



No
44
The Ultimate Palindrome
 What is a Palindromic Number? Examples
are 11, 123321 and 2002. They read the same backwards as forwards.
This is the number equivalent of a Palindrome which is a word
which reads the same forwards and backwards. Hannah is an
example.
Pick a number, reverse its digits and
add the resulting number to the original number. If the answer is
not palindromic then repeat the process. For example let's start
with 87:
Step 1: 
87 + 78 = 165

not palindromic so... 
Step 2: 
165 + 561 = 726

not palindromic so... 
Step 3: 
726 + 627 = 1353

not palindromic so... 
Step 4: 
1353 + 3531 = 4884

palindromic! 
You might like to explore the result of
doing this process to several other small numbers. Do all the
numbers that you try end up with a palindromic number?
 196 is a particularly stubborn number.
Nobody knows whether eventually doing this reversal and adding
process with 196 yields a palindromic number. Here is a quote from
an account written by John Walker on May 25th 1990. He had written
a computer program in an attempt to determine the outcome for the
number 196:
 "For almost three years the process of reversal
and addition continued. Last night, at five minutes
before midnight, the program printed the message:
'Stop point reached on pass 2415836. Number contains
1000000 digits.' and exited. The builtin endpoint had
been reached; after 2,415,836 reversals and additions,
196 had grown to a number of 1,000,000 digits without
ever yielding a palindrome. Does it ever produce one?
Still, nobody knows."

Recently computer tests have continued up
to nearly 9.5 million steps yielding a 4.9 million digit number
which is not yet palindromic! The search no doubt
continues!!
If you have answers, discoveries, new questions etc to
do with this Number Fact then...


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