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Can you guess my starting number?

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One night, I thought of ways that can be used for creating a palindrome. So I decided that I will turn into a larger number by adding the reversed digits to the original number and keep doing it till I finally obtained a palindrome.

I am not sure if this process will always result in a palindrome eventually but I was able to produce a four digit palindrome.

Can you guess my starting number?

posted Oct 13, 2014 by Rahul Vaidya

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One day, I thought of ways that can be used for creating a palindrome. So I............Can you guess my starting number?

One day, I thought of ways that can be used for creating a palindrome. So I decided that I will turn into a larger number by adding the reversed digits to the original number and keep doing it till I finally obtained a palindrome.

I am not sure if this process will always result in a palindrome eventually but I was able to produce a four-digit palindrome. Can you guess my starting number?

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Can you guess my "nifty operator" (#) ?

This is a very difficult puzzle, I bet you can't solve it.

Let (#) (a circled star) be called "nifty operator" which is an operator and takes two natural numbers and produces a natural number.
Here you got some definitions:

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5 (#) 7 = 5, 7 (#) 5 = 7
2 (#) 5 = 4
8 (#) 9 = 8
4 (#) 14 = 16

Can you tell me, how is a (#) b defined?

You maybe want some more tips:
~~~
If a is even then a (#) a = 0
If a is odd then a (#) a = a
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1 (#) n = 1
~~~

If you can't solve it, here is a tip:
SPOILER 1!
(#) cannot be defined for complex numbers.
SPOILER 2!
a (#) b < a+b
SPOILER 3!
a (#) b = a X b Y (a Z b) where X,Y,Z are operators
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The result is always a natural number

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