
Author  Message 

Bub
Registration date : 20071215
 Subject: 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 

 
Rad Davis
Age : 68 Location : Foley, Alabama, USA Registration date : 20071216
 Subject: 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 

 
Rob_In_MO
Age : 44 Location : Park Hills, MO Registration date : 20110119
 Subject: 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+CA.
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 AC1
It's interesting to observe that D + F = 9. Do you see why? D=AC1, and F=10+CA, so D+F = AC1+10+CA = 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. 

 
puros_bran Nightrider
Location : Brandenburg, Ky Registration date : 20071210
 Subject: 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. 

 
mark Admin
Registration date : 20080702
 Subject: 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 ????????????? _________________ .
Sometimes I wake up grumpy. Other times I let her sleep. .


 
puros_bran Nightrider
Location : Brandenburg, Ky Registration date : 20071210
 Subject: 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! 

 
Rad Davis
Age : 68 Location : Foley, Alabama, USA Registration date : 20071216
 Subject: 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 

 
MisterE Moderator
Location : Mexico City Registration date : 20090824
 Subject: 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+CA.
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 AC1
It's interesting to observe that D + F = 9. Do you see why? D=AC1, and F=10+CA, so D+F = AC1+10+CA = 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, I´m impressed! It reminds me why I became a trumpet player!! 

 
Bub
Registration date : 20071215
 Subject: 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
312213= 99 Here is an example 762267=495 495+594=1089 

 
Rad Davis
Age : 68 Location : Foley, Alabama, USA Registration date : 20071216
 Subject: 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 312213= 99 Here is an example 762267=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. Rad 

 
Harlock999
Location : Los Angeles Registration date : 20101022
 Subject: 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+CA.
Dude, I´m impressed! It reminds me why I became a trumpet player!!
It reminds me of why I didn't become an accountant! 

 
MisterE Moderator
Location : Mexico City Registration date : 20090824
 Subject: Re: The answer is 1089 Thu Apr 07, 2011 11:43 pm  
 

 
CLRV
Age : 33 Location : Tulsa, Oklahoma Registration date : 20101229
 Subject: 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.


 
puros_bran Nightrider
Location : Brandenburg, Ky Registration date : 20071210
 Subject: Re: The answer is 1089 Fri Apr 08, 2011 6:47 am  
 

 
mark Admin
Registration date : 20080702
 Subject: Re: The answer is 1089 Fri Apr 08, 2011 10:25 am  
 So the odds are 5050 that 23 board members match the 1089 posts at the same time?,,,,, _________________ .
Sometimes I wake up grumpy. Other times I let her sleep. .


 
MisterE Moderator
Location : Mexico City Registration date : 20090824
 
 
