0759: "3x9"

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Re: "3x9" Discussion (#759)

Postby RabbitWho » Mon Jun 28, 2010 7:20 am UTC

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)

Postby vodka.cobra » Mon Jun 28, 2010 7:24 am UTC

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.
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Re: "3x9" Discussion (#759)

Postby Eebster the Great » Mon Jun 28, 2010 7:26 am UTC

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 = xy. x↑↑y = x↑x↑x↑...↑x, where there are y x's. In general, x↑ny = x↑n-1x↑n-1x↑n-1x↑n-1...↑n-1x, where there are y x's.

Therefore 2↑n2 = 2↑n-12 = 2↑n-22 = ... = 2↑2 = 22 = 4.

Similarly, hyper(2, n, 2) = 4 for all n, and 2→2→X = 4 for any Conyway chain X.

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Re: "3x9" Discussion (#759)

Postby TheoGB » Mon Jun 28, 2010 7:31 am UTC

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.

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Re: "3x9" Discussion (#759)

Postby molnarm » Mon Jun 28, 2010 7:34 am UTC

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?

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Re: "3x9" Discussion (#759)

Postby Mr. Burke » Mon Jun 28, 2010 7:38 am UTC

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.

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Re: "3x9" Discussion (#759)

Postby snowyowl » Mon Jun 28, 2010 7:45 am UTC

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.
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Re: "3x9" Discussion (#759)

Postby Arakun » Mon Jun 28, 2010 7:48 am UTC

What, no one posted this yet!?
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Re: "3x9" Discussion (#759)

Postby skeptical scientist » Mon Jun 28, 2010 8:13 am UTC

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 alt-text. 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).
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Re: "3x9" Discussion (#759)

Postby Switch31 » Mon Jun 28, 2010 8:13 am UTC

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 TI-89's ability to solve complex integrals.
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Re: "3x9" Discussion (#759)

Postby skeptical scientist » Mon Jun 28, 2010 8:21 am UTC

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 English-speaking 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.
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Re: "3x9" Discussion (#759)

Postby shakeystacey » Mon Jun 28, 2010 8:39 am UTC

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.

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Re: "3x9" Discussion (#759)

Postby Icalasari » Mon Jun 28, 2010 8:42 am UTC

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...

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Re: "3x9" Discussion (#759)

Postby phlip » Mon Jun 28, 2010 8:46 am UTC

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 mostly-vertical 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)

Postby sendingsignal » Mon Jun 28, 2010 9:26 am UTC

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.

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Re: "3x9" Discussion (#759)

Postby bag » Mon Jun 28, 2010 9:29 am UTC

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 math-shaped 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)

Postby sendingsignal » Mon Jun 28, 2010 9:42 am UTC

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.

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Re: "3x9" Discussion (#759)

Postby bear_tracks » Mon Jun 28, 2010 10:17 am UTC

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.

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Re: "3x9" Discussion (#759)

Postby Layrajha » Mon Jun 28, 2010 10:25 am UTC

Isn't the alt text's suggestion kind of close to what COQ does? And if so, does it validates this method as the state-of-the-art way to derive a proof and, consequently, to graduate?

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Re: "3x9" Discussion (#759)

Postby littlelj » Mon Jun 28, 2010 12:20 pm UTC

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 alt-text trick many a time (in fact, I'm pretty sure that's how I ended up with Maths A Further Maths A on my A-Levels) 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^3-x^2)" without doing any working. Sometimes I hate him.
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Re: "3x9" Discussion (#759)

Postby CiDhed » Mon Jun 28, 2010 12:25 pm UTC

I always hated showing my work.

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Re: "3x9" Discussion (#759)

Postby BioTube » Mon Jun 28, 2010 12:30 pm UTC

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.
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).
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Re: "3x9" Discussion (#759)

Postby graatz » Mon Jun 28, 2010 12:49 pm UTC

It took me a few seconds to realize that the division ended up with the right answer. :oops:

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Re: "3x9" Discussion (#759)

Postby sween64 » Mon Jun 28, 2010 12:59 pm UTC

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)

Postby Loyal Lurker » Mon Jun 28, 2010 1:00 pm UTC

Am I the only one who noticed that if you have to show work to do 3x9, you're doing it wrong?

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Re: "3x9" Discussion (#759)

Postby madjo » Mon Jun 28, 2010 1:19 pm UTC

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. :)
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Re: "3x9" Discussion (#759)

Postby Freiberg » Mon Jun 28, 2010 1:30 pm UTC

Switch31 wrote:The day was once again saved by the TI-89's ability to solve complex integrals.


The ability of the TI-89 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.

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Re: "3x9" Discussion (#759)

Postby Lasher » Mon Jun 28, 2010 1:49 pm UTC

This brings back some memories. This was called "The confusion method/rule" among my peers quite useful to get partial credit. :P
On a side note, there's a urban legend that this caused a chronic migraine problem to a professor in the faculty.

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Re: "3x9" Discussion (#759)

Postby Rplot » Mon Jun 28, 2010 1:57 pm UTC

A long tradition. From another cartoonist.

http://www.artistmarket.com/artists/har ... -%2001.htm

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Re: "3x9" Discussion (#759)

Postby slashme » Mon Jun 28, 2010 1:57 pm UTC

Really, how did a bunch of self-professed geeks have so much discussion on the topic with no-one pointing out that ×≠x?

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Re: "3x9" Discussion (#759)

Postby Manial » Mon Jun 28, 2010 2:05 pm UTC

Wait, what?

How are you meant to show your work for 3 x 9? Draw 3 groups of 9 sheep or something?

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Re: "3x9" Discussion (#759)

Postby Tophe » Mon Jun 28, 2010 2:07 pm UTC

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.

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Re: "3x9" Discussion (#759)

Postby NeWtoz » Mon Jun 28, 2010 2:08 pm UTC

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)

Postby VioletDaGrinder » Mon Jun 28, 2010 2:15 pm UTC

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 pre-calc, can do it in approximately 2 seconds. I've always suspected that something like this is going on in their heads.

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Re: "3x9" Discussion (#759)

Postby am3930 » Mon Jun 28, 2010 3:32 pm UTC

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)

Postby Ghona » Mon Jun 28, 2010 3:44 pm UTC

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^3-x^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 (x-1) isn't that bad.
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Re: "3x9" Discussion (#759)

Postby thinboy00 » Mon Jun 28, 2010 3:51 pm UTC

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: ~

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Re: "3x9" Discussion (#759)

Postby Apeiron » Mon Jun 28, 2010 3:58 pm UTC

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 * A2 = A3

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)

Postby not baby Newt » Mon Jun 28, 2010 4:00 pm UTC

P
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 English-speaking 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)

Postby SpringLoaded12 » Mon Jun 28, 2010 4:03 pm UTC

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 x3 = x3?!

WHOA NO WAY!!!
:wink:

not baby Newt wrote:P
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 English-speaking 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 one-line calculation without it being incredibly strange and confusing.
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