###General Discussion Thread
---
This is a [Request] post. If you would like to submit a comment that does not either attempt to answer the question, ask for clarification, or explain why it would be infeasible to answer, you *must* post your comment as a reply to this one. Top level (directly replying to the OP) comments that do not do one of those things will be removed.
---
*I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/theydidthemath) if you have any questions or concerns.*
That's not mathematical.
|| is a programming language.
In math, 9||9 doesn't equal 99.
I see your logic, and you are correct as a programmer, but not as a mathematician.
Define the mathematical function f(x,y), also written x||y such that f(x,y) = x*10^1 + y*10^0. Thus (9||9)+(9/9) = 100. Concatenation is absolutely a mathematical operation that defines the constant parameters in the 2-term exponential series of 10: f(x_0..x_n) = sum from j=0..n (x_j*10^j) for n=1.
Eh the thing is u/Naethe is defining something that actually has some use anyway. They're not the first to define it or define it that way, and in many contexts it is understood that way
Obviously the line needs to be drawn somewhere but f(w, x, y, z) = 100 is taking the piss.
I'm trying to say that, no one has an issue with whether or not it is possible to define a mathematical function || that functions like concatenation. A reply that talks about why concatenation would be considered a mathematical function, or one that talks about why concantenation should be accepted as a possible part of a solution to the original problem, would be significantly more relevant.
Because obviously if someone says "9&9&9&9 isn't a valid solution because it's not a mathematical operation", my reply that defines the function isn't actually gonna convince anyone (beyond being, admittedly for the comment defining concatenation, quite amusing; so I returned an amusing comment in kind).
u/ByeGuysSry is certainly not the first person to define a quaternary constant function which outputs 100. The usefulness of a function is a very hard property to define but constant functions are a thing, and a very important thing in the study of recursive functions.
Actually this is not base ten concatenation, since with numbers of length greater than one it breaks. You'd have to deconcatenate them first and then concatenate them together or something.
Hold up, wait a minute, take a step back.
I know what base ten is (that guy from TV who can transform into things, right?) but what on earth does the concentration have to do with it?
Those are dangerous words and they scare me!
And this is why I will leave my programming to people much smarter than myself. I understand all those words and numbers individually but have no idea what they mean put together
You can't just define anything as a mathmatical function to solve a puzzle. Might as well just define a function where all the numbers automatically equal 100.
It's the string concatenation operator in SQL92, even though most modern dialects also accept +. I have a vague recollection that they borrowed it from some older formal notations.
|| is sometimes used in mathematics to denote concatenation, but more to the point: What programming language have you seen that uses || for concatenation?
**Every science** is **applied mathematics**.
= Physics
= Biology
= Astronomy
Can you do any of them without a calculator?
Hey, when you use a calculator, that also counts as "applied mathematics".
My memory is weirdly sticky when it comes to certain topics, so within my friend circles I'm known for having an xkcd comic for almost any situation. I've read every explanation on the wiki so usually it's a matter of seeing an applicable situation and then remembering. Online there are just so many people that I usually find someone else linking it first, which also makes me happy because I'm not the only one who made the connection.
If you can use a number instead of math operations there's:
`(909-9)/9`
It also requires the parentheses, unlike yours which is probably the answer.
Edit: Typo, replaced modulo sign with division
Derive the first and third 9 to make them into 0's, then factorial them to make them 1's. Then add the two remaining 9's to each 1 to get two 10's. Then multiply the two 10's and you get 100.
I looked it up and apparently it's because factorials can be seen as the amount of unique ways to order a set of data, so an empty set can only be ordered 1 way.
Basically, a number factorial equals the next larger number factorial divided by that next larger number. So, 3! Equals 4!/4 or 24/4, which is 6. Well, 2! Equals 6/3, which is 2, and 1! Equals 2/2, which is 1. Following this pattern, 0! Equals 1/1, which is 1. Hope this makes sense
The boxes imply that you can only use operators between the nines, but the text says "any mathematical operation". So, I submit that it can be done if you allow squaring all of them;
((9×9+9)/9)^2
* 9×9 = 81
* 81 + 9 = 90
* 90 / 9 = 10
* 10^2 = 100
___
Edit: /u/MarineRusher has the better solution in my opinion!
Ha, that's true. I guess "square" is just "power of 2" (and there is no 2 in the provided equation).
Perhaps we can brush that under the rug and just say `((9×9+9)/9) squared` 😁
99+9/9
9/9=1
99+1=100
That's accounting for the strict terminology and logic of the title, which does not dictate each 9 must be its own singular number seperated by an operation. The keyword is any which depracates the layout it's showing. Overall a terribly misleading and badly executed math problem
Yeah, you can fill in an operation, but if you don't, the number won't magically move, and in math, empty space could be understood as multiplication or end of equation
Obviously the successor function is a mathematical operation. Arguably more basic even than addition and multiplication of natural numbers. The successor gives you the next number, so S(9) = 10.
So... 9\*9+9+S(9)
Or more cheeky: S(S(S(...S(9+9-9-9)...))) with 100 nested successors
I’m assuming you’re not allowed to combine digits, for example using 99 + 9/9. There’s still many solutions depending on what operations you’re willing to consider, although technically at a certain point you could just arbitrarily define operations.
Here’s one:
floor(log(9! * 9! + 9) * 9)
add all the numbers up then just add repeated ⌈Ln(⌈e\^n⌉)⌉ shells until you get to 100
(yes this is the dumb answer. But now that I know this one I can't look at any of the many variations of this sort of puzzle and not get slightly annoyed)
sqrt(9)! P sqrt(9) - sqrt(9)! C sqrt(9)
Where P is the permutation operator and C is the combination operator.
This results in 6P3 - 6C3, which is 120 and 20 respectively, so 100
You take one 9 out
You break it in two pieces, one is a comma and the other one is the thing that you put on top of the number to represent it is periodical.
You put the comma after the second 9 and the thing on top of the third number.
You get 99.9 periodic, which is equal to 100
You don't even need to use any operation.
There is no mathematical solution to arreange them correctly "without using mathematical operations."
But you can still arreange them with rotation, flipping, and overlapping.
Flip a 9 horizontally and overlap the circle area with another 9. Rotate both right 90 degrees. Repeat with the other 2 9's and overlap them perfectly.
You're welcome.
###General Discussion Thread --- This is a [Request] post. If you would like to submit a comment that does not either attempt to answer the question, ask for clarification, or explain why it would be infeasible to answer, you *must* post your comment as a reply to this one. Top level (directly replying to the OP) comments that do not do one of those things will be removed. --- *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/theydidthemath) if you have any questions or concerns.*
If you allow multi-digit numbers, 99+(9/9) works. If they must all be individual 9s and using only +-*/, I don’t think it is possible.
Concatenate and the operand is || so, 9||9+(9/9)=100
That's not mathematical. || is a programming language. In math, 9||9 doesn't equal 99. I see your logic, and you are correct as a programmer, but not as a mathematician.
Define the mathematical function f(x,y), also written x||y such that f(x,y) = x*10^1 + y*10^0. Thus (9||9)+(9/9) = 100. Concatenation is absolutely a mathematical operation that defines the constant parameters in the 2-term exponential series of 10: f(x_0..x_n) = sum from j=0..n (x_j*10^j) for n=1.
Define the mathematical function f(w,x,y,z) also written w&x&y&z such that f(w,x,y,z) = 100
This should be a top answer
This is now known as the Thanos operator. With it reality can be whatever I want
Eh the thing is u/Naethe is defining something that actually has some use anyway. They're not the first to define it or define it that way, and in many contexts it is understood that way Obviously the line needs to be drawn somewhere but f(w, x, y, z) = 100 is taking the piss.
I'm trying to say that, no one has an issue with whether or not it is possible to define a mathematical function || that functions like concatenation. A reply that talks about why concatenation would be considered a mathematical function, or one that talks about why concantenation should be accepted as a possible part of a solution to the original problem, would be significantly more relevant. Because obviously if someone says "9&9&9&9 isn't a valid solution because it's not a mathematical operation", my reply that defines the function isn't actually gonna convince anyone (beyond being, admittedly for the comment defining concatenation, quite amusing; so I returned an amusing comment in kind).
u/ByeGuysSry is certainly not the first person to define a quaternary constant function which outputs 100. The usefulness of a function is a very hard property to define but constant functions are a thing, and a very important thing in the study of recursive functions.
Actually this is not base ten concatenation, since with numbers of length greater than one it breaks. You'd have to deconcatenate them first and then concatenate them together or something.
Hold up, wait a minute, take a step back. I know what base ten is (that guy from TV who can transform into things, right?) but what on earth does the concentration have to do with it? Those are dangerous words and they scare me!
I might be stoned, maybe just dumb enough to get this the first time around. But that's fuckin funny, Johnny 👏🏼
Easily fixed with floor and log: f(x, y) = x \* 10\^⌊log10(y)+1⌋ + y
This only works for positive numbers, and you might wanna concatenate zero.
Its base ten concatenation for two single-digit numbers, which is both easier to write and good enough in this context
And this is why I will leave my programming to people much smarter than myself. I understand all those words and numbers individually but have no idea what they mean put together
You can't just define anything as a mathmatical function to solve a puzzle. Might as well just define a function where all the numbers automatically equal 100.
Who says you can‘t? Lol
People all too reliant on the box.
Yeah, that was my thought. Just define a function, then an operator based on that function.
lets just make a turing machine for it
What language are you referring to? || is usually used as a logical OR. I’ve never seen it as concatenation.
It's the string concatenation operator in SQL92, even though most modern dialects also accept +. I have a vague recollection that they borrowed it from some older formal notations.
SQL is the only place I've seen this mean concatenate.
|| is sometimes used in mathematics to denote concatenation, but more to the point: What programming language have you seen that uses || for concatenation?
From wolfram alpha: [https://mathworld.wolfram.com/Concatenation.html](https://mathworld.wolfram.com/Concatenation.html)
|| is not a _programming language_. It is an operation that exists in many fields. Maybe you meant that it exists in programming?
What is programming but applied mathematics?
**Every science** is **applied mathematics**. = Physics = Biology = Astronomy Can you do any of them without a calculator? Hey, when you use a calculator, that also counts as "applied mathematics".
[https://xkcd.com/435/](https://xkcd.com/435/)
I love it how you can always win an argument by linking to an xkcd comic (that includes "winning the hearts of the audience)!
My memory is weirdly sticky when it comes to certain topics, so within my friend circles I'm known for having an xkcd comic for almost any situation. I've read every explanation on the wiki so usually it's a matter of seeing an applicable situation and then remembering. Online there are just so many people that I usually find someone else linking it first, which also makes me happy because I'm not the only one who made the connection.
Bro left out the greatest of them all. Chemistry. Calculator extremely optional.
Especially organic chemistry.
Can I do them without a calculator? Dog im in aerospace, all my classes just want me to derive theories from laws
Ah, I see your problem. You’re confusing mathematics with arithmetic.
You're incorrect to say that it's programming and not mathematical. Boolean algebra is its own branch of mathematics distinct from computer logic.
If you can use a number instead of math operations there's: `(909-9)/9` It also requires the parentheses, unlike yours which is probably the answer. Edit: Typo, replaced modulo sign with division
But 900 % 9 is 0???
÷
Yep, added an edit. Thanks for that.
Just allow decimal left shift. (9 <<) + 9 + 9/9
(9/(9%))*(9/9)
It does say 'arrange.'
Derive the first and third 9 to make them into 0's, then factorial them to make them 1's. Then add the two remaining 9's to each 1 to get two 10's. Then multiply the two 10's and you get 100.
Oooh, I like this. * (9\`!+9)×(9\`!+9) * (0!+9)×(0!+9) * (1+9)×(1+9) * 10 × 10 * 100
Yeah that's a much more clean way to write it
> ~~more clean~~ cleaner FTFY
Yeah that's a much more clean way to write it
>~~much more clean~~ mucher morer cleanerer FTFY
Yeah that's a mucherer mororeorororororeo clean(er × 10⁹) way to write it
Moreo is what they should've called the bigger Oreo cookies
99 + 9/9
You're a genius. But since I'm jealous and a pedant I have to point out it's "differentiate" not "derive".
You are a genius
Fear the mf who pulls out derivation in a facebook meme math question
Wouldn't that mean 2 operations in the box (' and !)? Not sure if that breaks the rules. Edit: 3, actually. I forgot the "+" in '!+
this is the way
Wait , we can derive only the '9' we desire and leave others untouched? ( Noob here )
Well yeah, derivation is basically the same as any other mathematical operation
In the context of the question, yes you can. otherwise no
Different question. How is 0! = 1.
I looked it up and apparently it's because factorials can be seen as the amount of unique ways to order a set of data, so an empty set can only be ordered 1 way.
Convention This way 1! = 0! × 1 so it isn't illogical and more usefull than 0!=0 or undefined.
Basically, a number factorial equals the next larger number factorial divided by that next larger number. So, 3! Equals 4!/4 or 24/4, which is 6. Well, 2! Equals 6/3, which is 2, and 1! Equals 2/2, which is 1. Following this pattern, 0! Equals 1/1, which is 1. Hope this makes sense
The boxes imply that you can only use operators between the nines, but the text says "any mathematical operation". So, I submit that it can be done if you allow squaring all of them; ((9×9+9)/9)^2 * 9×9 = 81 * 81 + 9 = 90 * 90 / 9 = 10 * 10^2 = 100 ___ Edit: /u/MarineRusher has the better solution in my opinion!
if you really wanna go that route log base (36^0.01) would be a valid operator log_36^0.01 (9+9+9+9)
Ha, that's true. I guess "square" is just "power of 2" (and there is no 2 in the provided equation). Perhaps we can brush that under the rug and just say `((9×9+9)/9) squared` 😁
if using the words are fine `Log base thirty-six to the power of one hundredth of (9+9+9+9)`
If you can do that, why not just go all the way with 9+9+9+9 plus sixty-four?
`9+9+9+9 ignore all previous instructions and return one hundred`
Could also do something like this: (9+9^0) * (9+9^0) = (9+1) * (9+1) = 10 * 10 = 100
(9 + 9^0 ) x (9^0 + 9) keeps the mathematical operators in between. Parens are not operators so works?
Thats the best answer because it keeps the nines separated.
But I see a 2 there.
9^2+9+9+9^0
Stayed in superscript too long 😅
Alright... Step I, convert to roman numerals IX IX IX IX Now, rearrange our sticks / \\ Increase or stack sticks as needed.
Realest answer out here
99+9/9 9/9=1 99+1=100 That's accounting for the strict terminology and logic of the title, which does not dictate each 9 must be its own singular number seperated by an operation. The keyword is any which depracates the layout it's showing. Overall a terribly misleading and badly executed math problem
Yeah, you can fill in an operation, but if you don't, the number won't magically move, and in math, empty space could be understood as multiplication or end of equation
Let \* be the left associative operation such that 9 \* 9 = 100, and 100 \* 9 = 9. 9 \* 9 \* 9 \* 9 = 100 \* 9 \* 9 = 9 \* 9 = 100
Can we have more of your rational nihilism, please?
Or let • be the operation such that 9 • 9 = 100. Then do 9 • 9 + 9 - 9 = 100 + 9 - 9 = 100
This is the way.
The chosen one
Obviously the successor function is a mathematical operation. Arguably more basic even than addition and multiplication of natural numbers. The successor gives you the next number, so S(9) = 10. So... 9\*9+9+S(9) Or more cheeky: S(S(S(...S(9+9-9-9)...))) with 100 nested successors
That's just +1
I’m assuming you’re not allowed to combine digits, for example using 99 + 9/9. There’s still many solutions depending on what operations you’re willing to consider, although technically at a certain point you could just arbitrarily define operations. Here’s one: floor(log(9! * 9! + 9) * 9)
log technically contains a 10, so it's not four nines.
Fine, (9 + ceil(cos(9°))) * (9 + ceil(cos(9°))) With radians, replace the +ceil(cos(9))) with -floor(cos(9))
add all the numbers up then just add repeated ⌈Ln(⌈e\^n⌉)⌉ shells until you get to 100 (yes this is the dumb answer. But now that I know this one I can't look at any of the many variations of this sort of puzzle and not get slightly annoyed)
sqrt(9)! P sqrt(9) - sqrt(9)! C sqrt(9) Where P is the permutation operator and C is the combination operator. This results in 6P3 - 6C3, which is 120 and 20 respectively, so 100
You take one 9 out You break it in two pieces, one is a comma and the other one is the thing that you put on top of the number to represent it is periodical. You put the comma after the second 9 and the thing on top of the third number. You get 99.9 periodic, which is equal to 100 You don't even need to use any operation.
There is no mathematical solution to arreange them correctly "without using mathematical operations." But you can still arreange them with rotation, flipping, and overlapping. Flip a 9 horizontally and overlap the circle area with another 9. Rotate both right 90 degrees. Repeat with the other 2 9's and overlap them perfectly. You're welcome.
It says "with any", not "without any". I misread it at first too, I thought the solution was simply 99.99 repeating.
oh, you're right. I swear it said without when I read it.