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NarcNobbler
Joined: 17 Feb 2007
Posts: 334
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 Posted: Mon Nov 05, 2007 10:44 am Post subject: Just plain Weird (think of a 2 digit number) |
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http://milaadesign.com/wizardy.html
Narc.
_________________
"You become what you Hate"
God loves a trier, but I can take a hint!
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louxloux
Joined: 20 Jul 2007
Posts: 1523
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| Posted: Tue Nov 06, 2007 12:19 am Post subject: |
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that is weird!
did it like 4 or 5 times... it was right each time.
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disengaging
Joined: 15 Feb 2007
Posts: 1340
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| Posted: Fri Nov 09, 2007 5:37 pm Post subject: |
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Thanks Narc!
It may seem "weird" but there's really no mystery about why it works--every time.
It's based on a very simple algebraic forumla--and my very favorite mathematical principle, "Multiples of 9"!
To explain this very simply, if you take any 2 digit number, add up the 2 digits, and then subtract that from your original number, the answer will ALWAYS be a "multiple of nine."
The "Multiples of 9" are as follows:
0 x 9 = 0
1 x 9 = 9
2 x 9 = 18
3 x 9 = 27
4 x 9 = 36
5 x 9 = 45
etc.
So the "multiples of 9" are as follows: 0, 9, 18, 27, 36, 45, 54, 63, 72, 81, 90 and so on.
So, if you chose 23, then 2+5=5. 23-5 = 18. 18 is a "multiple of 9".
If you chose 49, then 4+9=13. 49-13 = 36. 36 is a "multiple of 9".
Likewise, if you chose 56, then 5+6=11. 56-11=45. 45 is a "multiple of 9.
Now, go back and do it again and take a good look at that chart with all the numbers, and take a closer look at the symbols assigned to each number on that chart. Although it may appear that the symbols are all different and they may change position each time, however, each time, on every chart, all "multiples of 9" have been assigned the same exact symbol!
Again, the "multiples of 9" are the numbers: 0, 9, 18, 27, 36, 45, 54, 63, 72, 81, 90.
Look closely and you will see that on every chart, they are always assigned the same symbol.
And that's how it works!
(If you remember, I'm an accountant specializing in auditing, and as an auditor, I have all kinds of uses for those wonderful "multiples of 9!)
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disengaging
Joined: 15 Feb 2007
Posts: 1340
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| Posted: Fri Nov 09, 2007 6:23 pm Post subject: |
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| Quote: | | To explain this very simply, if you take any 2 digit number, add up the 2 digits, and then subtract that from your original number, the answer will ALWAYS be a "multiple of nine." |
Oh! And I almost forgot! to explain WHY that answer will always be a "multiple of 9", that can be proven by a simple algebraic formula as follows:
To represent the 2 digit number you've selected, let X = 23, let A=the first digit and B= the second number. So, if you selected the the number 23, then let:
23 = X
2 = A
3 = B
And also let Y equal the final result, or
Y = final result
As we are on a "base 10" number system, the number 20 would actually be represented as 2 x 10 = 20, and the algebraic representation of your original 2 digit number would be A x 10 or A(10). So,
A(10) + B = X (2 x 10 = 20, 20 + 3 = 23)
Now add A + B and subtract that from your original number to arrive at the final result, or Y, as follows:
A(10) + B - (A + B) = y
Removing the parenthesis, will turn the + into -, leaving:
A(10) + B - A - B = Y
the positive and negative "B" now cancel each other out, leaving
A(10) - A = Y
Now, the negative A is removed, leaving
A(9) = Y which can now be represented as
A x 9 = Y.
So, the final result, Y, will ALWAYS equal the first digit times the number 9, meaning that Y will ALWAYS be a "multiple of 9"!
So, if your number was 23. 2 x 10 = 10, 20 + 3 = 23. 2 + 3 = 5.
23 - 5 = 18, and 18 is a multiple of 9, reduced down by this algebraic formula, 2 X 9 = 18.
If you chose 22? Well, 2 x 10 = 20, 20 + 2 = 22. 2 + 2 = 4. 22 - 4 = 18, and 18 is a multiple of 9, reduced down by this algebraic formula, 2 x 9 - 18.
So, if you chose ANY number in the 20s--20, 21, 22, 23, 24, 25, etc., the result will ALWAYS be 18, because 2 x 9 = 18
If you chose ANY number in the 30s, the result will ALWAYS be 27, because 3 x 9 = 27.
If you chose ANY number in the 40s, the result will ALWAYS be 36, because 4 x 9 = 36.
If you chose ANY number in the 50s, the result will ALWAYS be 45 because 5 x 9 = 45.
Remember, the algebraic formula boils down to:
A(10) + B - (A + B) = Y
Which is then further reduced to
A x 9 = Y
Which is why the first digit of the number you selected times 9 will equal your result (Y)--which means it will ALWAYS be a "multiple of 9".
Yeah I know, more information than you were looking for there..... 
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NarcNobbler
Joined: 17 Feb 2007
Posts: 334
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| Posted: Fri Nov 23, 2007 12:38 am Post subject: |
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Hi disengaging,
Sorry for the delay in replying, what was it they say about blonde's?  (definitely a vicious rumor)
I figured out the multiples or 9 and randomly switching the symbols.
But had no idea of the formula behind it.
You must be a wizz at sudoku.
And thanks for the enlightenment.
Narc.
_________________
"You become what you Hate"
God loves a trier, but I can take a hint!
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disengaging
Joined: 15 Feb 2007
Posts: 1340
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| Posted: Fri Dec 07, 2007 1:29 am Post subject: |
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| Quote: | | You must be a wizz at sudoku. |
I like Sudoku, but enjoy crossword and logic puzzles far more. Too bad I suck at chess, huh? 
Even more fun though? I like to challenge myself with a video work-out game called "Dance, Dance Revolution", where I've been teaching myself to remember the dance steps by turning them into mathematical formulas! (doubt anyone here would find the details remotely interesting so I'll restrain myself from elaborating.)
The website you provided actually isn't the original game, which was actually developed and designed by Cambridge College in England, and published first on the internet by the British Counsel under the name of "Magic Gopher". Their website can be found by following this link:
http://www.britishcouncil.org/learnenglish-central-games-magic-gopher.htm
It's the same game, just a slightly different presentation of it.
Hugs!
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Milo
Joined: 23 Oct 2007
Posts: 807
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| Posted: Mon Mar 17, 2008 12:50 am Post subject: |
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Dis,
The 'formula' is sort of beyond me but I too am fascinated with mathematical patterns.
Multiply a number by any number that is divisible by 3 (eg. 3,6, 9, 12, 24, 120, 2400 etc) and then add together the digits in the answer and that final number will also be divisible by 3.
Examples :
3 x 25 = 75 > 7+5=12 > 12 is divisable by 3 > 1+2 =3 so ditto
9 x 67 = 603 > 6+0+3 = 9 > is divisable by 3
27x841= 22, 707 > 2+2+7+0+7 =18> 1+8=9 , you get the drift
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