Spooky Number

As, we are following the trails of the numbers, we come to know strange things about them. But, believe me, no thing is as strange as this characteristic is.

What, you have to do is,
1. Take any four digit number. (Leading zero is permitted. But, all four digits can't be same.)
2. Arrange the digits in the number in the descending order. Consider this new number as M.
3. Arrange the digits in the number in the ascending order. Consider this new number as N.
4. Subtract N from M.
5. Go to Step 2 and repeat this procedure with the answer you got from subtraction.

You may take any number whatsoever. But, with certain series of repeating this procedure, you will always end up with one number. Which will then, keep repeating itself.

Isn't it spooky?
You take any number and still you will end up with the same number after certain operations. This number is known as Kaprekar's constant. And the above procedure is called Kaprekar's routine.

You, after taking a single number and repeating the procedure for n number of times, you will get to the answer. But, in this puzzle, it is not about getting the answer. It is about learning the strange characteristic.

This Kaprekar's constant has been given name from an Indian Mathematician Dr. D.R. Kaprekar. He has given Kaprekar, Harshad and Self Numbers. You can learn more about the mathematician and various numbers he came up with, with the help of Internet. All the best to you. Research More and More. And, if you have any idea about such strange numbers, come up with those.

Numbers speak more than words

Today, I am here to bring your attention to some extraordinary numbers , which look just like other numbers but carry some special attributes. And, as always, I won't bring you the solutions , you have to identify these numbers :

1, Armstrong Number:
There are some three digit numbers, which possess this characteristic. Armstrong numbers are those numbers, which equal to the sum of cubes of all its digits. There are four numbers having this characteristic. I will give you one. Find the other three.
153- here cube of 1…5…3 is 1…125…27 and sum of 1,125,27 is 153 itself. So, this number is called Armstrong number. Bring me other three. :)

2. Ramanujan Number:
First number which can be written as sum of two cubes in two different way.
You don't need much information in this criteria. Just test your brain and come up with the answer.

3. Perfect Number:
A number is called perfect, if sum of all its positive divisors excluding itself equal to that number itself. For example: 6
6 has positive divisors- 1,2,3 (and 6, which is excluded) so, its sum is 6 too. (1+2+3) Thus, 6 is perfect number.
(FUN FACT: THIS IS SO CALLED REASON WHY 6 HAS BIGGER INFLUENCE IN HISTORY.)
Get me other perfect numbers.

All the best Logic Lovers. I hope you will succeed. 

8 Queens' Problem

Hello Logic Lovers,
Today I am back with a very interesting and well known puzzle of N Queens' Problem. This puzzle is based on the game of Chess.
If, you hadn't come across Chess ever before, take a look at the chess board. I will brief you with the details that you need to focus during solving the puzzle.



Here, YOU ARE SUPPOSED TO PUT EIGHT QUEENS IN A WAY THAT NO QUEEN CAN KILL ANY OTHER ONE. 

Now, In what all ways a queen can kill...
A queen can kill any other queen if it is in the same row or column. And, in the same diagonal.

Now, for naming conventions of each square, we use combination of row and column number.

So, here, if one queen is on A8, you can't put other queen in row 8 and column A. In addition, the diagonal containing squares like: B7, C6, D5,..., H1 too can't contain another queen.

This is what the situation is and you have to come up with the solution of putting all eight queens. This is a known puzzle but an amazing brain twister.
If I can say, it is quite an easy one. As, there are total 92 solutions possible for this Problem. I am sure that you will be able to come up with at least one solution. All the best. For any further queries, you may comment here.