How can we find the seed from a given palindrome?

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To find the seed from a given palindrome, one must consider the process of adding a number to its reversed digits, which typically leads to a palindrome. The discussion highlights that while most integers can produce a palindrome through this iterative process, there are exceptions known as Lychrel numbers, which may never yield a palindrome. The conversation suggests that extracting a seed involves identifying the immediate predecessor of the palindrome, as all intermediate steps are considered seeds. It is noted that the behavior of numbers in the range of 1-10 digits may not accurately represent the overall trend, as larger numbers are more likely to be Lychrel. The challenge remains in determining a method to trace back from a palindrome to its originating seed.
rsala004
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not really math but wondering if someone is clever enough to know answer to this..

Some of you may know that if you pick (almost) any integer and add its reversed digits to it, and repeat this process ..you will eventually get a palindrome.

for example:
# 56 becomes palindromic after one iteration: 56+65 = 121.
# 57 becomes palindromic after two iterations: 57+75 = 132, 132+231 = 363.
# 10,911 reaches the palindrome 4668731596684224866951378664 after 55 steps
(http://en.wikipedia.org/wiki/Lychrel_number)

If we call the numbers we start with as "seeds" ...we can easily produce a palindrome given (almost) any seed.

How do we extract a seed from a given palindrome?
(note that all intermediate steps count as seeds..so you only need to go back "1 step")

any ideas?
 
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rsala004 said:
if you pick (almost) any integer and add its reversed digits to it, and repeat this process ..you will eventually get a palindrome.

Actually, I would expect the opposite: that almost all numbers are 'Lychrel' numbers. I think looking at 1-10 digit numbers gives us a bad feeling for their asymptotic behavior, since ,ost numbers are large.
 
Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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