Is it just me, or does the average guy really suck at math?

For the discussion of math. Duh.

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Is it just me, or does the average guy really suck at math?

Postby Kurushimi » Sun Jul 04, 2010 12:02 am UTC

I was just watching the movie The Cube recently. It's about a bunch of strangers waking up in a cube with many rooms (each room being a cube with six doors, on on each side, leading to other rooms). Now, a lot of these rooms have deadly traps in them. Luckily, these rooms are all have 3, 3 digit numbers on their entrances. They figure out that these numbers could tell them which rooms have traps. If any of the three numbers are primes or powers of primes, it'd be a trapped room.

I was very disappointed. First of all when they actually figured out the pattern, the girl who discovered it, who was supposed to be a math student, claimed that it would be impossible for her to figure out whether or not the numbers met the criteria. No human alive could do it. They're astronomical. Seriously? The highest possible number was 999. Thus, the highest number they had to go to to test whether a number was prime or not. That makes 11 primes you have to test to divide by. At most. Not to mention that in almost 75% of the cases, you'd only have to try 2, 3, and 5 (all of which are incredibly easy and should only take a moment to do). And if it wasn't prime you could easily check if it was a power of a prime by repeatedly multiplying/dividing by the prime you found that divided it. This was just too much for her. Luckily, they had an autistic savant with them. He was able to instantly count the number of prime divisors of a number. Sadly, they still couldn't get it right.

On two instances he simply calculated the number of divisors wrong. Said 3 when it was supposed to be 4 and things like that. But what took the cake were incredibly obvious cases. They saw the number 384, and said it had one prime divisor. Really. It took too much effort to divide by two and notice it was not a power of two. The hilarious part was that they were in a hurry to get out of the room, and avoided the completely safe room because it was trapped. And on two separate instances, they entered a room with a prime number in it. Not a power of a prime. A basic prime.

Is it me? Is it too much to expect a script writer to take 2 minutes of his day and actually google what it means to be prime? Is it too much to ask that they take the 10 seconds required to with a calculator to determine whether the numbers they chose actually fit the stated criteria? I mean, I can understand having an explosion in space for flashy effects, or having computers beep every 5 seconds to let us know they're doing something, but really what was there to gain from this? I mean, primes aren't that complicated. Really.

[/rant]

So, for discussion purposes, are there any times where you've noticed movies get math (not science) just plain wrong?

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Re: Is it just me, or does the average guy really suck at ma

Postby ++$_ » Sun Jul 04, 2010 12:12 am UTC

According to Wikipedia:
Wikipedia wrote:Natali states in the commentary that a professor was hired to do the math for Cube
I can only hope that at least one of the following things is true:

1. The professor was hired to do the math, and then they took the sheet with his recommendations on it, set it on fire without looking at it, and scattered the ashes.
2. The professor they hired was not a professor of mathematics.
3. The professor decided to find out just exactly how stupid these people were by giving them blatantly wrong information to see if they'd notice.
4. They didn't actually hire anyone and just decided to lie about it later so they could blame their unbelievable stupidity on someone else.

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Re: Is it just me, or does the average guy really suck at ma

Postby Patashu » Sun Jul 04, 2010 12:18 am UTC

Relevant: The average person sucks at math because the math taught in schools is very boring. http://www.maa.org/devlin/LockhartsLament.pdf

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Re: Is it just me, or does the average guy really suck at ma

Postby hnooch » Sun Jul 04, 2010 12:31 am UTC

Did the script get it wrong, or did the characters get it wrong? If it's just the latter, then there's no contradiction with a (smart!) professor being consulted on the math, because it just means the characters are very dumb.

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Re: Is it just me, or does the average guy really suck at ma

Postby ++$_ » Sun Jul 04, 2010 12:44 am UTC

hnooch wrote:Did the script get it wrong, or did the characters get it wrong? If it's just the latter, then there's no contradiction with a (smart!) professor being consulted on the math, because it just means the characters are very dumb.
But, as we know, it would fly over the heads of the audience members. Besides, a character who was supposedly educated in math claimed that no normal human could factor 3 digit numbers. She could easily have factored numbers incorrectly (although no one smarter than a rock would ever think 384 was a prime power), but there's absolutely no way anyone could think that factoring 3 digit numbers is an impossible problem. I think the script is at fault.

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Re: Is it just me, or does the average guy really suck at ma

Postby Six Fingers » Sun Jul 04, 2010 2:35 am UTC

Kids are not taught that math can be fun/cool. All the adults I knew approached math like they approached vegetables: "I know you hate it...but its good for you." Its for this very reason that I hated math until I started studying it outside of school. We wonder why the average person doesn't know/care much about math? Compare how many kids books make rocks and dinosaurs fun - and how many make math an adventure.

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Re: Is it just me, or does the average guy really suck at ma

Postby achan1058 » Sun Jul 04, 2010 2:35 am UTC

Maybe it was originally supposed to be a single 9 digit number instead of three 3 digit numbers?

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Re: Is it just me, or does the average guy really suck at ma

Postby Shotglass » Sun Jul 04, 2010 3:31 am UTC

being good at math != being good at mental arithmetic

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Re: Is it just me, or does the average guy really suck at ma

Postby Kurushimi » Sun Jul 04, 2010 4:02 am UTC

Doesn't take much mental arithmetic. I'm pretty sure in a life or death situation, anyone would be able to calculate

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Re: Is it just me, or does the average guy really suck at ma

Postby Cleverbeans » Sun Jul 04, 2010 4:31 am UTC

The average person doesn't even know what mathematics is.
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Re: Is it just me, or does the average guy really suck at ma

Postby Shotglass » Sun Jul 04, 2010 4:49 am UTC

Kurushimi wrote:I'm pretty sure in a life or death situation, anyone would be able to calculate


i liteally cant do mental calculation to safe my life but i am able to solve reasonably complicated equations in my head and ive found that this seems to be the case with many other engineers too

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Re: Is it just me, or does the average guy really suck at ma

Postby Torn Apart By Dingos » Sun Jul 04, 2010 10:59 am UTC

I was amused when one of the characters pondered for a moment before deciding 645 was not a prime.

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Re: Is it just me, or does the average guy really suck at ma

Postby PM 2Ring » Sun Jul 04, 2010 11:32 am UTC

achan1058 wrote:Maybe it was originally supposed to be a single 9 digit number instead of three 3 digit numbers?

Let's hope so. Otherwise, that professor has a lot of explaining to do. :)

Shotglass wrote:
Kurushimi wrote:I'm pretty sure in a life or death situation, anyone would be able to calculate


i liteally cant do mental calculation to safe my life but i am able to solve reasonably complicated equations in my head and ive found that this seems to be the case with many other engineers too

Some facility with mental arithmatic is helpful when solving equations, though, whether in your head or on paper.

Let's face it, there's not a lot of joy in doing basic mental arithmetic (unless you're OCD or a bit Aspie :) ), and if you don't learn how to do it when you're young & your brain is still very adaptable, you probably never will.
Cleverbeans wrote:The average person doesn't even know what mathematics is.

This. All they know about is arithmetic, which they find boring, so anyone who likes mathematics must be a weirdo. They probably think advanced mathematics means learning the multiplication tables upto 100 x 100. :)

I'm no lightning calculator, but I guess I'm proud of my mental arithmetic skills. Arithmetic in itself is boring, but finding & using shortcuts is kinda neat. I'm not as fast as I was 20 or 30 years ago, but I can still multiply 2 digit numbers pretty quickly in my head, and I'm not bad at factorization and estimating square roots. OTOH, I think I'm better these days at doing algebra in my head, and keeping track of intermediate results.

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Re: Is it just me, or does the average guy really suck at ma

Postby Shotglass » Sun Jul 04, 2010 4:43 pm UTC

PM 2Ring wrote:Some facility with mental arithmatic is helpful when solving equations, though, whether in your head or on paper.


cant speak for everyone but when i solve equations in my head i do so by visualising them as if they were written on paper
which is an approach that doenst get you anywhere for mental arithmetics

more importantly though i just dont see the point when i have a calculator and matlab to do the job for me a million times faster

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Re: Is it just me, or does the average guy really suck at ma

Postby PM 2Ring » Sun Jul 04, 2010 5:17 pm UTC

Ok. How would you solve x² - 20x + 51 = 0 in your head?

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Re: Is it just me, or does the average guy really suck at ma

Postby mister k » Sun Jul 04, 2010 5:27 pm UTC

(x-10)^2-100+51=0
(x-10)^2=49
(x-10)=+/-7
x=17 or 3

certainly possible in your head! Admittedly if the root wasn't calculable that'd be harder. I don't know any root finding algorithms off the top of my head.
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Re: Is it just me, or does the average guy really suck at ma

Postby The EGE » Sun Jul 04, 2010 6:03 pm UTC

Shotglass wrote:
PM 2Ring wrote:Some facility with mental arithmatic is helpful when solving equations, though, whether in your head or on paper.


cant speak for everyone but when i solve equations in my head i do so by visualising them as if they were written on paper
which is an approach that doenst get you anywhere for mental arithmetics

more importantly though i just dont see the point when i have a calculator and matlab to do the job for me a million times faster


Because you don't always have these crutches to help you. Are you going to whip out your laptop in the middle of a restaurant to figure the tip, or are you going to do some basic arithmetic? There are many situations where pulling out an aid would look awkward, while doing mental arithmetic is better. Plus it's fun when you have a dozen items and you hand exact change before the cashier is finished ringing the items up.

I know mental mod-arithmetic methods for determining the day of the week given a date, and the phase of the moon. The former is very useful (and a great way to impress adults, oddly enough); the latter is nice when you're an amateur anstronomer like me.

I almost never visualize in my head what it'd look like on paper. Mod calculations I just store one number at a time and continually add to that.

2Ring: (x-17)(X-3). Easy. EDIT: Ninja'd by mister k.
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Re: Is it just me, or does the average guy really suck at ma

Postby PM 2Ring » Sun Jul 04, 2010 6:24 pm UTC

mister k wrote:(x-10)^2-100+51=0
(x-10)^2=49
(x-10)=+/-7
x=17 or 3

certainly possible in your head!

I made it easy on purpose. But you did have to use some mental arithmetic, and shotglass said he can solve equations in his head, but he's no good with mental arithmetic. So i want to see how he'd tackle something like this. :)

It's nice to see you using the tactic of completing the square. I generally prefer to use that method, rather than wheel out the quadratic formula. But first I try factorization, as illustrated by The EGE. Factorizing 51 takes me almost no thought at all. :)

mister k wrote:Admittedly if the root wasn't calculable that'd be harder. I don't know any root finding algorithms off the top of my head.

One approach to estimating square roots is closely related to completing the square:
sqrt(x² + d) ~= x + d/2x if |d| is small compared to x. You can repeat that procedure a few times to get close to the root.

Another way is to use Heron's method (a special case of Newton's method), and you can use the complete the square method to get a good initial approximation to plug into Heron's method. If x ~= sqrt(n), then (x + n/x)/2 is a better approximation. This method was known in ancient times. I will admit that it's a bit painful for mental arithmetic, though, due to the division by x. Even if you work in fractions, they soon become unwieldy. But one or two iterations (with rounding to keep things simple) isn't too bad.


The EGE wrote:Plus it's fun when you have a dozen items and you hand exact change before the cashier is finished ringing the items up.
I love doing that. The look on their face is priceless. I don't know about your part of the world, but around here plenty of shop assistants these days can't even add two amounts under $10 without a calculator of some form.

The EGE wrote:I know mental mod-arithmetic methods for determining the day of the week given a date, and the phase of the moon. The former is very useful (and a great way to impress adults, oddly enough); the latter is nice when you're an amateur anstronomer like me.

I know a couple of algorithms for day of the week calculation, and used to impress people with it when I was a kid. But I'm a bit slower these days - I have to double check my work, because I learned this trick in the 20th century, and can sometimes forget to compensate with modern dates. :)

I'd like to know your moon phase algorithm. I have a fairly accurate one that uses trig, so it's not suitable for mental arithmetic. But it gets the time of the major phases correct within 2 minutes or better for dates from 1900 to 2100, and is good enough for eclipse prediction.

Calculating sines mentally is possible, but I won't pretend that it's particularly easy. One handy approximation is sin(x) ~= x(12 - x²)/(12 + x²).

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Re: Is it just me, or does the average guy really suck at ma

Postby achan1058 » Sun Jul 04, 2010 8:02 pm UTC

PM 2Ring wrote:
mister k wrote:(x-10)^2-100+51=0
(x-10)^2=49
(x-10)=+/-7
x=17 or 3

certainly possible in your head!

I made it easy on purpose. But you did have to use some mental arithmetic, and shotglass said he can solve equations in his head, but he's no good with mental arithmetic. So i want to see how he'd tackle something like this. :)
I know the factors of 51, so......

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Re: Is it just me, or does the average guy really suck at ma

Postby Yakk » Mon Jul 05, 2010 12:48 am UTC

Two things:
1> Make the numbers bigger. Using smaller numbers makes the problem easier to grasp for people watching the movie, while it probably doesn't change the script one iota.
2> Realize that sets and shots are expensive. So if you are making a shot, and the wrong number is in the background, and you haven't noticed, and the shot is good -- you use the good shot.

Ie, through the simple trick of making it 3 12 (or whatever it takes to make it hard enough) digit numbers, and fixing a few shots where the numbers are wrong, the plot holes you detected in the movie go away, right?

And that, to someone who isn't obsessed with mathematical correctness, is a minor and unimportant difference. You, yourself, can imagine this edit while watching the movie without all that much effort.
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Re: Is it just me, or does the average guy really suck at ma

Postby Shotglass » Mon Jul 05, 2010 3:15 am UTC

PM 2Ring wrote:Ok. How would you solve x² - 20x + 51 = 0 in your head?


i was thinking more of solving physical equations containing nothing but variables

the sort of thing you posted im naturally rubbish at thanks to my complete inability to deal with numbers in me head
usually i rely on vieta to solve quadratic equations but 17 is a bit beyond the point of where i can see the solution immediately

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Re: Is it just me, or does the average guy really suck at ma

Postby DavCrav » Mon Jul 05, 2010 9:14 am UTC

mister k wrote:(x-10)^2-100+51=0
(x-10)^2=49
(x-10)=+/-7
x=17 or 3

certainly possible in your head! Admittedly if the root wasn't calculable that'd be harder. I don't know any root finding algorithms off the top of my head.


Hmm. My standard way is: 51 = 3 * 17. Note that 3+17 is 20, which is what we want. Check that the signs are right (if it's +51 I should sum the factors, -51 I should take the difference of the factors) and done. I have never really used completing the square...

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Re: Is it just me, or does the average guy really suck at ma

Postby PM 2Ring » Mon Jul 05, 2010 9:58 am UTC

Shotglass wrote:
PM 2Ring wrote:Ok. How would you solve x² - 20x + 51 = 0 in your head?


i was thinking more of solving physical equations containing nothing but variables

Like getting Kepler's T² = kR³ from Newton's law of gravitational attraction & the formula for centripetal acceleration, for example?

Shotglass wrote:the sort of thing you posted im naturally rubbish at thanks to my complete inability to deal with numbers in me head
usually i rely on vieta to solve quadratic equations but 17 is a bit beyond the point of where i can see the solution immediately

I see. :) But it's pretty easy to tell that 51 is divisible by 3, and that 51 + 9 = 60 = 3 x 20.

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Re: Is it just me, or does the average guy really suck at ma

Postby mister k » Mon Jul 05, 2010 10:33 am UTC

I just complete the square at any opportunity. To the point where I confused some tutees in a "maths for oceanographers" class when I explained completing the square to them rather than just telling them to use the quadratic formula, which I was probably meant to... Oh, and from my experience teaching that class of 18 year old students who were clearly quite smart, yes, yes the average guy really sucks at maths.
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Re: Is it just me, or does the average guy really suck at ma

Postby Tirian » Mon Jul 05, 2010 11:36 am UTC

Meh. If it bothers you that much, go watch "Die Hard with a Vengeance" where the heroes solve the four gallon jug puzzle in three minutes with a bomb underneath them. That's the scene that taught me that proper math makes for horrible movie dialog and that I should never wish for it again.

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Re: Is it just me, or does the average guy really suck at ma

Postby mike-l » Mon Jul 05, 2010 12:54 pm UTC

My guess at what happened here

"Hey mister math prof, what's a hard math problem that isn't too hard to explain to an audience"
'Factoring large numbers'

Script writers interpret large as over 100, and you have your movie.

Also, while I don't disagree with the conclusion, making judgments on the general populace's math skills based on one cult movie is pretty bad statistics :P
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Re: Is it just me, or does the average guy really suck at ma

Postby snowyowl » Mon Jul 05, 2010 1:57 pm UTC

mike-l wrote:My guess at what happened here

"Hey mister math prof, what's a hard math problem that isn't too hard to explain to an audience"
'Factoring large numbers'

Script writers interpret large as over 100, and you have your movie.


Oh my goodness... that makes perfect sense. Even explains where they got the idea that "a normal person can't factorise numbers" from.
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Re: Is it just me, or does the average guy really suck at ma

Postby Shotglass » Mon Jul 05, 2010 9:30 pm UTC

PM 2Ring wrote:Like getting Kepler's T² = kR³ from Newton's law of gravitational attraction & the formula for centripetal acceleration, for example?


cant say ive done that before but it doesnt seem too complicated except for a rather large number of variables to keep track of
usually its more about bringing equations into forms you wont find in refernece works (or for the most part on wikipedia) without having to pull out a sheet of paper

I see. :) But it's pretty easy to tell that 51 is divisible by 3, and that 51 + 9 = 60 = 3 x 20.


not for my arithmetically challenged mind

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Re: Is it just me, or does the average guy really suck at ma

Postby webby » Mon Jul 05, 2010 11:56 pm UTC

The spokesman for finance from one of the two major parties in Australia... Not sure if a politician fits the definition of 'average guy', but after it happened there was so much sympathy for him - 'it's easy to mix up millions and billions' etc. :P

http://www.youtube.com/watch?v=SNLkCRgHrbA

"Let us look at the cost of this policy, we are looking at $3.2 billion over the next four years. We have expenditure over the MYEFO statements, if I'm correct of about $1.4 billion, that we're going to spend. The Labor Party is about to spend 1400 million dollars. So I think I can find 3.2 from 1400, I really do, I think I'm up to that match."

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Re: Is it just me, or does the average guy really suck at ma

Postby the tree » Tue Jul 06, 2010 11:11 am UTC

Shotglass wrote:
I see. :) But it's pretty easy to tell that 51 is divisible by 3, and that 51 + 9 = 60 = 3 x 20.


not for my arithmetically challenged mind
Not sure how you define 'pretty easy'. My thought process went that 51+9=60, so 51 must be divisible by 3. Then since 60=3*20 and 9=3*3, it must be that 51=(20-3)*3=17*3 oh and hey look there's a 20 in the rest of the equation etc. etc. Not exactly headache inducing but it takes a good few seconds. Does that make it difficult? I wouldn't say so, just, time consuming.

For that matter how do you define really sucks? In comparison with someone who took maths to the end of high school - yeah, maybe. But in comparison with say, a rock, I'd say that the average guy is fairly good at arithmetic at least.

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Re: Is it just me, or does the average guy really suck at ma

Postby SlyReaper » Tue Jul 06, 2010 11:38 am UTC

Shotglass wrote:
I see. :) But it's pretty easy to tell that 51 is divisible by 3, and that 51 + 9 = 60 = 3 x 20.


not for my arithmetically challenged mind


It's even easier than that. 5+1 = 6 which is divisible by three. If the digits in a number add together to make a multiple of three, the number itself is a multiple of three. I used to know the proof of that.
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Re: Is it just me, or does the average guy really suck at ma

Postby the tree » Tue Jul 06, 2010 11:42 am UTC

SlyReaper wrote:
Shotglass wrote:
I see. :) But it's pretty easy to tell that 51 is divisible by 3, and that 51 + 9 = 60 = 3 x 20.


not for my arithmetically challenged mind


It's even easier than that. 5+1 = 6 which is divisible by three. If the digits in a number add together to make a multiple of three, the number itself is a multiple of three. I used to know the proof of that.
That doesn't make things much easier. Unless, for some reason, you suspect that it's a multiple of 3 and you're looking for confirmation. But finding things is always easier when you already know what you're looking for.

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Re: Is it just me, or does the average guy really suck at ma

Postby PM 2Ring » Tue Jul 06, 2010 12:36 pm UTC

SlyReaper wrote:If the digits in a number add together to make a multiple of three, the number itself is a multiple of three. I used to know the proof of that.

I learned it as a "magic formula" in primary school. But the proof's not hard. Here's a hint:
10a + b = 9a + (a + b)

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Re: Is it just me, or does the average guy really suck at ma

Postby tesseraktik » Tue Jul 06, 2010 1:40 pm UTC

I see somebody went ahead and referenced this thread on Cube_(film)#Mathematics. Given the fact that adding xkcd strips as pop culture references on Wikipedia often leads to heated arguments, I'm guessing this won't be entirely uncontroversial.
mike-l wrote:My guess at what happened here

"Hey mister math prof, what's a hard math problem that isn't too hard to explain to an audience"
'Factoring large numbers'

Script writers interpret large as over 100, and you have your movie.
Win for truth.

mike-l wrote:Also, while I don't disagree with the conclusion, making judgments on the general populace's math skills based on one cult movie is pretty bad statistics :P
I was wondering why <site which shall not be named, so as to save you all from tab explosion> didn't have an article called "You Fail Statistics Forever"... ...but after I just flippin' Google:d it, I saw that they did; huzzah!
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Re: Is it just me, or does the average guy really suck at ma

Postby mike-l » Tue Jul 06, 2010 1:42 pm UTC

the tree wrote:That doesn't make things much easier. Unless, for some reason, you suspect that it's a multiple of 3 and you're looking for confirmation. But finding things is always easier when you already know what you're looking for.


Well, generally when factoring small numbers, you just check divisibility by primes up to it's square root. For 51, these are 2,3,5,7.
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Re: Is it just me, or does the average guy really suck at ma

Postby Black » Tue Jul 06, 2010 1:50 pm UTC

Given some arbitrary field of knowledge, the average person probably sucks at it.

Unless it's sex.

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Re: Is it just me, or does the average guy really suck at ma

Postby Yakk » Tue Jul 06, 2010 1:53 pm UTC

Factoring numbers up to 100:
Is it even, or does it end in a 5? If so, divide by 2 and/or 5.
Is the number a perfect square?
Is the number 91? If so, the answer is 7*13.
Add up the digits. Is the answer divisible by 3? If so, it is divisible by 3.
The number is prime.

Or, in short: all non-primes and non-squares, except 91, up to 100 are divisible by 2, 3 or 5. Checking for divisibility by 2, 3 or 5 is easy. Just remember 91 as the lowest number that looks prime, but isn't.
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision - BR

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gmalivuk
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Re: Is it just me, or does the average guy really suck at ma

Postby gmalivuk » Tue Jul 06, 2010 1:56 pm UTC

DavCrav wrote:Hmm. My standard way is: 51 = 3 * 17. Note that 3+17 is 20, which is what we want.
Yeah, same here. Though admittedly I was helped by knowing this particular example was put there as an example the poster thought should be possible mentally, and so I immediately went to the simplest mental method I could think of, which is really fast in the few cases when you're lucky enough for it to work, but in general not that helpful.
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Re: Is it just me, or does the average guy really suck at ma

Postby jaap » Tue Jul 06, 2010 2:03 pm UTC

Yakk wrote:Factoring numbers up to 100:
Is it even, or does it end in a 5? If so, divide by 2 and/or 5.
Is the number a perfect square?
Is the number 91? If so, the answer is 7*13.
Add up the digits. Is the answer divisible by 3? If so, it is divisible by 3.
The number is prime.

Or, in short: all non-primes and non-squares, except 91, up to 100 are divisible by 2, 3 or 5. Checking for divisibility by 2, 3 or 5 is easy. Just remember 91 as the lowest number that looks prime, but isn't.


... and 77.
I agree it doesn't look prime, but you left it out.

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Re: Is it just me, or does the average guy really suck at ma

Postby PM 2Ring » Tue Jul 06, 2010 2:06 pm UTC

gmalivuk wrote:I immediately went to the simplest mental method I could think of, which is really fast in the few cases when you're lucky enough for it to work, but in general not that helpful.

Fair call. Perhaps I'm a tad biased from doing lots of factorizing drill when I was learning quadratics, back in the early 1970s. And since I'm pretty fast at factorizing, I always give it a try before moving on to completing the square.


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