0759: "3x9"
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Re: "3x9" Discussion (#759)
I'm delighted because this is the first time something mathy has been posted and I've understood it.
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Re: "3x9" Discussion (#759)
PROTIP: I do not actually know how to do the gradient of a vector without using partial derivatives.
Yet, I aced the test on it. Similar concept to the comic, only it was calculus not arithmetic.
Yet, I aced the test on it. Similar concept to the comic, only it was calculus not arithmetic.
If the above comment has anything to do with hacking or cryptography, note that I work for a PHP security company and might know what I'm talking about.
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Re: "3x9" Discussion (#759)
rjk1994 wrote:Shay Guy wrote:
You've heard of Graham's number, right? That absurdly huge number equivalent to 3↑↑↑...↑↑↑3, with a much smaller but still absurdly huge number of up arrows?
Change those 3s to 2s, and it reduces to 4.
Two and two is four, no matter how you do it.
What? Are you serious? I really don't think it does.
2^2 = 4
2^2^2 = 2^4 = 16
2^2^2^2 = 2^2^4 = 2^16 = 65536
65536 != 4
Q.E.D.
Anyway, great comic. Wish I'd read this before Thursday's fail of an FP2 exam.
You are misunderstanding the Knuth up arrows. x↑y = x^{y}. x↑↑y = x↑x↑x↑...↑x, where there are y x's. In general, x↑^{n}y = x↑^{n1}x↑^{n1}x↑^{n1}x↑^{n1}...↑^{n1}x, where there are y x's.
Therefore 2↑^{n}2 = 2↑^{n1}2 = 2↑^{n2}2 = ... = 2↑2 = 2^{2} = 4.
Similarly, hyper(2, n, 2) = 4 for all n, and 2→2→X = 4 for any Conyway chain X.
Re: "3x9" Discussion (#759)
iGeek wrote:On a physics exam, a friend of mine couldn't remember whether a particular equation had "squared" or "times two" in it, so he decided to pick a number and try it both ways and see which one looked right. Unfortunately, he realized later, the number he picked was 2.
2^2 = 2*2
Reminds me of when I've been trying to work out if I'm dealing with a plural in a sentence correctly and for some reason my brain always picks the word 'sheep' out, which is obviously the same as singular and plural and thus completely useless to me.
Re: "3x9" Discussion (#759)
This trick works every time! Another useful one: if you don't understand something, write some grammatically incorrect or nonsense sentences containing words related to the problem. The examiner will decode them as the right answer.
ps: So this is the US notation for division?
ps: So this is the US notation for division?
Re: "3x9" Discussion (#759)
molnarm wrote:ps: So this is the US notation for division?
It is. Apparently, they wanted to make it intentionally confusing.
Now I'm off to C.L.A.S.S.
Re: "3x9" Discussion (#759)
I had a friend who did this all the time. I think he barely scraped a pass in Maths. I'll have to ask him.
As for me, I have a tendency to sneakily remove terms that shouldn't be there just when I'm cancelling everything else out (so it doesn't look too suspicious). I get caught out a lot though. I may have to be more humorous about it.
As for me, I have a tendency to sneakily remove terms that shouldn't be there just when I'm cancelling everything else out (so it doesn't look too suspicious). I get caught out a lot though. I may have to be more humorous about it.
The preceding comment is an automated response.
Re: "3x9" Discussion (#759)
What, no one posted this yet!?
Abbott And Costello 13 × 7 is 28
Abbott And Costello 13 × 7 is 28
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Re: "3x9" Discussion (#759)
Max2009 wrote:airshowfan wrote:Well, I do usually manage to close up the seam. And when I don't, the gaping hole is pretty obvious (and I have to resist the temptation to write "Then a miracle happens" into the gap)
I did that once.
I actually wrote "and then we conduct a voodoo ritual and transform x into y (or whatever step I was missing).
I got 85% for that one and a big smiley. Proving that even though all mathematicians are crazy, some of them have a sense of humor.
Or possibly the grader was just really happy that you didn't do what Randall was suggesting in the alttext. If I were grading that, I would probably not be terribly amused by the joke, but I'd be much happier at you pointing out where the missing steps are rather than making me hunt for the error in the hopes that I wouldn't find it (or that I would give up and give you full credit out of laziness).
I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.
"With math, all things are possible." —Rebecca Watson
"With math, all things are possible." —Rebecca Watson
Re: "3x9" Discussion (#759)
I got to say, the alt text on this one was spot on. I have definitely done exactly that on an exam. I derived forward and backward and couldn't link them completely. I got a 9/10 on the question and the professor pointed to the seam and just wrote "how did you get here?"
The day was once again saved by the TI89's ability to solve complex integrals.
The day was once again saved by the TI89's ability to solve complex integrals.
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Re: "3x9" Discussion (#759)
molnarm wrote:ps: So this is the US notation for division?
According to the Wikipedia page on long division, this is standard notation throughout the Englishspeaking world, and also in Japan. It's not standard notation for division in general, but it's the standard way of writing things when you perform the long division algorithm.
I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.
"With math, all things are possible." —Rebecca Watson
"With math, all things are possible." —Rebecca Watson

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Re: "3x9" Discussion (#759)
We used to do this all the time in maths at college. It became a bit of a frustration for our teacher, especially when we started getting quite good at it, and she couldn't tell whether we actually knew the answer or not. Another trick she taught us was to write "by inspection" if there was a bit of an obvious gap in our workings out, implying we had made the leap in our heads and it was too obvious to write down. Don't know if it ever worked, but if it did we must have looked quite clever.
Re: "3x9" Discussion (#759)
Damnit, I was trying to figure out how he got 27 from that division. It took me about 30 minutes to figure it out
And this is why reading XKCD at 3 AM is NOT a good idea...
And this is why reading XKCD at 3 AM is NOT a good idea...
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Re: "3x9" Discussion (#759)
molnarm wrote:ps: So this is the US notation for division?
It isn't quite, but it's very similar...
Long division looks like this:[math]\begin{align} 27 &\\ 3 \overline{) 81} &\\ 6\unicode{x2007}&\\ \overline{21} &\\ 21 &\\ \overline{\unicode{x2007}0}& \end{align}[/math]Or, possibly, with a straight vertical line instead of a curved one, between the divisor and dividend... especially when it's typed. Strangely, there doesn't seem to be a way of writing that symbol properly in LaTeX, so just imagine that the paren and the horizontal line are joined at a corner.
Square roots, on the other hand, look like this:[math]3\sqrt{81}[/math]
The comic is playing on the fact that the radical sign and the long division sign look similar  a number, then a mostlyvertical squiggle that ends as a horizontal line that goes over another number.
Now, while searching Google Images, I did find one page that uses the radical sign for long division... but I think they're an anomaly... I don't think this is at all standard anywhere.
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Re: "3x9" Discussion (#759)
I did this all the time on math exams. Well, not exactly this, but I was terrible about showing my work.
The worst was when they wanted you to write it out in sentence form. Something about that seemed extremely counter productive to my early high school mind.
The worst was when they wanted you to write it out in sentence form. Something about that seemed extremely counter productive to my early high school mind.
Re: "3x9" Discussion (#759)
Interesting technique  i always ended up having to do similar thing back when i was in school, since they always wanted you to show workings out, even when it was easier to do in your head.
So i'd just answer them all, then write a load of mathshaped crap in unreadable scrawl next to them to pretend it was the working out was faster than making something mathematically accurate. I'm pretty sure no one ever reads it as none of my stuff even remotely resembled making sense o.o
it was literally;
(2*8)/4 = 4
With something along the lines of
((7*4/88 +11 100) % 4 + 1000^15)*0+4 = 4
Written next to it  none of it having any relation to any actual workings out or method of gaining the answer, and more often that not, adding up to a totally different number than my answer too...
Disjointing it from the answer so it wasn't obvious which question the "workings out" related to may have helped too
So i'd just answer them all, then write a load of mathshaped crap in unreadable scrawl next to them to pretend it was the working out was faster than making something mathematically accurate. I'm pretty sure no one ever reads it as none of my stuff even remotely resembled making sense o.o
it was literally;
(2*8)/4 = 4
With something along the lines of
((7*4/88 +11 100) % 4 + 1000^15)*0+4 = 4
Written next to it  none of it having any relation to any actual workings out or method of gaining the answer, and more often that not, adding up to a totally different number than my answer too...
Disjointing it from the answer so it wasn't obvious which question the "workings out" related to may have helped too
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Re: "3x9" Discussion (#759)
This also reminds me of a college math class where I would literally sleep through every class (I was somehow not allowed to test out, though it was basically algebra II...)
The teacher was really nice, but it was an 8am. I felt kind of bad, so at the end of the quarter I apologized to her. She said she totally understood, as it was pretty boring. With no trace of irony. Big smile.
Man, I kind of feel sorry for her. She always had a huge cup of coffee  probably required to teach math at an art school.
The teacher was really nice, but it was an 8am. I felt kind of bad, so at the end of the quarter I apologized to her. She said she totally understood, as it was pretty boring. With no trace of irony. Big smile.
Man, I kind of feel sorry for her. She always had a huge cup of coffee  probably required to teach math at an art school.

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Re: "3x9" Discussion (#759)
In a similar but alternative strategy I totally blanked on a physics exam and I used the units I knew the results were suppose to be in and the units of the things I had to figure it out. I got the problem completely right.
Re: "3x9" Discussion (#759)
Isn't the alt text's suggestion kind of close to what COQ does? And if so, does it validates this method as the stateoftheart way to derive a proof and, consequently, to graduate?
Re: "3x9" Discussion (#759)
shakeystacey wrote:We used to do this all the time in maths at college. It became a bit of a frustration for our teacher, especially when we started getting quite good at it, and she couldn't tell whether we actually knew the answer or not. Another trick she taught us was to write "by inspection" if there was a bit of an obvious gap in our workings out, implying we had made the leap in our heads and it was too obvious to write down. Don't know if it ever worked, but if it did we must have looked quite clever.
Wish I'd had your teacher. I did the alttext trick many a time (in fact, I'm pretty sure that's how I ended up with Maths A Further Maths A on my ALevels) but nothing quite so neat as "by inspection".
Having said that, I have a frighteningly clever friend who can look at a big pile of hideous algebra and say "oh that factorises by (x^3x^2)" without doing any working. Sometimes I hate him.
Dudes, I'm a woman.
Re: "3x9" Discussion (#759)
I always hated showing my work.
Re: "3x9" Discussion (#759)
I remember having to do that once in middle school  it was part of a day devoted to writing as much crap as possible as "preparation" for the writing TAKS test(which is, for reasons only known to senseless bureaucrats, must be passed or your score for the entire English test is pegged one point below passing).sendingsignal wrote:The worst was when they wanted you to write it out in sentence form. Something about that seemed extremely counter productive to my early high school mind.
Frédéric Bastiat wrote:Government is the great fiction through which everybody endeavors to live at the expense of everybody else.
Re: "3x9" Discussion (#759)
It took me a few seconds to realize that the division ended up with the right answer.
Re: "3x9" Discussion (#759)
iGeek wrote:On a physics exam, a friend of mine couldn't remember whether a particular equation had "squared" or "times two" in it, so he decided to pick a number and try it both ways and see which one looked right. Unfortunately, he realized later, the number he picked was 2.
2^2 = 2*2
And 2+2=4. Crazy!
Last edited by sween64 on Mon Jun 28, 2010 1:05 pm UTC, edited 1 time in total.
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Re: "3x9" Discussion (#759)
Am I the only one who noticed that if you have to show work to do 3x9, you're doing it wrong?
Re: "3x9" Discussion (#759)
Better still, use QED at the end, according to my maths teacher, that would bring tears to the examiners eyes to see that, and forget whatever was in the "proof" and give you an A.
Of course that's a load of rubbish, but so was the comic.
Of course that's a load of rubbish, but so was the comic.
:)
You are carrying:
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You are carrying:
 a slightly paranoid Android
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 a still unfed and very hungry hippo
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 a
Re: "3x9" Discussion (#759)
Switch31 wrote:The day was once again saved by the TI89's ability to solve complex integrals.
The ability of the TI89 to get any answer is the only way I passed my AP Calc class. Sadly, it doesn't seem to work on the actual AP exam.
Re: "3x9" Discussion (#759)
This brings back some memories. This was called "The confusion method/rule" among my peers quite useful to get partial credit.
On a side note, there's a urban legend that this caused a chronic migraine problem to a professor in the faculty.
On a side note, there's a urban legend that this caused a chronic migraine problem to a professor in the faculty.
Re: "3x9" Discussion (#759)
Really, how did a bunch of selfprofessed geeks have so much discussion on the topic with noone pointing out that ×≠x?
Re: "3x9" Discussion (#759)
Wait, what?
How are you meant to show your work for 3 x 9? Draw 3 groups of 9 sheep or something?
How are you meant to show your work for 3 x 9? Draw 3 groups of 9 sheep or something?
Re: "3x9" Discussion (#759)
happysteve wrote:Kinda reminds me of this fun math tidbit...
Solve for x:
[imath]x^2  x  20 = 10[/imath] ... hmm okay, factor the left hand side...
[imath](x + 4)(x  5) = 10[/imath]
ah great, now it's just a matter of solving for (x + 4) = 10 and (x  5) = 10
x is either 6 or 5
Check with the original statement:
[imath]6^2  6  20 = 10[/imath] ... yup, that works
[imath](5)^2  (5)  20 = 10[/imath] ... yup, that works too.
yay, problem solved.
no, its not "just a matter of solving for (x + 4) = 10 and (x  5) = 10"
it's a matter of solving for (x + 4) = 10 AND (x  5) = 1
or (x + 4) = 1 AND (x  5) = 10
or (x + 4) = 10 AND (x  5) = 1
or (x + 4) = 1 AND (x  5) = 10
2 of those dependencies don't work
the better way to solve this is:
x^2  x  20 = 10 ...subtract 10 from both sides
x^2  x  30 = 0
(x  6)(x + 5) = 0
x  6 = 0 OR x + 5 = 0
x = 6 or 5
Last edited by Tophe on Mon Jun 28, 2010 2:11 pm UTC, edited 1 time in total.
Re: "3x9" Discussion (#759)
wow, I saw the problem right away and easily would have marked it wrong. I was a TA for a semester for a very simple Algebra class, and I would never pass over this.

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Re: "3x9" Discussion (#759)
I've noticed when dining with math geeks that they always take an unreasonably long time to figure out the tip. Whereas I, with my most advanced math being precalc, can do it in approximately 2 seconds. I've always suspected that something like this is going on in their heads.
Re: "3x9" Discussion (#759)
sween64 wrote:iGeek wrote:On a physics exam, a friend of mine couldn't remember whether a particular equation had "squared" or "times two" in it, so he decided to pick a number and try it both ways and see which one looked right. Unfortunately, he realized later, the number he picked was 2.
2^2 = 2*2
And 2+2=4. Crazy!
Think back to elementary school definitions.
2^2 is defined as 2*2 (until there are a total of two twos) and 2*2 is defined as 2+2 for the same reasons.
Call it a property of two.

I'm kind of reminded of something that happened on a linear algebra test. There was some strange matrix thingie that I can't remember what it's called or ever really saw the point in. The only thing I could remember on the test was how to find the inverse with it. I simply used a simpler method to find the inverse and work backwards and then stared awkwardly at the next question: Find the inverse.
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Re: "3x9" Discussion (#759)
littlelj wrote:Having said that, I have a frighteningly clever friend who can look at a big pile of hideous algebra and say "oh that factorises by (x^3x^2)" without doing any working. Sometimes I hate him.
Well, that's pretty straightforward, right? I mean, factoring by x^2 is obvious at a moment's inspection, and (x1) isn't that bad.
:p
If you're taking me too seriously, you probably are making a mistake.
Re: "3x9" Discussion (#759)
Not entirely related, but...
When I was taking my AP CS exam (in Java; the whole thing was absurdly easy), one of the methods I had to write (on paper, no IDE) involved floating point math. So, just for kicks, I wrote "should this whole class be strictfp?" in a comment (to confuse the graders). strictfp is a really obscure Java keyword which might have made a small difference in the ～10th decimal place or so... (unless you're unlucky and/or using floats instead of doubles in which case it could be the ～5th or so instead)
also: using weird tilde since the real one looks like this: ~
When I was taking my AP CS exam (in Java; the whole thing was absurdly easy), one of the methods I had to write (on paper, no IDE) involved floating point math. So, just for kicks, I wrote "should this whole class be strictfp?" in a comment (to confuse the graders). strictfp is a really obscure Java keyword which might have made a small difference in the ～10th decimal place or so... (unless you're unlucky and/or using floats instead of doubles in which case it could be the ～5th or so instead)
also: using weird tilde since the real one looks like this: ~
Re: "3x9" Discussion (#759)
Grumbleduke wrote:A quick bit of algebra shows that this will work for any two numbers where:
[math]\begin{eqnarray*}a \times b & = & a \times \sqrt{b^2} \\ & = & a \sqrt{b^2}\\ & = & \frac{b^2}{a} \\ \therefore a^2 & = & b \end{eqnarray*}[/math]
It's not all that exciting; try it with 2 and 4, or 3 and 9...
However, the alt text is very good advice.
Edit: Ah, assuming that a isn't 0 of course  although I think it still works algebraicly, if you use l'Hopital's rule on the fraction.
i figured that it's:
A * A^{2} = A^{3}
The whole equation is an interestesting way of saying that multiplying a number times its square is the same as cubing it.

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Re: "3x9" Discussion (#759)
P
To me it's fairly reasonable for actually doing division by hand, but nonsensical as part of an answer or equation.
skeptical scientist wrote:molnarm wrote:ps: So this is the US notation for division?
According to the Wikipedia page on long division, this is standard notation throughout the Englishspeaking world, and also in Japan. It's not standard notation for division in general, but it's the standard way of writing things when you perform the long division algorithm.
To me it's fairly reasonable for actually doing division by hand, but nonsensical as part of an answer or equation.
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Re: "3x9" Discussion (#759)
rwald wrote:Initially this looks like another example of this, but it actually makes sense why this works; any time you multiply x by x^2, you'll get the same result as if you divide x^4 by x.
Wait, so x^{3} = x^{3}?!
WHOA NO WAY!!!
not baby Newt wrote:Pskeptical scientist wrote:molnarm wrote:ps: So this is the US notation for division?
According to the Wikipedia page on long division, this is standard notation throughout the Englishspeaking world, and also in Japan. It's not standard notation for division in general, but it's the standard way of writing things when you perform the long division algorithm.
To me it's fairly reasonable for actually doing division by hand, but nonsensical as part of an answer or equation.
Agreed. It completely breaks format with other notations; you could not put that in the middle of a oneline calculation without it being incredibly strange and confusing.
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