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# Math - pattern "discovery"

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I'm sure this is common knowledge to the math community but I stumbled upon an interesting pattern of sorts while being bored and multiplying numbers in my head. Here is what I found:

If you take two numbers that equal 20 when added together, and multiply them, you get various totals.

10 x 10 = 100 and the two numbers being multiplied equal 20.

9 x 11 = 99 and the two numbers being multiplied equal 20.

8 x 12 = 96

7 x 13 = 91

6 x 14 = 84

5 x 15 = 75

4 x 16 = 64

3 x 17 = 51

2 x 18 = 36

1 x 19 = 19

0 x 20 = 0

Look at the totals for each. What is significant about each?

Hint: Think inversely.

I will post the answer shortly. But people first have to reply with feigned interest and effort at finding the hidden pattern here.

The totals go down in this fashion: 1-3-5-7-9-11-13-15-17-19.

EDIT: Nyuck Nyuck Nyuck!

The totals decrease by 1, 3, 5, 7, 9, 11, 13, 15, 17, and 19 in order.

Edit: Damn you J >=\

Each sum is a square number less than the original number? e.g. n* n = n² = 100, (n - 1) * (n + 1) = n² - 1, (n - 2) * (n + 2) = n² - 2² ... (n - x) * (n + x) = n² - x²

0_0
Pardon.

Math make heady go boom boom.

*paff*

Ah, Fibonacci Sequence.
Is there anything you can't do?

Wow, there's a name for it -- most impressive.

you fried my damn brain!!!!
i hated math, thats why i never got into or stayed with programing, like C and C++

i am horrible at math, but i know plenty to get by. if i need more i can always take classes, even though it is my least favorite subject

some of the responses seemed pretty intelligent but I think GS-1719 was the closest. No, it wasn't related to the fibonacci sequence.

100 - 100 = 0
100 - 99 = 1
100 - 96 = 4
100 - 91 = 9
100 - 84 - 16
100 - 75 = 25
100 - 64 = 36
100 - 51 = 49
100 - 36 = 64
100 - 19 = 81
100 - 0 = 100

Hellbent said:

I think GS-1719 was the closest

Well, he pointed out the algebraic identity (n - x) * (n + x) = n² - x², so I'd say he pretty much pwned it. :p

I don't think he meant to show off with the word "discovery." Heh.

Hellbent said:

some of the responses seemed pretty intelligent but I think GS-1719 was the closest. No, it wasn't related to the fibonacci sequence.

100 - 100 = 0
100 - 99 = 1
100 - 96 = 4
100 - 91 = 9
100 - 84 - 16
100 - 75 = 25
100 - 64 = 36
100 - 51 = 49
100 - 36 = 64
100 - 19 = 81
100 - 0 = 100

so when the answers are subtracted from 100 they are all square roots besides 0 and 1? heh, ok. I see the 'think inversely' clue, though I never though about subtracting them from 100.

Sephiroth said:

i hated math, thats why i never got into or stayed with programing, like C and C++

Where exactly is the connection between this problem (or math in general) and programming C/C++?

Eh, so it wasn't Fibonacci. It was odd numbers-- something even less amazing. To be honest, I only paid attention to about 3% of the post.

you guys broke my brain even more.
nuff said, i need a beer now

"Not all negative thoughts are bad" prolly would have been a better clue. Didn't think of it till after the post, though.

It works with any two numbers, not just 10 and 10.

So you could do 37 and 37 and it would work just the same.

Anwyay, thanks for taking interest in my nerdiness, although I don't understand any of the algebraic representations that people replied with. I hate symbolism.

Ooh, I think I might get it. :P It counts from zero to ten. :D
100 - 100 = 0 SqR = 0
100 - 99 = 1 SqR = 1
100 - 96 = 4 SqR = 2
100 - 91 = 9 SqR = 3
100 - 84 = 16 SqR = 4
100 - 75 = 25 SqR = 5
100 - 64 = 36 SqR = 6
100 - 51 = 49 SqR = 7
100 - 36 = 64 SqR = 8
100 - 19 = 81 SqR = 9
100 - 0 = 100 SqR = 10
That took me forever to figure out, whether it was what you were thinking or not. :P

And more funny:

0²=0 0+1=1
1²=1 1+3=4
2²=4 4+5=9
3²=9 9+7=16
4²=16 16+9=25
5²=25 25+11=36
and so on, look at the added numbers, they are odd numbers: 1, 3, 5, 7 etc.
Why?
n²+something=(n+1)² so something=(n+1)²-n²=n²+2n+1-n²=2n+1 which is odd. And you can even find why you add 11 to 25 to obtain 36: 25=5² and 2×5+1=11.
Funny, heh?

math is hard, and it pisses me off

ducon said:

And more funny:

0²=0 0+1=1
1²=1 1+3=4
2²=4 4+5=9
3²=9 9+7=16
4²=16 16+9=25
5²=25 25+11=36
and so on, look at the added numbers, they are odd numbers: 1, 3, 5, 7 etc.
Why?
n²+something=(n+1)² so something=(n+1)²-n²=n²+2n+1-n²=2n+1 which is odd. And you can even find why you add 11 to 25 to obtain 36: 25=5² and 2×5+1=11.
Funny, heh?

hahaha, you just made my day!

I already knew the square pattern, but then you said

Hellbent said:

Hint: Think inversely.

and I started looking at inverse functions. And from there it went to shit.

Hellbent said:

Anwyay, thanks for taking interest in my nerdiness, although I don't understand any of the algebraic representations that people replied with. I hate symbolism.

Mathematics is all about using symbols. heh

Grazza said:

Use the source, Luke!

It's true that having a good grasp of maths helps to be a proficient programmer, but not all math computer science requires is calculus, linear algebra or whatever. From what I've seen, formal methods, decidability, type theory and that kind of stuff is - while not exactly easy to understand - much more relevant to the theoretical aspects of the thing.

But then again, I'm becoming a Haskell zealot :D

Discrete math is what programmers deal with most of the time, and it's a whole different can of worms from the math you do most of the time (btw, mathematical treatment of algorithms falls under the broad umbrella of discrete math, too).

I got a C in Discrete Math :(

Algorithm analysis is one of the most fun things I've learned since I entered uni...