Can You Solve The Four 9s Puzzle?

[@ericdraken]

9 x 9 x 9 x 9 = 100 (in base 81)

[@bigolbearthejammydodger6527]

beautiful! I saw the obvious answer, I thought about makeing a silly comment for sultions in base - you got there first. nice one.

[@lucascaracas4781]

This was posted on the community tab a few months ago, there it didn't explicitly say that you can't use the other digits, so in that case it was possible to just 9+9-9-9+100=100 That exploit was fixed in the more well explained version, which is this video

[@bonkser]

​@@lucascaracas4781no thats 82

[@phuonglinh4775]

Wait what

[@lox7182]

9 x 9 x 9 x 9 = 0 base 81

[@DrFunkman]

Damn, I spent around 15 minutes looking at the thumbnail and trying to brute force the answer, not knowing I was allowed to just use 99

[@drublu]

I feel your pain, I did the same thing!

[@lowlevelcodingch]

same

[@lowlevelcodingch]

but this mf over you...

[@anujparihar6350]

The closest i got was 99 while using operation between each 9 like 9x9+(9+9)

[@_somerandomguyontheinternet_]

Yeah, the thumbnail was a bit misleading. I struggled, but then I realized he said you just have to “press 9” four times.

[@wyattstevens8574]

99+9/9 (who said there had to be an operation between *every* pair of 9s?)

[@rogerkearns8094]

It's All Fools day, so perhaps that's it.

[@wyattstevens8574]

@@rogerkearns8094 I had heard of this question before and remembered that this was at least one solution to the problem.

[@YouTube_username_not_found]

@@wyattstevens8574 Yeah, me 2, but because of the thumbnail, I got an impression that I should put something between each 9

[@kimspence-jones4765]

That was my solution

[@mensaswede4028]

That was my first thought when I saw the thumbnail.

[@therat1174]

I got to 118.62... Close enough for engineering

[@artemisfowl7307]

For myself I assume 9=10 so I just have to do 9*9*9/9

[@1a1u0g9t4s2u]

Not close enough for engineering. You must be thinking of the kids game response...close enough for horseshoes and hand grenades.

[@skilz8098]

I'd think that 99.99 would be closer and still good enough for engineering.

[@kkkaaa1210]

I got the same answer 😂😂😂😂

[@richarddecker9515]

No wonder Sheldon Cooper has no respect for engineers

[@HanzoHimemiya]

basic solutions: 99+9/9 adult solutions: logaritms,trigonometric an exponents

[@mjs28s]

math is skill based. Age doesn't mean that you are or are not educated and skill in it. Simplicity is more adulting. Adding unnecessary complexity is over thinking. Remember, the KISS principle?

[@boom-jr8vi]

@@mjs28sWell I assume he is referring to the common subjects that most if not all adults have learnt in later education but maybe I’m wrong.

[@YellowBunny]

In my opinion sqrt() shouldn't be allowed as it contains a 2 that we just don't write by convention and % should definitely not be allowed because it is just a symbol for division by 100. Edit: Concatenation and stuff like .9 also feels like it's just cheating.

[@snelake]

never said you have to put an operation between each 9, so it’s technically not concatenation, the thumbnail’s just misleading

[@catburner1896]

Seeing % confuses me as in programming it stands for modulo( remainder ).

[@noobartz0890]

same applies to log

[@FocusLRHAP]

.9 is actually 0.9

[@FireyDeath4]

Same applies to any non-enneative hyperoperation

[@SanketAlekar]

Anything that uses "0.9" or "99%" isn't "pure", as it uses 10 implicitly.

[@walterengler5709]

A agree. Any answer suddenly tossing in a period (as .9) implies you divided by 10 or some other value and hence is invalid. Hence 99/99% is allowed (as 99/.99 = 100). But (9x9+9)/.9 directly would fail. However (9-9+9)/9% would be fine.

[@Kram668]

Agree: 99 also implies 9*10+9

[@walterengler5709]

@@Kram668 Though I will admit the overall out of the box creativity coming up with all the varied solutions .. that was a joy watching lol.

[@stevenfallinge7149]

Square root also feels cheaty, would like a solution without concatenation, the decimal point, or square root.

[@Angi_Mathochist]

0.9 isn't legit because the 0 isn't allowed. The question is whether .9 is a legitimate representation of the number 0.9 or not. It is commonly used and understood, so I think it pretty much has to be accepted as legit. And there's nothing wrong with using 10 implicitly. The % operator divides by 100. That's the definition of that operation. It's still just one *common symbol*. Similar for concatenation, which is defined as multiplying the first number by 10^x, where x is the number of digits in the second number, and adding the second number. And the decimal point, which divides by some multiple of 10, depending on where you put it. And factorial, which multiples together every number from 1 up to the given number. The puzzle isn't to get to 100 mathematically by only using 9s and nothing that could be interpreted as involving any other numbers. It's to get to 100 by only using 4 9s *and common mathematical symbols* (operations).

[@leickrobinson5186]

6:43 Small nitpick, but you say arccos of “zero degrees”, but the input to arccos is not an angle. It should be just arccos of zero.

[@MindYourDecisions]

Good catch, I said "arccos 0 degrees" when I should have said "arccos 0 in degrees mode". It's a dangerous thing to omit a word or two in mathematics!

[@forcelifeforce]

On the same topic, cos(720) will not work in this video, because it assumes degrees goes with 720.

[@robotech2566]

@@forcelifeforce thats wrong, cos 720 will work,as the deg button in calculator is allowed

[@mb-3faze]

If you're allowed log, arccos and cos, why not antilog? antilog(9/9 + 9/9) Or antilog((9-9)! + (9-9)!)

[@victorkaplansky]

The last solution is known universal solution which works not only for 9s and 100 as result.

[@agilsaelan]

Indeed. I've seen this kind of solution in another video

[@pranavyadav208]

9 || 9 + 9 ÷ 9 = 100 || is the sign for concatenation. Saw it on Numberphile's video, Matt Parker.

[@Sqrt.Infinity]

Ok

[@cheeseparis1]

Yes! let's play magic squares!

[@mrblakeboy1420]

look at the calculator. concatenation isn’t on there

[@harrytsang1501]

Depends on the programming language you speak, ++ also works

[@skilz8098]

@@harrytsang1501 Typically || is OR not concatenation.

[@cmilkau]

I like the cheekyness of the last solution as you can use it to make any number from almost any 4 copies of the same digit (only 0 and 1 fail) just by adjusting the number of square roots

[@thisisachannelwhy42069]

All rational numbers can be achieved using this method, and it can be written as a beefy 2-layer logarithm, to avoid base 10/base e bias

[@白先生-e8w]

（909-9）/9

[@joachimsimon1433]

Basically we can use 3 and 6 for the 9 since • 3 = sqrt 9 • 6 = 3! = (sqrt 9)! Furthermore we can also use 1/2 because 1/2 = cos (tan-1(sqrt 3)) Finally we have (1/2)^-6 + 6*6 = 100

[@matthewthompson6455]

beautiful

[@nekoafterlyfe]

sqrt isnt allowed because its like pi

[@benhur2806]

Based radians solution...

[@TheJaguar1983]

That last one is just insane. I was looking for a log-based solution, but that is nuts.

[@skld-xm]

same LOL

[@bernhardkrickl5197]

In the last one, it doesn't actually matter if you use 9s or any other numbers (as long as you use the same number four times, and I actually mean number, not only digits). The trick is that pressing the sqrt function 100x ultimately gives you the 100. You could press it any number of times to get any number you like. It's sort of a magicians trick where the magician makes you think of a number and gives you instructions to compute another number from it and then proceeds to guessing that number correctly. It mostly works because the computation cleverly cancels out the number you started with and always gives the same result which the magician can then conveniently "guess". In conclusion, I consider this method cheating.

[@MastuurOogwaay]

I believe i found a really good solution that doesnt 'twist' any of the rules: (9+cos(9!)) * (9+cos(9!)) = 100 because cos(9!) = 1 Or another one: arccos(9-9) + 9 + cos(9!) = 100

[@Buzz-o7]

woah, this is really clever! and its much simpler than the ones shown in the video. Good job!

[@BonjourMonde-cx8mt]

very unique solution

[@billbender4005]

cool, as long as you use degrees and not radians

[@hannafabian1965]

Dang, this is smart!

[@obsidi2]

Better then the ones in the video

[@Gruuvin1]

It's annoying when the video thumbnail is not the same as the challenge. The video thumbnail implied there must be some operator between each nine, and so I worked on it a bit before clicking. Then I felt cheated. Wasted time.

[@blazingstar9638]

Happy April fools day?

[@darryllmaybe3881]

That last one is actually just so beautiful and can be applied to literally any number so long as they are all the same number since it derives its answer from the properties of logs rather tricks with the specific number. Technically, "(x/.x)(x/.x) will also evaluate to 100 as well regardless of x's value, but that's a little cheap since ".x" implies dividing by 10 or using a 0, plus it's not nearly as elegant.

[@Sam_2014]

I have an interesting solution 9.9with a line on top of nine multiply itself=9.999…x9.999…=10x10=100

[@felipedutra5276]

Neat!

[@JonathanLidbeck]

Or simply: "99.99..."

[@Sam_2014]

@@JonathanLidbeck That’s simple and decent!

[@ur.local.deuterium.atom.6974]

uhhhhhhhhhhhhhhhhhhhhhhh😂😅😢

[@electricportals3644]

The logarithm one at the end was my favorite, it literally just incremented to 100 in a clever way. In degrees, arccos(sin(9!))+9+9/9=100 If you allow using different meanings of common mathematical operations you can also do (9^3)*(9^3)=100 using ^ as a bitwise xor

[@orionspur]

Gluing digits together, or using the decimal point, or using the % sign, are all quietly invoking 10s. Seems unfair.

[@AlejandroGarcia-co8uk]

how is concatenation involving 10?

[@orionspur]

@@AlejandroGarcia-co8uk It is 10x+y.

[@justanotherLunny]

Agreed, the idea should be to use only four 9s to solve it, not to use the massive myriad of numbers you can get from 9 to do it.

[@edgeman83]

I wonder if there is a solution using the graphic from the thumbnail, where there is a single operation between the numbers. This would remove being able to turn 2 9s into 99 and also prevent multiple operations between the numbers.

[@sy8146]

Thank you for explaining. I found 3 other answers. 99 + 9/9 , 99 + log[9] 9 {Base: 9} , 99 + (9-9)!

[@supermilktv557]

9-9=0

[@sy8146]

@@supermilktv557 Excuse me? What do you mean? I know 9-9=0. And (9-9)!=1

[@CecilPonsaing]

"What an incredible solution" and What an incredible solution (the log example) ... RC: and it's goodnight from me, RB: and it's good night from him.

[@Macciejable]

(9 + sgn(9)) * (9 + sgn(9)) Or with 3 9s, without sgn(), but with square function, which I think should be allowed if a sort is allowed: square(9 + 9/9)

[@alienn_o.o]

using sgn function is smart 👍

[@alexanderschreiter943]

That last solution is beautiful as it’s a wonderful general case solution allowing you to replace the nice with any number as long as they are all the same as their purpose is only to cancel the logs and you can get any integer you want by just increasing or decreasing the number of sqrt in your numerator quantity

[@dreael]

The last solution has also a nice property: It works with any base. You can use the natural log, the common log or any base b of your choice. Reflected to the calculator, it doesn't matter if the log key used the natural or the common log.

[@DeleteKernel]

the immediate successor of 9 * 9 + 9 + 9

[@kefrov]

cos(9-9) + 99

[@dgtheone]

How did you get 99?

[@TearTheRoof0ff]

​@@dgtheoneConcatenation

[@RobloxBacon_Playz123]

no but that gave me ((cos(9)) - 9) + 99 = *90.9877*

[@lethalty6055]

I have to say, this was a pretty good April Fool's video!

[@Inspirator_AG112]

*Here you go...* 9 ^ ((√9)! ÷ √9 ÷ log(9)) = 100 Assumption: 'log' refers to the common log (base 10). (Which is true for most calculators...)

[@aadfg0]

Another log solution: (a_0 - a_2 + a_5)/a_7 where a_n = log √ √ ... √ 9 = 2^(-n) log(9) with n square roots. It equals 2^7 + 2^5 - 2^2 = 128-32+4 = 100.

[@navadeepkandre6741]

I am watching you, after a lot of time... You're still the same amazing, when I used to watch you earlier... Now I think I will continue watching your content.

[@shrshar99]

Same!

[@cmilkau]

I would rule out the percent sign, as it literally means 1/100 making this way too easy. 9/9% = 100 already (using two more 9's without changing the result is an easy exercise). While you could see it as an "operation", I think it is more commonly viewed as *notation*, a shorthand for writing "over 100" so it's similar to why you would rule out e^x and π

[@1mattwilson83]

I love how the simplest solution is right, but they had to make it complicated because it was too easy XD

[@paulobouhid6648]

Hi, Presh. Of course you are familiar with the well-known Four 4´s challenge. A long time ago, after solving it, I wondered if I could do the same using FIVE 3´s... and I succeeded. If you are interested in this, just let me know how do I send it to you. Cheers from Brazil.

[@jedagelijksebraintraining]

I made a video about this...

[@kenrickman6697]

This reminds me of something I do at work to entertain myself (using locomotive numbers, if anyone is curious). Given any four random digits in a given order , make an equation using any mathematical operator which does not introduce a new digit (I.e. X^2 is not allowed, but X^Y is, as is square root). I have found very few numbers for which I could not come up with something.

[@lagomoof]

Logarithms can often be used to pull out how many times a square root was used, like in the last example. Seriously overpowered. There was a mathematical paper about it. And it has an implicit 2, so technically it ought to be disallowed. X^Y is still OK though.

[@gyletre675]

with python code: int("9" + "9") + 9/9

[@Badspot]

((9*9)+9+9)++ = 100 If concatenation and adding a decimal point (multiplying and dividing by 10) are considered common mathematical operations, then surely increment counts as well.

[@hhhhhh0175]

i remember numberphile showing off the last solution years ago for the four 4s problem, glad to see it's still around when you said you just wanna see 100 displayed in the calculator in the intro, my immediate thought was to just keep pressing factorial and square root until it happens to get close enough to 100 to round to it in whatever floating point data type the calculator is using

[@wengtongwong991]

You only need one 9 to make 100 by using the identity csc(arccot(x))=sqrt(1+x^2) csc(arccot(sqrt(9)))=sqrt(1+9)=sqrt(10) csc(arccot(sqrt(10)))=sqrt(11)...and continue until you reach sqrt(10000) Both csc(arccot(x))=sqrt(1+x^2) and sec(arctan(x))=sqrt(1+x^2) will do the task.

[@OGSomeOne]

I am not certain that you can do .9 under your rules because the actual nomenclature is 0.9 so you using numbers other than 9

[@Mike-H_UK]

Inv log (9/9+9/9)=100 but probably too easy to count.

[@BKNeifert]

It'd be addition, multiplication, subtraction and division. Cosine and Sin both use ratios, which are a kind of number. So do radians. It's also bad literary theory, to try and defy the meaning that's obvious. Like, intrinsically, the square root of 9 is 3, not 9. You know? You don't treat a square root as the number being square rooted, but as its own separate number. But, even so, it's clear they meant the four standard operations, and trying to be tricky and get around that is not listening to the instructions, nor trying to comprehend what is meant.

[@n00b2001]

In my opinion, "common" operations are addition, subtraction, multiplication, division and maybe exponents - can this be done with those operations? and no concatenation (or however it's spelled, the creation of new numbers like 99 in this example)

[@nvid]

Only if you accept counting in base 81 instead of 10, in that case it would be 9*9*9*9=100.

[@the-boy-who-lived]

99+9÷9=100 You just said I have to press 9 four times. Operations between all of then wasn't necessary Edit: I just watched the video and realized this answer was presented in the video

[@pbenikovszky1]

13:02 Presh: "It's going to show something that's very close to 100, but not exactly 100" Calculator shows: 100.00000000000 Presh: My point exactly :D

[@ramuk1933]

My failed attempt: 9×9+9=90 you can use trig and inverse trig functions to swap any number for a another number in ghe same pythagorean triple, and using an online list, 9->15->8->10 90+10=100 ... Except you can't do that because you need numbers for the fractions P.S. I didn't allow concatenation (not a common mathematical function), adding a decimal point (b.c. that's just dividing by 10, sqrt (2 rt 9, 2 isn't allowed), or log or ln (b.c. they are log_e and log_10, respectively, and e and 10 aren't allowed).

[@bigolbearthejammydodger6527]

before watching the anwser: my answer is (9 9)+(9/9) = 100. just because you CAN, put an opperator between those numbers doesn't mean you have to - and i think this is the simplest solution.

[@XerosOfficial]

9 * 9 + 9 + floor(W(9!)) or if you'll allow the preincrement operator then we can do 9 * 9 + 9 + ++9

[@noobartz0890]

2:00 i love how both mazes can easily be solved by going around them

[@M1Miketro]

(ln 9 + ln √9 + ln √√√√9) / ln √√√√√√9 Yes, I am a programmer.

[@benbooth2783]

Divide 9 by 9 to make 1, then concatenate the other two 9s. 99 + 1 = 100.

[@ChrisM-tn3hx]

The least number of keypresses would be 9/9+99. I am of the opinion that the most efficient answer, not the most creative answer, is the most intelligent one. A working solution is better than a theoretical one. Intelligence and intellectualism are distinct qualities, and not synonymous. I think over-analyzing something that can be quickly solved is a trap of intellectualism. In fact, it's one I'm engaging in right now lol. In a practical sense, though, I think that if I was able to solve this "puzzle" in a split second with the most efficient solution possible, the benefit in a practical sense is in having another 13 minutes and 30 seconds of extra time to use for some other purpose, such as answering another 200 puzzles, or getting some other task done, putting information to practical use, etc. Then I realized that I used it to compose this instead, which in retrospect is kind of ironic. So much for making good use of my time. Damnit. See what I mean?

[@mugiseyebrows]

I changed rules slightly and found interesting solutions for three nines: exp(log(9 * 9) / log10(9)) and two nines: exp(log(9) / log10(sqrt(9)))

[@IamGod13th]

To be honest i didn't liked sqrt, .9 or % methods, because they imply there is ^(1/2) or 1/10, or 1/100. But still it is a good puzzle! Thank you! =)

[@hhgygy]

% is not a basic mathematical operation. It's a sign for the basic operation of division by 100.

[@djconnel]

I'd argue a decimal place is not a mathematical operation. Mathematical operations take input values (a number) and return output values (a number). The decimal place modifies the meaning of proximate symbols, but it is not transforming a number. For example,, "5" is a number, ".5" is a different number, but "..5" is undefined. 0.5 is equivalent to .5, but "0." is certainly not an operator. "%" is arguably a mathatical operation (as is per mille: ‰). "%" as a binary operator is typically taken to be modulo division: 99 % 9 = 9. Is "%" as percent a unary operator? I would guess yes -- it converts a number into another number. any number % is another number, and 5%%% could be claimed to have well-defined meaning (5/million). As to trigonometric functions: degrees are not the default unit of angle in mathemetics: radians are. You can specify degrees with a symbol, but that symbol is not an operator.

[@eroraf8637]

99 % 9 = 0.

[@djconnel]

LOL! You’re right, of course.

[@Meshamu]

I didn't see that you included a solution that matches what was implied by the thumbnail. Did I miss that part of the video, or just not pay enough attention? How can you do it in 8 button presses, counting the equals sign? With a single operation key pressed between each of the 9s, and only in those places?

[@nickfoght3181]

A bit cheeky, but my calculator can also handle gradians (as well as convert units between degrees, radians, & gradians) so: While in degrees mode: 9*(9+9/9)=90 Convert 90⁰-> 100 gradians. Done

[@raffimolero64]

I think the purest version of this puzzle must exclude: - sqrt (implicit 2) - % (implicit /100) - decimal point (implicit /10) - concatenation (implicit *10+) - log (implicit base 10, replace with ln instead) - degree mode (implicit 360 degree turn) I'm not sure if we should include floor/round/ceil operators. i wonder if it's still possible.

[@MakNabil10]

If you include the ceiling function I think the solution would be : ceil(9 + sin(9) )^( ceil(sin(9)) + ceil(sin(9)) )

[@legobrainbikergaming7422]

should the natural log, log base 10 and the square root be allowed?

[@kevskevs]

If you get rid of e^x and 10^x, you should also remove ln and log.

[@vh2296]

Putting a decimal dot is not a mathematical operation. You are changing the number to something else 9 is not equal to 0.9

[@pozzowon]

The way to get around e^x in this type of problems is to write exp(x) for exponential

[@ASAPSquatterRemoval]

99 != 9, .9 != 9, cos(9) != 9, arccos(9) != 9 & log(9) != 9. I believe the equation must contain 4 quantities of 9 & not just have 4 expressions of the symbol 9. Therefore there was truely only 1 equation that was presented in the video that was valid which was a genius solution btw 👍.

[@deerh2o]

The concluding solution is just fabulous!

[@cheeseparis1]

and it's universal, the goal number is the number of times you have to press "square root"

[@jonkmist]

the only reason i clicked on the video is to make sure that 99 + 9/9 is allowed. figured it out in seconds no flex

[@NihaarB]

What I have gotten is (9^(1/log9))*(9^(1/log9)) where log9 is log nine base 10(like in a calculator) but I cant write it like this as i can't write 1. Can anyone find a way to express it in terms of log other than the one in the vid?

[@joeschmo622]

9*9 + 9 + 9 = 100, for extremely large values of 9.

[@vezeryk6706]

I have it like this: arcctg[sqrt(sqrt(9))]*arctg[sqrt(sqrt(9))]/(9+9)=100 1800/18=100 Just switch to degrees when you have sqrt(3) so that the arctg and arcctg give 60 and 30

[@clivegreen7139]

9+9+9+9 = 36, which is 100 in base 6. The problem doesn't explicitly stipulate denary numbers. Just saying.

[@douggarfinkel2415]

There is no nine in base 6

[@clivegreen7139]

@@douggarfinkel2415 Agreed.

[@Rahaf_98]

I spent a whole week thinking about this bc of the thumbnail & I was so frustrated bc I wasn’t able to solve it so today I gave up & decided to just see the answer.. this was not satisfying at all.. all this thinking was for nothing? why did you put squares between all 9s in the thumbnail😭😭😭

[@Warmine000905]

Easy answer, you should have removed one more button 😄 Presses 9/9=1+(9/9)=19=20= and so on

[@PhinioxGlade]

When did the % button on a calculator work as percentage? It was always modulus on every physical calculator I’ve used. So confused as a kid why percent output seaming random integers

[@Andy_Paluzzi]

Wait, so for that last solution, does that mean you can make any number the same way? For any number "n" you just need a "n" number of square roots and everything else should follow the same, right? That's pretty cool... However, despite many of these being mindblowing, I don't agree with allowing log, square root and even the percentage sign, since all of these have numbers hidden in them. log is the inverse of 10^ , so there's a 10 in there (Log base 9 would be fair, I guess). Square root has a 2 hidden in there and the percentage sign is really 1/100.

[@DylanSargesson]

".9" shouldn't be allowed because it's introducing a 0. "%" shouldn't be allowed because it is introducing two 0s (divides by 100). In my mind "common operators" are just addition/subtraction and multiplication/division, nothing else.

[@gnusnotutopia]

the arccos solution is very fun, definitely my favourite here it strikes a nice balance between simplicity and flashiness with minimal repeat operations also it could’ve been fun to use log base 9(9) as a 1 substitute as in the main solution tho i guess arbitrary-base log isn’t a super common operator

[@matthewkrambeer2480]

I was able to come up with the 2nd to last solution in this video on my own, and I thought that would be the best. But that last one was really something. Kudos.

[@finlandtaipan4454]

I spent about 2 seconds coming up with the simplest solution 99+9/9. When you deleted the 10^x function, I immediately saw 10^(9/9+9/9) but it was gone.

[@MeNowDealWIthIt]

I think I saw on a numberphile video that that logs and sqrts trick works with any "four of one number, combine with operations to equal a goal number" problem

[@friedmule5403]

Since you are allowed to use factorial, what about double factorial?

[@oscarfreemantle5883]

Although there's no recurring function on a standard calculator, I still think that it could be considered a mathematical function. ? In which case, 99.99(recurring) = 100 (100÷3=33.33 recurring. 33.33 recurring × 3= 99.99recurring) Would like to hear arguments against this method.

[@xerotoninz]

99.99 = 100, floating point rounding

[@ViniciusCortezao]

My solution: 9/9% 9/9 I put it on the calculator and the result is 100 The % is percentage and the 9 after % means multiplication. I like this solution because it fills in exactly the gaps in the thumbnail

[@joelakowei1757]

11:49 *Extra "9" is 2^100 equals 1.267 nonillion (the 9th -illion number)

[@collingallaway5541]

I love the answer using logarithms and 100 square roots, it’s so clever

[@joestevens5467]

I can't find the "over" key. Shouldn't one say "divided by" when using a horizontal bar?

[@kevlingcustomtitantrons9375]

Before watching the full video my answer is: (cos(√(9)!!)+9)×(cos(√(9)!!)+9) = 100 I decided i wanted to find a way to use 4 of the 9s (without combining or adding decimals because those aren't 9s, they're .9s and 99s, but i also didnt wanna make it too complicated) so i did this. After about an hour of trying it for myself i finally got this. Now if i had realized i couldve done the first part twice, i probably would've done it in half that time, but i was trying too hard lol

[@kevlingcustomtitantrons9375]

It was in the video lol I didn't realize as I hadn't watched the full thing

[@shruggzdastr8-facedclown]

The conjoining of two or more isolated digits into a number unto itself actually has a mathematical term, which is: concatenation

[@alexanderschreiter943]

Another option is using infinitely many square roots to turn two nines into ones than add them to the other two nines to make two tens and multiply them together

[@alexanderschreiter943]

(9+sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(9))))))))))))))))) * (9+sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(9))))))))))))))))) ≈ 100

[@Black_hole_hungry]

I got it the answer is (9^0 + 9)×(9^0 + 9) Explanation: 9^0=1 so it will be (1+9)×(1+9) And 1+9=10 so next is will be 10×10=100

[@stella.excite]

I'm seeing a lot of comments saying sqrt is cheating because it invokes 2 (which I agree with), but don't think anyone's mentioned this applies to log implicitly invoking 10.

[@chrishelbling3879]

99.99....... = 100. Or so they want you to believe.

[@absolutezero9874]

Hi Need your help in this question Thanks Question: Seven children ABCDEFG started walking from the same point at the same time with speeds 1:2:3:4:5:6:7 respectively and they were running around a circular park. Each of them carried flags of different colours. Whenever two or more children meet, they place their respective flags at that point. However, nobody places more than 1 flag at the same point. They are rubbing in an anticlockwise direction. How many flags will there in total, when there will be no scope of putting more flags?

[@absolutezero9874]

Is my solution correct? G meets A k/6 s later When they meet, Distance A walks = k/6 m G meets B k/5 s later When they meet, Distance B walks = 2k/5 m G meets C k/4 s later When they meet, Distance C walks = 3k/4 m G meets D k/3 s later When they meet, Distance D walks = 4k/3 m G meets E k/2 s later When they meet, Distance E walks = 5k/2 m G meets F k s later When they meet, Distance F walks = 6k m F meets A k/5 s later When they meet, Distance A walks = k/5 m F meets B k/4 s later When they meet, Distance B walks = 2k/4 = k/2 m which is at the same point as where G meets E F meets C k/3 s later When they meet, Distance C walks = k m which is at the same point as where G meets F F meets D k/2 s later When they meet, Distance D walks = 2k m which is at the same point as where F meets C F meets E k s later When they meet, Distance E walks = 5k m which is at the same point as where F meets D E meets A k/4 s later When they meet, Distance A walks = k/4 m E meets B k/3 s later When they meet, Distance B walks = 2k/3 m E meets C k/2 s later When they meet, Distance C walks = 3k/2 m which is at the same point where F meets B E meets D k s later When they meet, Distance D walks = 4k m Hence, They meet at the starting point, which is at the same point as where F meets E D meets A k/3 s later When they meet, Distance A walks = 4k/3 m which is at the same point as G meets D D meets B k/2 s later When they meet, Distance B walks = k m which is at the same point as where F meets E D meets C k s later When they meet, Distance C walks = 3k m which is at the same point as where D meets B C meets A k/2 s later When they meet, Distance A walks = k/2 m which is at the same point as where F meets B C meets B k s later When they meet, Distance B walks = 2k m which is at the same point as where D meets C B meets A k s later When they meet, Distance A walks = k m which is at the same point as where C meets B Therefore, The points where no 2 other ppl meet are at where G meets A, G meets B, G meets C, G meets D, G meets E, G meets F, F meets A Hence, Total 7 flags?

[@skwest]

Keypresses in order, separated by commas: 9, 9, +, 9, ÷, 9, = (on my cellphone's calculator I don't even have to use the "()" keys)

[@forcelifeforce]

*@ MindYourDecisions* -- If you were allowed cos, then cos(0) would be short for cos(0 radians) = 1. However, you cannot use cos(720) to mean 1, because it means cos(720 radians) ~ -0.76. Any solutions you have that rely on a trig function of an argument, where the argument would have to be in degrees, are not legitimate.

[@cheeseparis1]

he puts the calculator in degrees mode. cos 0 degrees is also 1.

[@forcelifeforce]

@@cheeseparis1 -- No, a degree symbol is an extra character that is required to do it for cos(720). You have to be able to write it out, and it independently work. No setting to "degree mode."

[@cheeseparis1]

@@forcelifeforceOf the calculator, the "DRG" button is allowed. You can set the mode you want according to the math to perform, at least it's what I understood.

[@AndrijGhorbunov]

arccos argument is not in degrees, it's just a number between -1 and 1, since arccos x is just 'an angle whose cos is equal to x'

[@daboffey]

I would have liked to include an overdot (for a recurring decimal).

[@32a34a]

Short answer. Nope. I can't even solve real life problems let alone Math Puzzles. Kudos to all the smart people out there.

[@RyanG-ks9ev]

Thumbnail made me think it has to be four nines with three common functions between each (e.g. 9+9+9+9, 9+9x9-9, etc) and of course no combination of +-÷x ends up at 100 doing it that way.

[@fluffycritter]

That last one is incredibly creative, unlike me, who only went for the 99+9/9 one.

[@biggerdoofus]

9 back 9 * 9 + 9 = 100 Looking at the thumbnail I immediately thought of 9 < 9 * 9 + 9 = 100 That said, I don't most of these solutions, because they all feel like either loopholes to use more digits (like %) or using functions rather than operators (like square root).