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Forming Palindromic Numbers


Date: 12/04/98 at 09:34:10
From: ANDREJ KECKES
Subject: Palindromic Numbers

Hello, 

I'm interested in palindromic numbers. I'm wondering if there is a list 
that tells which numbers can be made into palindromic sums and how many 
steps would be required. Could you please write me a list for numbers 
under 10,000? I'm interested in operations with plus, minus, divide, 
multiply. 

For example: 

     32 + 23 = 55
   322 - 223 = 99                           
     21 * 12 = 252                            
     11 / 11 = 1


Date: 12/04/98 at 11:32:54
From: Doctor Rob
Subject: Re: Palindromic Numbers

I found 1532 examples for plus with at least one summand with four
decimal digits, such as 8431 + 1348 = 9779, or 8610 + 168 = 8778, or
8200 + 28 = 8228, or 7020 + 207 = 7227. I found 149 examples with the 
largest summand with three digits. I found 33 examples with the largest 
summand with two digits. There are 5 examples with the largest summand 
with one digit. This is too many to list for you. For a start on the 
list, please see:

   http://mathforum.org/dr.math/problems/barnes10.11.html   

There is a similar profusion for minus.

Times is much more tractable, with only seven solutions up to 10000:

   0 * 0 = 0
   1 * 1 = 1
   2 * 2 = 4
   3 * 3 = 9
   11 * 11 = 121
   12 * 21 = 252
   22 * 22 = 484

For division, you can take any palindrome and divide it by itself:

   1239874789321 : 1239874789321 = 1.

Aside from these, I found the following two with numerator and
denominator < 10000.

   8712 : 2178 = 4
   9801 : 1089 = 9

- Doctor Rob, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Number Theory
Middle School Number Sense/About Numbers

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