   # 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

One solution is 8
16 77 154 605 `1111` answer Jul 13, 2015 by anonymous
Wonderful :)

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+1 vote

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:

4 (#) 3 = 1, 3 (#) 4 = 4
9 (#) 2 = 4, 2 (#) 9 = 6
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
n (#) 1 = n
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
SPOILER 4!
The result is always a natural number

I'm a four-digit number! My 2nd digit is twice greater than my 3rd. The sum of all my digits is thrice greater than my last digit! The product of my 3rd and 4th digits is 12 times greater than the ratio of my 2nd to 3rd. What am I?

+1 vote

There's a three digit number which:
If you add seven to it it divides exactly by seven;
If you add eight to it it divides exactly by eight;
If you add nine to it it divides exactly by nine.
What is the number?