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### Forming Palindromic Numbers

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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

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/
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Associated Topics:
High School Number Theory