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 The answer is 1089

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Bub

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Registration date : 2007-12-15

PostSubject: The answer is 1089   Thu Apr 07, 2011 12:31 pm

1. select a three digit number
2. reverse the digits and subtract the two numbers
3. reverse the digits
4. add the two numbers

caveats:
1 all numbers must have three digits
2. no negative numbers

request: tell me why this works
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Rad Davis

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Age : 68
Location : Foley, Alabama, USA
Registration date : 2007-12-16

PostSubject: Re: The answer is 1089   Thu Apr 07, 2011 1:56 pm

Bub wrote:
1. select a three digit number
2. reverse the digits and subtract the two numbers
3. reverse the digits
4. add the two numbers

caveats:
1 all numbers must have three digits
2. no negative numbers

request: tell me why this works

I think I need better instructions.

Rad
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Rob_In_MO

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Age : 44
Location : Park Hills, MO
Registration date : 2011-01-19

PostSubject: Re: The answer is 1089   Thu Apr 07, 2011 2:18 pm

Here's why it works. Let the digits of the original number be ABC, and assume without loss of generality that A is larger than C. Now consider the subtraction,

ABC
-CBA
----
DEF

When you do the subtraction, you find that you can't take A from C because A is larger than C, so you need to "borrow".
So the ones digit, F, is 10+C-A.

Since you borrowed from the 10's column, and you have B minus B in that column, so you have to borrow again.
The result must be 9 in the 10's column, so E=9.

Since you borrowed from the 100's column, the result in that column must be A-C-1

It's interesting to observe that D + F = 9. Do you see why? D=A-C-1, and F=10+C-A, so D+F = A-C-1+10+C-A = 9.
This will come up later, so it's good to be clear about this point.

Now, let's go on to the addition of DEF to FED. Did you remember that E is 9? I'll just write it that way:

D9F
-F9D
----
1XYZ

Did you also remember that F+D=9? So Z must be 9, too.

D9F
-F9D
----
1XY

And there's no carry out of the one's place, so Y must be 8, but then there's a carry into the 100's place.
Here's what we have so far.

1
D9F
-F9D
----
1X89

I wrote a little "1" over the hundreds column to show the carry out of the tens place. We'll use, again, the fact
that D+F=9, and with the carry, the result becomes 10, so the final result is

1
D9F
-F9D
-----
1089

No matter what ABC we start with.
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puros_bran
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Location : Brandenburg, Ky
Registration date : 2007-12-10

PostSubject: Re: The answer is 1089   Thu Apr 07, 2011 4:25 pm

After ten Amber Bock and two more standing in front of me I can assure you the answer is 42 not 1089.. The answer to everything is 42 my friend. And Radio Margaritaville rocks..never forget that either.
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mark
Admin
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Registration date : 2008-07-02

PostSubject: Re: The answer is 1089   Thu Apr 07, 2011 4:35 pm

Bub wrote:
1. select a three digit number
2. reverse the digits and subtract the two numbers
3. reverse the digits
4. add the two numbers

caveats:
1 all numbers must have three digits
2. no negative numbers

request: tell me why this works



1) 999
2)-999
_____
3) 000
4)+000
_______
000 ?????????????

_________________
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Sometimes I wake up grumpy. Other times I let her sleep.
.
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puros_bran
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Location : Brandenburg, Ky
Registration date : 2007-12-10

PostSubject: Re: The answer is 1089   Thu Apr 07, 2011 5:02 pm

You boys are making life difficult...lol

Stars on the water in the rain!
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Rad Davis

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Age : 68
Location : Foley, Alabama, USA
Registration date : 2007-12-16

PostSubject: Re: The answer is 1089   Thu Apr 07, 2011 6:44 pm

See, I started off with 312. No matter what I did I couldn't come up with 1089.

It comes out 198.

Rad
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MisterE
Moderator
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Location : Mexico City
Registration date : 2009-08-24

PostSubject: Re: The answer is 1089   Thu Apr 07, 2011 7:15 pm

Rob_In_MO wrote:
Here's why it works. Let the digits of the original number be ABC, and assume without loss of generality that A is larger than C. Now consider the subtraction,

ABC
-CBA
----
DEF

When you do the subtraction, you find that you can't take A from C because A is larger than C, so you need to "borrow".
So the ones digit, F, is 10+C-A.

Since you borrowed from the 10's column, and you have B minus B in that column, so you have to borrow again.
The result must be 9 in the 10's column, so E=9.

Since you borrowed from the 100's column, the result in that column must be A-C-1

It's interesting to observe that D + F = 9. Do you see why? D=A-C-1, and F=10+C-A, so D+F = A-C-1+10+C-A = 9.
This will come up later, so it's good to be clear about this point.

Now, let's go on to the addition of DEF to FED. Did you remember that E is 9? I'll just write it that way:

D9F
-F9D
----
1XYZ

Did you also remember that F+D=9? So Z must be 9, too.

D9F
-F9D
----
1XY

And there's no carry out of the one's place, so Y must be 8, but then there's a carry into the 100's place.
Here's what we have so far.

1
D9F
-F9D
----
1X89

I wrote a little "1" over the hundreds column to show the carry out of the tens place. We'll use, again, the fact
that D+F=9, and with the carry, the result becomes 10, so the final result is

1
D9F
-F9D
-----
1089

No matter what ABC we start with.

Dude, Im impressed! It reminds me why I became a trumpet player!! lol! lol!
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Bub

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Registration date : 2007-12-15

PostSubject: Re: The answer is 1089   Thu Apr 07, 2011 8:29 pm

Rad said
Quote :
See, I started off with 312. No matter what I did I couldn't come up with 1089.

It comes out 198.

Rad
Bub said
Quote :
caveats:
1 all numbers must have three digits
312-213= 99
Here is an example
762-267=495
495+594=1089
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Rad Davis

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Age : 68
Location : Foley, Alabama, USA
Registration date : 2007-12-16

PostSubject: Re: The answer is 1089   Thu Apr 07, 2011 11:16 pm

Bub wrote:
Rad said
Quote :
See, I started off with 312. No matter what I did I couldn't come up with 1089.

It comes out 198.

Rad
Bub said
Quote :
caveats:
1 all numbers must have three digits
312-213= 99
Here is an example
762-267=495
495+594=1089

That just gets too complicated for me.

I can think up a three digit number very easily, but to think up one that when the digits are reversed and then you subtract one from the other to come up with another three digit number? No Way. That's where I draw the line. Laughing

Rad
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Harlock999

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Location : Los Angeles
Registration date : 2010-10-22

PostSubject: Re: The answer is 1089   Thu Apr 07, 2011 11:26 pm

MisterE wrote:
Rob_In_MO wrote:
Here's why it works. Let the digits of the original number be ABC, and assume without loss of generality that A is larger than C. Now consider the subtraction,

ABC
-CBA
----
DEF

When you do the subtraction, you find that you can't take A from C because A is larger than C, so you need to "borrow".
So the ones digit, F, is 10+C-A.

Dude, Im impressed! It reminds me why I became a trumpet player!! lol! lol!

It reminds me of why I didn't become an accountant!
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MisterE
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Location : Mexico City
Registration date : 2009-08-24

PostSubject: Re: The answer is 1089   Thu Apr 07, 2011 11:43 pm

Harlock999 wrote:
MisterE wrote:
Rob_In_MO wrote:
Here's why it works. Let the digits of the original number be ABC, and assume without loss of generality that A is larger than C. Now consider the subtraction,

ABC
-CBA
----
DEF

When you do the subtraction, you find that you can't take A from C because A is larger than C, so you need to "borrow".
So the ones digit, F, is 10+C-A.

Dude, Im impressed! It reminds me why I became a trumpet player!! lol! lol!

It reminds me of why I didn't become an accountant!

Yeah, I know- my brain hurts just looking at it!! lol!
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CLRV

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Age : 33
Location : Tulsa, Oklahoma
Registration date : 2010-12-29

PostSubject: Re: The answer is 1089   Fri Apr 08, 2011 5:36 am

Ok, MisterE, at the time of me writing this you have, I $&!# you not, 1089 posts.

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puros_bran
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Location : Brandenburg, Ky
Registration date : 2007-12-10

PostSubject: Re: The answer is 1089   Fri Apr 08, 2011 6:47 am

Now thats funny!!!
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mark
Admin
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Registration date : 2008-07-02

PostSubject: Re: The answer is 1089   Fri Apr 08, 2011 10:25 am

So the odds are 50-50 that 23 board members match the 1089 posts at the same time?,,,,,

_________________
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Sometimes I wake up grumpy. Other times I let her sleep.
.
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MisterE
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Location : Mexico City
Registration date : 2009-08-24

PostSubject: Re: The answer is 1089   Fri Apr 08, 2011 11:43 am

Geez, thats hilarious!! Youre right! Its truly the "magical equation" for sure.

Oops- once I send this it will be 1090.

lol! lol! lol!
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