Hellbent Posted July 23, 2004 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 What do you notice about this pattern? 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. 0 Share this post Link to post

Janderson Posted July 24, 2004 The totals go down in this fashion: 1-3-5-7-9-11-13-15-17-19. EDIT: Nyuck Nyuck Nyuck! 0 Share this post Link to post

Infinite Ammunition Posted July 24, 2004 The totals decrease by 1, 3, 5, 7, 9, 11, 13, 15, 17, and 19 in order. Edit: Damn you J >=\ 0 Share this post Link to post

GS-1719 Posted July 24, 2004 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 Share this post Link to post

Bucket Posted July 24, 2004 Ah, Fibonacci Sequence. Is there anything you can't do? 0 Share this post Link to post

Mogul Posted July 24, 2004 Wow, there's a name for it -- most impressive. 0 Share this post Link to post

Sephiroth Posted July 24, 2004 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 0 Share this post Link to post

Hellbent Posted July 24, 2004 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 0 Share this post Link to post

Grazza Posted July 24, 2004 Hellbent said:I think GS-1719 was the closestWell, he pointed out the algebraic identity (n - x) * (n + x) = n² - x², so I'd say he pretty much pwned it. :p 0 Share this post Link to post

Mogul Posted July 24, 2004 I don't think he meant to show off with the word "discovery." Heh. 0 Share this post Link to post

Quast Posted July 24, 2004 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. 0 Share this post Link to post

boris Posted July 24, 2004 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++? 0 Share this post Link to post

Bucket Posted July 24, 2004 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. 0 Share this post Link to post

Sephiroth Posted July 24, 2004 you guys broke my brain even more. nuff said, i need a beer now 0 Share this post Link to post

Hellbent Posted July 24, 2004 "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. 0 Share this post Link to post

DOOM Anomaly Posted July 24, 2004 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 0 Share this post Link to post

ducon Posted July 24, 2004 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? 0 Share this post Link to post

MaximusNukeage Posted July 24, 2004 math is hard, and it pisses me off 0 Share this post Link to post

Mogul Posted July 24, 2004 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! 0 Share this post Link to post

=laff=Mish Posted July 24, 2004 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. 0 Share this post Link to post

Grazza Posted July 25, 2004 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 0 Share this post Link to post

ducon Posted July 25, 2004 Grazza said:heh This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article Philosophy of mathematics Use the source, Luke! 0 Share this post Link to post

spank Posted July 25, 2004 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 0 Share this post Link to post

Quasar Posted July 25, 2004 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 :( 0 Share this post Link to post

spank Posted July 26, 2004 Algorithm analysis is one of the most fun things I've learned since I entered uni... 0 Share this post Link to post