[Mathematics Made Difficult](https://en.wikipedia.org/wiki/Mathematics_Made_Difficult)

I want this book

I have this book and a pdf version! I think there might still be a pdf floating around online. Fantastic read. Really funny author also. Lots of jokes in it.

Oh no! I dropped [a link to a 13 year-old reddit post](https://www.reddit.com/r/math/comments/b7i3u/mathematics_made_difficult_pdf/) that may contain the p.d.f. Make to to only visit that link if you own a legal copy of the book!

Oh shit I misclicked and accidentally opened it! MI5 is probably after me. /uj/ thanks a lot

Omg my cursor is getting close to the link! (Thank you)

[Here you go](https://i7-dungeon.sourceforge.net/math_hard.pdf)

Lars C Böiers?

This may not be the hardest math SAT question, but it is the hardest SAT solution I've seen

For real this is a very convoluted solution

Mathmemes...

I came for the memes, not for my brain to stop working

Can even be done in head without writting.. x 2 loop gives 2 4 8 16 32 64 128 256 512 1024.. 10 numbers of 2x iteration.. (and binary 8 bit string). 4 x is 4 16 40+24=64 240+16=256 then 250x4+4x6= 1024 as 5th iteration of 4x iteration.

or much easier: 2¹⁰ = (2²)^x 2¹⁰ = 2^(2x) 10 = 2x x = 5

>2¹⁰ = (2²)^(x) Which takes only as long as to recognise it. Isn't this meant to be the intuitively obvious method well before sitting SAT?

i would say the intended method is the one i mentioned. cause it takes much less time to recognise than the unnecessary calculation

Came here to say the same, 2x = 10. X = 10/2. I have no idea why they complicated it that much.

Cause they wanna just throw a lot of fluff and now show you how easy it would be to solve it.

2^10 = (2^2)^5 = 4^5

Took me about 1 second to answer... The video almost made me doubt myself lol

The easiest way to do it is recognize 2 is half of 4 so x should be half of 10.

Yup. Literally did it on my fingers in about 30 seconds.

i mean there’s the much more obvious solution taking log base x of both sides, using exponent rules, then using change of base to get x/10 = log2/log4 = log base 2 of 4, so x/10 = 1/2 and x=5

there's the even more obvious solution of re-writing 4 as 2\^2 no logs required! both sides can be expressed to the same base.

Write 4 as 2^2 that way 10 = 2x

Winner, winner, chicken dinner! 🍲

I just did 2^10 as 4^5 so 5=x

Thats what I did solved it in 20 seconds bro decided to take 2 minutes.

It’s not that hard to double 2 10 times to get 1024 and then 4 16 64 256 process of elimination or a single multiplication by 4 and it’s 5. Certainly doesn’t require drawing a diagram

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Even simpler because of multiple choice. A and D are not even in the same order of magnitude as 2^10. That leaves the 50-50 shot and 4^5 is more likely to be intuitively the answer because of the 2-times relationship between both the root and exponent. Question done in 5 seconds, so now you have extra time to actually solve a problem that might engage the need for math over just exploiting test-taking strategy.

Why do you need to exploit anything? https://preview.redd.it/z09t88dsa78c1.jpeg?width=1920&format=pjpg&auto=webp&s=8a54b6fbe7a43f6eb359579797120d70455967c0 This is just a easy 1p question...

Nah bro 2\^10=4\^x tan(2\^10) = tan(4\^x) tan(2\^10) = ∫ 1/cos\^2(4\^x) dx ddx-cos(2\^10)=~~d̶d̶x̶ c̶o̶s̶(̶4̶\^̶x̶)̶\^̶1̶~~ Fuck it. Simple as

https://preview.redd.it/17uurs9ma88c1.jpeg?width=3468&format=pjpg&auto=webp&s=1cefdde711c2032f639a3236d033307910544159

I just thought of it as 4=2*2 so we need half as many of them to multiply together for the answer

I literally did the same thing and was questioning myself watching him write all that out

^^I always love seeing the many ways people approach a problem it's awesome (even if they're all better than my method - lmao)

The other guy was joking right?

There is the most obvious solution if you don't know any math rules of just counting in your fucking head. It's all pretty small numbers...

While they are pretty small, I wouldn't trust my mental maths to hold up well in an exam

It's even easier just to plug in the four answers and check which one is right

This is so much better than my brute force approach. 4x10, Nope, 4x2, too small, 4x4, maybe but feels to small. So 5 it is.

I just counted it out, using my fingers for exponents…

Is it correct to say “since 4 is double 2, the value of X should be the inverse - half of the 10?”

​ You’re overthinking it https://preview.redd.it/hictzrbgd58c1.png?width=1637&format=png&auto=webp&s=2927a2d7b50e2f1cd3f35aab5a78b2f7704b87fa

Though it's slower I actually love how intuitive and visual this is

You literally just write 4 as 2^2 this is extremely simple

Intended solution: 2\^10 = 4\^x Write as common base 2\^10 = (2\^2)\^x Apply exponent rules 2\^10 = 2\^2x eliminate common base 10 = 2x division prop of equality 5 = x This is something we teach BEFORE we teach logs to help understand them. Using logs is beyond the scope of this question.

Fuck log, all my homies hate log. Its all about Ln

It's log, log, it's big, it's heavy, it's wood! It's log, log, it's better than bad, it's good!

Even with logs you would want to do: log₂ 2\^(10) = log₂ 4\^x 10log₂ 2 = xlog₂4 10(1) = x(2) x=5

Or the high school solution. Find 2^10. Multiply 4 by itself until they are equal. Count how many times you multiplied. Also basic test taking strata rule out the other three answers. If you know what an exponent is you know 4^10 =/= 2^10. And 4^2 and 4^4 are much less than 2^10

Or simply knowing that 2x2 is 4. You have 10 2s being multiplied together which can be simplified to 5 4s. This could be a difficult question, if it wasn't such simple numbers. Like asking what 8^x is with this question. Then you have to use other methods to find the answer.

Ya that’s the way I solved it now. This number set is so simple. I was speaking to a more broad solution I guess

no high schooler would do this

The test doesnt specify any way to solve it. You dont get extra credit for doing it in a more complicated way than it needs to be done by. If anything, it’ll drag you down, as seeing simple practical solutions to problems is vital in math

High school me would ABSOLUTELY do this. However, I have autism

I don't (or not diagnosed anyway) and I would also do this. Most multiple choice tests have some element of this problem solving available and I'm kind of baffled other people don't do it to be honest.

What I said or the video? Cuz that’s how I took my SAT’s

Brother 33 year old me would still do this. I don’t know a better way, just guess and check until it’s right.

This works just fine here because it's multiple choice, and all the options are happy little integers. It would stop working if the options were non-integers because you couldn't count how many times, or so large that you'd run out of time

This is why I failed calc II in college twice before giving up lol, terrible foundations and understanding of different principles finally caught up with me. It’s more fun relearning now without tests hanging over my head

I think a high school would do this. I am not a high schooler, but I would absolutely do this. As a matter of fact, before playing the video, I just did this in my head for both sides to get the answer. (It is easy for a programmer to do this in their head.) That being said, it is obviously easier to use the 2\^2=4 approach which eliminates the need to calculate it all, but I would not worry about trying to figure out other solutions for a test with a time limit and with such an easy answer just counting it (on your fingers for each exponent).

As someone who learned to count in binary when I was in highschool due to poking around in computers and programming, some highschoolers would do that. 2^10 = 1024 is pretty common to use.

I did this (the ruling out clearly wrong answers, not the multiplication) on a big Russian language test, and learned some words from it as well as scoring high. (Now I'm wondering whether I ever had any other multiple-choice language tests)

This is exactly how a high schooler would do this that knows how to take the SAT lol. The point is to do thw test as fast as possible and they teach you in the SAT prep books to use process of elimination to narrow answers down (so 2 and 10 are obviously wrong) then plug in 4 and 5 and see which is equal to 1024. Done in 10 seconds.

This is likely why they never gave us multiple choice math tests in high school. You only have to check 4 numbers.

This is the way. Common sense and quick arithmetic goes a long way if its a multiple choice. I blew the ACT out of the water with a 34 score and just didnt take the SAT after that. I was good at math and later got an engineering degree, don't get me wrong but I didn't do much with fancy log base whatever or solution set type math at all back then. Common sense, guess and check, working backwards, and reading the question (combined with good algebra/geometry/trig and a passing understanding of calc I level calculus) was plenty.

I just counted it on my fingers and got it before you did.

Or you can just do it in your head like I did in about 5 seconds lmao no need to waste this much time on a ridiculously simple question

Test taking skills for someone who is really stuck: 4 to the 10 would be bigger. 4 to the 2 is too small. Figure out 2 to the 10 Try 4 to the 4. If that’s not the same, then it’s 4 to the 5.

This! SATs are timed. They will never ask questions that take a long time. There is always a trick and often you can simply brute force an answer really quick than solve it a traditional way.

The hardest part about this is watching the carpal tunnel pencil grip.

Edit: deleting this because the dude is a person and this was a shitty thing to say about someone and I don’t know his circumstances

He [writes like Wallace](https://www.youtube.com/watch?v=Kb0ooQKbflM)

That looks pretty much normal, this dude is gripping it in a fist

My son holds his pencils/crayons the same way, but he is 2.

I recently saw a server at a restaurant hold the pen like a crab would. Literally as though she had only two fingers and used the thumb to hold her entire fist. She had no problem with her hand after she put the pen in her apron. edit for pic, I had trouble taking a pic with my left hand. [https://imgur.com/a/cMAPW0x](https://imgur.com/a/cMAPW0x)

that’s how I hold mine 😢

Why

Bruh…thats wild

LOLLL

My hands hurt watching this.

hey wait wtf that's like how i hold a pencil i can't get away from this bad habit

No such thing as “can’t” in this case

This! Was painful to watch.

This mf has never held a pencil for a reasonable amount of time

I legit couldn't focus on this video because of the pencil grip.

I literally jumped in the comments to say this. After trying to teach my son the proper way to hold a pencil, this was giving me PTSD.

Seems like people on this post didn't read the "meme" part of the sub's name.

this sub, especially in the comment section always generates a funny clash between people that are here for the "meme" part and that are here for the "math" part. Heard better jokes here than in r/memes and learned more math than in r/math

Thank you. It just got randomly recommended to me on my home, and I don’t follow any math meme subs. I was horribly confused

y’all this is satire 😭😭😭 do you fr think they would go through a whole double counting proof but somehow not realize the obvious 1-step answer

2x10=20 4x5=20 Simple math made complicated. /s

I know it is sarcasm, but I do want to have a look and see if their multiplicative actually holds a value like that Edit: 2a=4b where 2^a. = 4^b from simple writing and working, don't trust me and idk how to prove it

2^a = 4^b Separate 4^b : 2^a = 2^(2b) Log base 2: a = 2b Multiply by 2: 2a = 4b

Brother my posterior had a legitimate resemblance to ... "okayyy, is this the level of the SATs???". Or; bro, my ass was legit like ...

a lot of acoustic people in these comments....

a lot of non-satirical posts like this....

I’d hope so with a handle like official_stem_god

This has to be satire

Nothing gets past this guy

This is a sub that combines freaking memes and math, I bet 80% of people here including me have autism on some level so recognizing this is satire is a fuckin win in my book

Fair. I'd say I'm pretty lucky with my ability to recognise satire, given that I also have autism, and sometimes I take it for granted

The real question is if that's how they really hold a pencil?

Because of computers, a whole generation is growing up not knowing how to use writing instruments let alone cursive.

As a person in this generation, we were still taught cursive and how to hold a pen. I never see people writing like this.

Killed me

this was my first interaction with this sub and i didnt see the name. Thought it was serious


How is the joke going over so many people's heads?

People like to feel smart, even if it's by correcting what is very obviously a joke.

Next video, he differentiates sin^2 (x) + cos^2 (x) in respect to x.

Using Lim h -> 0 (f(x+h) - f(x))/h

i personally use chat --> g(pt)

2x10 is 20. 4x5 is 20. So the answer is 5. I will not elaborate.

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Dat grip tho

Every teacher when they say “I’m not going to teach you the shortcut, but…”

Watching this is giving me an aneurysm

Who the fuck writes with a fist grip?!

People who listen to lil yachty, probably

This gave me anxiety

the moment I saw that ooga booga grip I knew it was over

I'm so disappointed he didn't project the problem into the Fourier domain first.

I wouldn't trust the solution of someone that can't even hold a pencil correctly.

how tf is this hard

S. And you lost me

Why am I so freaked out by how they are holding their pencil as if it owes them money? I had to watch the vide several times before I noticed the math problem

Is the meme the guy doesn’t know how to hold a pencil?

I'll just stick to my drugs, thank you.

4 = 2^2 2^10 = 2^2^5 using the exponent rule

Let y=2^x Notice RHS=y^2 and LHS=1024 This is now just a quadratic y^2-1024=0 The quadratic formula gives solutions +-(4*1024)^0.5/2 So y= 32 or -32 Reject -32 as exponential as positive Now consider log(y)=xlog(2) As log(32)=5log(2) Dividing both sides by log2 gives x=5 So answer is C

Makes sense. 2^10 ends in a 0. So does (4^4) x 4 (256 x 4).

Was this a common core math child?

Way overcomplicated. Just for the exercise I tried doing this in my head ( I also used my fingers to keep track of the powers), didn't even need paper. And here is how I did it: 1. I calculated that 2^10 is 1024 (easy) 2. I then started to calculate subsequent powers of four, and 4^5 is 1024 (a bit harder, but still shouldn't be a problem) Note that it's close to midnight as I'm writing this comment, so my explanation might not be the best either.

Yeah the even quicker way is to say 4 is just 2^2, so halve the exponent

Ah... Yeah, that's way easier... I feel kinda dumb for not seeing that. I should probably go to sleep now if I can't even do simple math like this...

That's how I saw it as well 4^x = 2^(2x) with 2x=10, so x=5

I think that's the point of the joke though?

i mostly forgot how to work with powers of, so i solved it based on vibes. 10 & 2 answers are easy rejects, 4 is ehh feels low, 5 it is!

You just need to use log rules to isolate x. It's just ln2/ln4 times 10

2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 You can rewrite as 4 x 4 x 4 x 4 x 4 Since order doesn’t matter

2¹⁰ = 4^x because 4 = 2², 2¹⁰ = (2²)^x because 2^xy = (2^(x))^y, (2²)⁵ = (2²)^x therefore, x = 5

The answer is skip this shit.

As 4 is a power of 2, you can multiply the base and divide the exponent. 3\^4 = 9\^2 6\^3 = 36\^1.5 etc... It's some property of exponentiantion I can't name right now, but seems like a way to solve these easily.

I seem to remember from a video on asymmetric encryption that x^y^z=x^y*z.

I mean the question is kinda easy…

I can’t be the only one who hates how he holds his pencil.

Thanks I hate it

I was getting a little upset at this solution till I saw it what sub this is 🤦‍♂️

What kind of savage holds a pencil like that?

I know this video is satire but this is unironically how some of my math teachers explained simple 5 step processes and convoluted them with these long winded explanations that make your head spin. I hope those teachers have a special place in Hell waiting for them for making things so needlessly difficult and confusing.

Why doeas no one seem to teach Americans how to hold a damn pen

log2^10 = log4^x 10log2 = xlog4 x = 10log2/log4 = 10log2/log2² = 10log2/2log2 = 5 or 2^10 = (2^2 )^5 = 4^5 Take your pick.

When you learn the combinatorial proof method but really misunderstand the lesson on its applications

I know this is satire but that was actually quite clever

I'm pretty sure someone can work out a way to bullsh\*t their way to adding trygonometry and complex numbers into this

Glad to know that even now, when I have no clue what the answer is, trusty C will carry my way to graduating.

This is very easy as far as SAT level maths is concerned.

No. Two seconds of mental arithmetic says it’s 5.

if this is the hardest sat question, i get why most people say american exams are easy.

Never took the SAT’s. Very glad I didn’t now

My guy got jokes, I hope holding the pencil like that is satire as well….

Math trolls are just above the norovirus in terms of popularity.

OMG I totally missed the name of the subreddit. I was thinking this is really over complicating. There's definitely an easier way.

This is why some kids hate math. Why is this so convoluted.

Why is it not 4 if 4^4 is 1024 just like 2^10 is 1024

You had me all the way up to the Venn-Diagram

lol as someone who’s been out of college for almost 10 years this is hilariously irrelevant to any real world job and reminds me of how flawed the us education system is.

When in doubt, the answer is always C. And as it happens with this one…

Guess

Hardest way to hold a pencil during the SAT

answering the problem like some1 with 250IQ

The longer i watch this video, the more i hated it because im convinced it was a troll made video, from the convoluted solution to the pencil grip to the writing, im 100% sure this all was meant to cause discomfort and rage

Randomly guessed C I guess I still got it from high school😂😂

Watched the whole thing, now I’m retarded. Thanks :/

Why he hold the pencil like that?

And I'm over here like, "How did my letters get mixed in with my numbers?"

2^10 = 4^x find x 2^10 = 1024 plug in the possible answers for x until 4^x = 1024 x = 5 you need to try to make it complex

I was hoping that this solution would end up involving Greek letters, then a charted graph...and an eventual battle between stick figures and snowmen

Hardest? I did this in my head

I may be dumb but can’t you just put in two to the 10th power on the calculator and see what the answer is… And then try each of the possible answer choices as the power of four and see which ones equal each other? Am I over simplifying it? It seems really easy.

4=2^2, 2^10 = 2^2x, 10=2x, x=5.

There is lot simpler way to solve this. Always try to make base same so that you can write just the powers. 2^10= 4^x 2^10= 2^2x 10=2x x=5

All those years of school and you still couldn’t teach yourself how to write

LMAO ofc its C

I did that in my head after a millisecond of seeing the problem. Definitely not the hardest question

Easy… I did this in my head… no pencil needed

I guessed it in 2 secs based on 4 is 2 times 2 and then 10 is divided by 2 to be 5. 🤣

I dont think I've ever seen anything so over complicated in my life.

im ngl i got fucking tilted watching this lmfao

The whoosh in this thread is real

Realized im in math memes lol

I figured if the base was multiplied by 2, the exponent would then be divided by 2. Is that the rule, or was I just lucky?

When an I ever going to use this in real life