Orchid XP v8 <voi### [at] devnull> wrote:
> >   Unfortunately not many people have that kind of deduction power at
> > that age (or at any age).

> For what it's worth, I can never ever remember *exactly* what the 
> correct formula for that is. It's roughly half the square, but I can 
> never remember the exact figure.

  You shouldn't memorize the formula (like most people do). You should
understand where it comes from (as I wrote in my previous post).

  Basically the general rule is: If you have to sum n numbers (whatever
those numbers might be), then summing the average of those numbers n times
with itself (or, in other words, multiplying the average by n) gives the
same result. If you think a bit about why this is so, it should be rather
simple.

  (Answer: The average of the numbers is calculated by summing the numbers
and dividing the result by n (which is the total amount of numbers). If you
multiply this average by n, you are nullifying the division, which gives you
the original sum.)

  With random numbers this rule doesn't help much (because calculating the
average of some random numbers would require you to sum those numbers
together, which was what you wanted to avoid doing in the first place), but
with consecutive numbers it does, because calculating the average of a
consecutive series of numbers can be done without having to all sum those
numbers.

  For example, the average of all the numbers between 1 and 100 (inclusive)
is (1+100)/2. Now just multiply that by the total amount of numbers, and
you have the sum.

  This same deduction works for any other ranges as well, even if the
numbers are not consecutive, as long as you can easily calculate their
average.

  Example: Calculate the sum of all the even numbers between 2 and 100
(inclusive).

  Answer: The average of all those numbers is (2+100)/2. The total amount
of even numbers in that range is 50, so multiply that average by 50, and
you got your result.

  Exercise: Calculate the sum of all the numbers between 100 and 1000
which are divisible by 7. (Obviously the range is non-inclusive because
neither 100 nor 1000 are divisible by 7.)

-- 
                                                          - Warp

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Orchid XP v8 wrote:
> Oh well, I got a famous mathematician who's name starts with the right 
> letter! ;-)

And one who was also a child prodigy, too bad Galios had to go and kill 
himself in a duel so early in his life.

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Warp wrote:
> http://www.youtube.com/watch?v=lCJ3Oz5JVKs

Full story if anyone wants it:

http://verizonmath.blogspot.com/

-- 
I think animal testing is a terrible idea. They get all nervous and give
the wrong answers.


                    /\  /\               /\  /
                   /  \/  \ u e e n     /  \/  a w a z
                       >>>>>>mue### [at] nawazorg<<<<<<
                                   anl

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Kevin Wampler wrote:
> This reminds me of a story told by my high school physics teacher about
> a survey done to test people's understanding of basic science concepts
> which contained the question:
> 
> "is there gravity on the moon"
> 
> A large number of people got this wrong, which is odd but maybe not so
> surprising.  What's more surprising is that the they were then asked:
> 
> "You've seen the videos of people walking on the moon, if there's no
> gravity how do they do that?"
> 
> Some people changed their answer at this point, but aparently a large
> number responded:
> 
> "Because they have heavy boots!"
> 
> I completely fail to understand the reasoning that would give rise to
> such a conclusion.

	Trust me, I had this very discussion (with the same and similar
nonsensical answers) with a number of my high school friends in those days.


-- 
I think animal testing is a terrible idea. They get all nervous and give
the wrong answers.


                    /\  /\               /\  /
                   /  \/  \ u e e n     /  \/  a w a z
                       >>>>>>mue### [at] nawazorg<<<<<<
                                   anl

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Kevin Wampler wrote:
> Orchid XP v8 wrote:
>> Oh well, I got a famous mathematician who's name starts with the right
>> letter! ;-)
> 
> And one who was also a child prodigy, too bad Galios had to go and kill
> himself in a duel so early in his life.

	Yes. Pity about his more famous brother, Galois, who died a similar death.

	(I couldn't let *two* people make the same mistake and get away with it).

-- 
I think animal testing is a terrible idea. They get all nervous and give
the wrong answers.


                    /\  /\               /\  /
                   /  \/  \ u e e n     /  \/  a w a z
                       >>>>>>mue### [at] nawazorg<<<<<<
                                   anl

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Mueen Nawaz wrote:
> Kevin Wampler wrote:
>> Orchid XP v8 wrote:
>>> Oh well, I got a famous mathematician who's name starts with the right
>>> letter! ;-)
>> And one who was also a child prodigy, too bad Galios had to go and kill
>> himself in a duel so early in his life.
> 
> 	Yes. Pity about his more famous brother, Galois, who died a similar death.
> 
> 	(I couldn't let *two* people make the same mistake and get away with it).


You know, I actually double-checked the spelling before I posted yet 
somehow I *still* messed it up!

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Warp wrote:
> http://www.youtube.com/watch?v=lCJ3Oz5JVKs

As one of the comments said,

   "Let me explain in simple terms why there stupid. There yanks!"

(I couldn't help noticing that whoever wrote this is actually using the 
wrong word. Who's stupid, again?)

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Warp wrote:
> Orchid XP v8 <voi### [at] devnull> wrote:
>>>   Unfortunately not many people have that kind of deduction power at
>>> that age (or at any age).
> 
>> For what it's worth, I can never ever remember *exactly* what the 
>> correct formula for that is. It's roughly half the square, but I can 
>> never remember the exact figure.
> 
>   You shouldn't memorize the formula (like most people do). You should
> understand where it comes from (as I wrote in my previous post).

Indeed yes. It just takes a minute or two to puzzle it out each time, 
which is mildly irritating...

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>  I suppose the kid's reasoning was something like: "Hmm, actually if I
> take the *average* of all the numbers, and multiply it by the amount of
> numbers, I should get the correct result, because summing the average
> 100 times should be the same as summing all the original 100 numbers.
> Now, what is the average of all the numbers between 1 and 100? It must
> be (100+1)/2. Now multiply that by the amount of numbers, ie. 100, and
> we have the answer."

The version I heard was that he imagined the numbers written 1-100, and then 
the same numbers written 100-1 underneath.  Like this:

  1  2  3  4  5  6 ...
100 99 98 97 96 95 ...

Now if you sum up both of those you should get twice the answer right?  But 
first he summed each column of two numbers to get:

101 101 101 101 101 ...

Then of course it's trivial.

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Kevin Wampler wrote:
> WE HAVE 300 MILLION CITIZENS. IF WE GAVE EVERYONE 1 MILLION DOLLARS
> WOULDN'T THAT BE 300 MILLION DOLLARS?

Oh dear god >_<

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