@Able89535 yeah but I don't like to use floor or ceiling because they annot be described with regular math.

@Perezafer8 4 года назад

On 10 i did: (lg 10 + lg 10 + lg 10)! just another way to do it

@RB-cl8tc 4 года назад

@Govinda Solanki Vlogs how about (ceil(log(8))+ceil(log(8))+ceil(log(8)))! :O

@marcoasturias8520 4 года назад

If ypu exclude log, you should also exclude sqrt, both have a intrinsic number to the operation

@faraonzeu9462 4 года назад

@Bjjs you can use

@maithreebogoda8824 4 года назад

When u include lg you automatic include log base 10. You can't include extra digits

@mariush.215 4 года назад

@@RB-cl8tc and how about: ( sin(8!)! + sin(8!)! + sin(8!)! )! = 6 8! = 40320 sin(40320) = 0 0! = 1 1+1+1 = 3 3! = 6 voila, a hard way to solve it! :D (I figured it out myself)

@RichardChen 6 лет назад

We can use the function: (lnx+ln(sqrt(x))/ln(sqrt(sqrt(x))). It is always equal to 6 when x is not 0 or 1.

@asmodeojung 6 лет назад

It's a shame such an elegant solution went unnoticed.

@johannesvanderhorst9778 5 лет назад

Beautiful, and this even doesn't depend on the base of the logarithm you choose, so (log(x) + log(sqrt(x)))/(log(sqrt(sqrt(x))) also works.

@89Kravien 5 лет назад

Very nice one! Just move one parenthesis to make it work: (lnx+ln(sqrt(x)))/ln(sqrt(sqrt(x)). Should be three ending before the division.

@DasMonitor1 2 года назад

I would say it's a good trick to remember that 3! is because this means if any operation gets you to 3 you have solved the problem. For 10 10 10 and 8 8 8 I also used the fact that 9 is the square of 3 and so getting a result of 9 also immediately yields a solution. Finally any of these numbers can yield their own digit + or - 1 by simply addying or subtracting the quotient of the last two digits. And you have just gotten a rule for basically any of these numbers. ( For 0 0 0 you simply use the fact that you can reduce it to 1 1 1 and then 1+1+1 is 3, and thats all your numbers done in very few steps)

@XYZGarfieldZYX 9 месяцев назад

But square was not allowed I guess

@Joeljr110 9 месяцев назад

He isn't squaring 3 in his example he is sqrting 9 to get 3 which then he factorials to get 6.@@XYZGarfieldZYX

@Joeljr110 9 месяцев назад

I used the same approach but made a mental list along the way to knock off more variations. In the example below I am only going to match the previous number and not all the operations to get back to the original 6 = 3! = sqrt(9) Then I also though of ways to manipulate the original equation: to get to these numbers x/x = 1 x-x = 0 (x+x)/x = 2

@dablitter5719 Год назад

this is one of the few puzzles i could actually do and it was actually pretty fun

@NestorAbad 6 лет назад

This ones are very amusing! In fact, there's another trick to solve any equation of this type, N N N = 6, for any positive integer N: if we consider the "floor" function as an allowed one to use (defined as floor(x)=the biggest integer less than or equal to x, so for example floor(pi)=3 and floor(e)=2), we can always concatenate square roots of N until we have 1 < sqrt(sqrt(sqrt(...sqrt(N)))...) < 2 , hence floor(sqrt(sqrt(sqrt(...sqrt(N)))...))=1 and we have reduced the problem to "1 1 1 = 6", so adding up the ones and taking factorial, we're done: ( floor(sqrt(sqrt(...sqrt(N))...)) + floor(sqrt(sqrt(...sqrt(N))...)) + floor(sqrt(sqrt(...sqrt(N))...)) )! = 6

@MindYourDecisions 6 лет назад

Wonderful, I think that is fair game since the floor function is commonly used. And your method also leads to a good mathematical question: why does repeatedly applying the square root lead to a number between 1 and 2? Alternately stated: why does the nth root of a number tend to 1? Here's one proof: planetmath.org/limitofnthrootofn

@NestorAbad 6 лет назад

That's right! Or even easier: given a fixed N we can always find n big enough so that 1

@Tehom1 6 лет назад

Interesting. One could do the same with the ceiling function and get everything into the form (2,2,2).

@Mutlauch 6 лет назад

I also used the floor and the ceiling function but because when those equations were introduced to me I also thought that sqrt isn't allowed, I solved them with the e-function and its inverse. Greetings from Germany :)

@Sam_on_YouTube 6 лет назад

That's like the 4 4s problem, which can be done for any number using the same method. I forget the exact method, but there is a numberphile video on it.

@chitrakshsinha9007 6 лет назад

I have another way for 4 4 4 = 6. It is 4+4-√4.

@7llininthedream 6 лет назад

Well done. BLOG IT

@16anurag9 6 лет назад

Same

@valdehuesagoddessphoebej.1082 6 лет назад

does that read 4 plus 4 negative square root of 4?

@chitrakshsinha9007 6 лет назад

@@valdehuesagoddessphoebej.1082 Yes.

@ba2138 6 лет назад

Sphynx it’s minus not negative

@tushermajumder7211 5 лет назад

In binary method 10 implies 2 Thr for, 10 +10+10 equal to 6

@21nod 5 лет назад

In binary method there is no 6

@lotsofd6739 5 лет назад

bachelors of trolling degree, 2013 there are 110,but it’s not 6 also 110₍₂₎=6₍₁₀₎ but it’s useing diferent number, “2” so we can’t do that

@21nod 5 лет назад

@bachelors of trolling degree, 2013 I know my comment didn't encourage your creativity (which is something that has to be praised) but all I wanted to achieve is challenge you even harder.

@supercool1312 5 лет назад

Tusher Majumder 6 is 110 in binary. 10*10+10 is 110. easy

@ralphy1054 5 лет назад

No 10+10+10=110

@StevenTorrey Год назад

A good part of the solutions relies on the student knowing the basic laws of mathematics and what it is that the student is allowed to do with math to solve these problems.

@Shad0wWarr10r 6 лет назад

Well... since cube root is illegal so should square root, as thats badicly the same thing, just doing 2 factors instead of 3. Its the most common root and therefor the 2 is not written. But theres still a "hidden" 2 there

@feastures 6 лет назад

Yeah, I hate these obvious mistakes in a puzzle that's supposed to be smart.

@yurenchu 6 лет назад

You need to learn the difference between a _digit_ and a _number_ . Digits are symbols/characters; if a digit is not written, then it is not used.

@TheAkashicTraveller 6 лет назад

Can't introduce new digit. Doesn't say can't remove digit. Doesn't say can't re-use a digit. 6=6 for everything. Done. The rules are just badly designed. He should have just given a list of operations you can use and the three digits and said use those to make these digits equal six.

@yurenchu 6 лет назад

Jack Evans, - "Can't introduce new digit." Exactly, that's what one of the two rules explicitly says. - "Doesn't say can't remove digit." If you remove a digit, for example, from the cube root function, then the cube root function will not function as a cube root function anymore; instead, it wil be a square root function. (For example, the statement ³√(3³) + 3 = 6 cannot be changed into √(3³) + 3 = 6 without also changing its truth value.) If you're referring to one of the three given numbers: The problem states that you have to start with these three numbers. There is, as far as I know, no mathematical operation that simply "removes" a number. (Well, someone in the comments mentioned "Waiter Mathematics" and wrote 6 + IGNORE(6) + IGNORE(6) = 6, LOL!) - "Doesn't say can't re-use a digit." If you insert another number, that counts as introducing a new digit; for example, 3 + 3 + 3 - 3 = 6 doesn't count, because the addition of the fourth 3 requires adding another digit "3". - "The rules are just badly designed." The rules given are clear and simple. Just because you don't like them and don't want to accept them, doesn't mean that they are badly designed. - "He should have just given a list of operations you can use and the three digits and said use those to make these digits equal six." He didn't give three digits, he gave three _numbers_ . When will people learn that digits and numbers are not the same thing?

@qaerkyr9197 6 лет назад

By same logic factorial should be illegal as well since N! has hidden all the terms until N-1 - N! = 1*2*3*..*N

@yassinesafraoui4540 5 лет назад

for 444=6, there is an easier way to solve it: 4+4-√4=6

@65EKS65 5 лет назад

Define easier? It's just different way to solve it. Also knowing that √4=2 we can solve it the same way than we solve 2 2 2 without need of inventing new method to solve it so I'd say √4+√4+√4 is more simple.

@oenrn 5 лет назад

@@65EKS65 "Easier" as in requiring the minimum amount of steps.

@65EKS65 5 лет назад

@@oenrn I'd see what you mean if the problem was long but in this it doesn't take any more time to calculate either way. The easy part is that 2 2 2 is already solved and everyone knows that √4=2 so I think it's more complicated to try calculate something different even if it requires less steps if the other answer is already on the table to be seen. But yeah idk. Not big difference either way.

@threej4pope 5 лет назад

Given that square roots are technically illegal in a strict reading of the rules, I solved this one via (4 nPr 4) /4

@InterestingStuffWithMe 5 лет назад

Personally I feel that subtraction is harder and more of a hassle than addition hence I don't think it's an easier way Anyone else thinks the same way?

@mayinho 5 лет назад

A moment of silence for those who don't know what the heck is factorial

@dougthegamer8920 5 лет назад

@lipo-tz2qn 5 лет назад

I knew something fishy was up with this video so i learned factorials and then returned back to this

@alexandramuller9055 5 лет назад

It basically expresses in how many ways you can arrange a set of numbers e.g. 4! Is 24 because if you can have (just an example) 24 ways 4 people can sit on 4 chairs.

@MightyBiffer 5 лет назад

4! = 24 1 * 2 * 3 * 4

@alexandramuller9055 5 лет назад

@@MightyBiffer I already edited it maybe you should refresh your page.

@theunknownspeedrunner276 Год назад

I don't know if logarithms and exponentials are allowed, if they are, I might have found a way to break this problem: we know that ln(e) = 1, and we can add or substract an unlimited amount of these, since they don't use any digits. So 4 4 4 could be solved this way: 4+4-4+ln(e)+ln(e) = 6 This works with all integers not only the one from 0 to 10, and frankly you could do anything you want with the 3 numbers, as long as the result is an integer, and you balance it with the appropriate number of ln(e). This however makes the problem useless and a lot less fun.

@tarbosh917 3 года назад

This seems more like a conversation starter on: 1.) How to define 'Common Mathematical Operations' 2.) Whether square root or factorial notations are cheesy ways to follow a 'no new digits' constraint. Seems more like we get there on wordplay more than anything. Still a great video on how to get creative with math notations to make seemingly impossible sets of digits get to a given result. I'd have left the rules/wordplay out of it because it feels like for anyone else to arrive to the correct answers you need to debate the instructions and what is or isn't allowed.

@eugenesaint1231 2 года назад

Cheesy is the correct answer. Just sane... :^) Saint

@bradleyhuffer2429 5 лет назад

For 6 6 6=6, would the sixth root of (6^6) be allowed? I wouldn’t be adding any new numbers...

@indzcvlixnnm4286 5 лет назад

{[(😂😂😂)']!+[(😂😂😂)']!+[(😂😂😂)']!}!=6

@MartinPuskin 5 лет назад

Of course.

@adityakrishna11 5 лет назад

sweet

@davids3094 5 лет назад

6x6:6

@juhoaurejarvi6942 5 лет назад

You could just 6+6-6=6

@crazzanthictlabbar1056 2 года назад

Was stuck on a few until you mentioned factorial. I completely forgot about factorial!!! As soon as you mentioned it, things became so much clearer...

@yousufmohammad9309 Год назад

(x^0+x^0+x^0)!=6 will work for any value of x If you think that violates the law of adding a new digit by adding zero, try turning it into a set and take the cardinality. |{x,x,x}|!=6 But it doesn’t violate it because ^0 is an opperation.

@sanp2032 3 года назад

I did something similar to this known as the four fours challenge where you have four fours and you could use arithmetic operations upto factorial to make any number out of the four fours. I find challenges like this super interesting and cool

@Aerxis 3 года назад

Try doing it with 3 copies of 3. It's solvable

@Aerxis 3 года назад

@@JossWainwright any natural number is possible, but that's somewhat advanced. As a direct continuation of the four fours puzzle, I recommend the three threes puzzle, in which you must express each digit as a combination of three copies of the number three and math operators and parentheses.

@Aerxis 3 года назад

@@JossWainwright both versions of the puzzle are solvable, the factorial operator is very helpful either way.

@Jasmineaq 3 года назад

Honestly, these videos are so helpful. They have helped me grow a real interest with maths, and a substantial increase in my grades. Thanks for making these!

@bradmorris67 5 лет назад

for 10 10 10, can I use (LOG(10)+LOG(10)+LOG(10))! = (1+1+1)! = (3!) = 6 ??

@dominuspiritus 5 лет назад

u should use LG, not LOG (which means LN)

@johannesvanderhorst9778 5 лет назад

I won't allow that, because for me unspecified logarithms have base e, not base 10.

@googlestore4830 5 лет назад

All depends on the notation. In calculators (and outside pure math), log x can be interpreted as log base 10. In Russia, however, lg x is log base 10, elsewhere lg x is considered log base 2, which brings us to another possible solution for 8 8 8: lg 8 + lg 8 - lg 8. But since the use of logs can be ambiguous, it is best to always specify the base (and to never split infinitive).

@weirdBatt 5 лет назад

Johannes van der Horst who asked you? Nobody cares about your personal opinion, that’s just false, and not how logs work. ln is shorthand for log base e and log without a specified base should be assumed to be log base 10.

@medexamtoolscom 5 лет назад

Rather than log(10), how about ╓.10╖? That's the least integer function. Then it works with any natural number.

@marinerusher5252 Год назад

technically there is a universal solution to any set of 3 numbers, as you can just take the derivative of all of the digits to make them all 0's, then you can take the factorial of all the digits to make them all into 1's. Then add them all together to get 3. Then take the factorial to get 6. This solution works with everything I believe.

@captaincroissandwich6950 3 года назад

My alternate solution for 10 10 10 = 6 was [ Log(10) + Log(10) + Log(10) ]! = 6. A Logarithm of 10 in base 10 is 1, reducing it to a 1 1 1 = 6 solution path.

@phantm487 3 года назад

log base 10 introducing a digit there

@qo7052 3 года назад

in some customs, log without a base can either symbolise base e, 10, or 2

@rex17ly62 3 года назад

@@qo7052 hence why a 10 is needed to discern that it is base 10 and not base e for example.

@lamexd 3 года назад

@@phantm487 bro if you could use square root without introducing 2, why can't log. Everyone knows log without a base written is log base 10 and ln is log base e

@lamexd 3 года назад

@@rex17ly62 bro log is base 10 only if it's not mentioned otherwise, log base e is ln

@cday9206 4 года назад

So basically... just use factorials and you’re all good

@hao_cuii 4 года назад

@ThomasTheThermonuclearBomb 2 года назад

For the tens, you could also take the log (assumed base 10 since there is no base written) of all of them and then use the solution for the ones

@huyxiun2085 2 года назад

I thought of that. However isn't log alone kind of forbidden? Log in decimal must be written "log10" "default log" doesn't exist in correct mathematical writing, and is closer to "ln", which if "just log" is written should be the one applied (in my opinion) Still, works with the assumption. Or you can NOT make the assumption. (... don't read the solution if you want to give it a try) Use the second "10" to specify which log you are refering to: sqrt(10-log10(10))! = 6

@ThomasTheThermonuclearBomb 2 года назад

@@huyxiun2085 I thought the “common log” was log base 10. It’s also common for calculators to not support based logs other than common and natural. For example you have to say for log base 2 of 3, (log3)/(log2)

@Foxy_Fan1200 Год назад

I learned what a factorial is because of this video!I love learning new things!

@mimikal7548 5 лет назад

Square root shouldn't count because you are introducing a new digit (2).

@elijahlefavour8562 5 лет назад

Then you can’t use parentheses because you are multiplying by one (distributive property)

@naunidhdixit2878 5 лет назад

Actually we don't use the digit 2 while using an under root/ square root

@kapilbusawah7169 5 лет назад

Naunidh Dixit it is x**(1/2)

@naunidhdixit2878 5 лет назад

@@kapilbusawah7169 ya ik what it is but the thing is it can be written in a form where we need not use "2", but in case of a cube root there is no such form that exists, we have to use a "3" anyhow to symbolise a cuberoot, but in case of under root it is "possible without using a 2"

@detachsoup6061 5 лет назад

Also he says you cant use the cubit root, but using a sqaure root over a sqaure root makes a cubit root, he cheats!

@nickp1942 5 лет назад

Watching this video and its comments, kills my brain cells.

@sharrydominguez15 5 лет назад

Nick Ko 😂 feelings are mutual

@Legendnewer 5 лет назад

We should not stay here, one of the nerd's bases

@Green24152 5 лет назад

And if we ask for real questions, everyone tells us to drop dead. He's brainwashed them to think we are math meanies.

@rgwashere8723 5 лет назад

I did 8 in a much more complicated way: The square root of 16 (8+8) is 4. 4!=24. 24÷8=3. 3!=6

@retsoptihs0 5 лет назад

That's exactly how I did it.

@Viritox 4 года назад

Me too.

@sonoritta 4 года назад

((√(8+8)!)÷8)! So like this? That's cool 😃

@rgwashere8723 4 года назад

@@sonoritta yeah

@hilariomaluka1284 4 года назад

8+8+8=24 and 2+4=6 so simple is not it

@fernandoalonsooliveira6090 Год назад

Consider n as a generic Real number. If you take the limit of x/x when x tends to n, the result is always 1, whe then can get to the 1 1 1 = 6 case, and solve the puzzle for any number, even if it is negative, has several digits and decimals.

@Rytroic 4 года назад

Me sitting in my room and is in 4 grade: WHAT da heck

@jackwaibel8812 4 года назад

The legend Of god709 Pathetic, I’m a junior and still dont get it

@52.yusrilihsanadinatanegar79 4 года назад

if we know each other, then hi

@tentic 4 года назад

I solved this by myself in 7th grade weird flex but ok

@sameash3153 3 года назад

Legend 🙌

@javedansari-nb2pk 3 года назад

@@tentic wait, Whatt!?? I am in 9th and I still don’t know what is factorial?....

@dlu0813 4 года назад

I know the 0 0 0 one: (0! + 0! + 0!)! = 6 YaYYYY!!

@inx1819 4 года назад

Ahhhh that's smart

@Sid37612 4 года назад

Congrats!

@lolol-real8752 4 года назад

or you can just do 0 0 6 = 6, then remove the 0's since again there're no rules for that, and then get 6 = 6!

@hadi174 4 года назад

@@lolol-real8752 You cannot introduce a new number on left hand side.

@lolol-real8752 4 года назад

@@hadi174 i was kidding

@manurohit6867 4 года назад

For 4 we have a method as follows: 4+4-√4=6

@Osirion16 3 года назад

You can also do 4!/√4/√4

@u.s.4129 Год назад

A nice one, thanks Presh

@selcouthdood4622 3 года назад

My math teacher gave me this problem like last week. Only seen this video right now. If only I had seen this video a week ago.

@rbm0307 3 года назад

do you think that your teacher might have watched this video 1 week and 1 day ago??

@harfian471 3 года назад

@@rbm0307 no doubt

@gblargg 3 года назад

These remind me a lot of optimizing bit operations in assembly code, especially trying to get it to operate on multiple values packed into a word (without using SIMD instructions).

@Florakinz 3 года назад

Nice analogy!

@merdansoltanow2049 5 лет назад

(n°+n°+n°)!=6 for any n-real number 😎🤓

@maxwellndlovu4461 Год назад

Wait a minute, isn't one of the rules not to use the square root of 3 cause it involves a new number 3? Well in the same way can't we say the square root cannot be used cause it involves the new number 2? At 0:33.

@maxwellndlovu4461 Год назад

@@JossWainwright But the square root has 2 in it as a different number.

@maxwellndlovu4461 Год назад

@@JossWainwright Plain Root Sign has an unwritten 2 sitting on it plain and simple.

@natanboyd5749 2 года назад

For any number greater than 1 which we’ll call n, you can get 6 by doing (log base sqrt(sqrt(n)) of n * sqrt(n)) Edit: I know log is a function and not an operation I was just trying to generalise it lmao