136-Number pattern and its beauty

Nowadays, the following pattern is being observed on some social networks.

Nowadays, the next convention is being observed on some social networks.

Now we will see the basics behind this pattern of numbers.

For any positive integer "a" 

(100a+10a+a)/(a+a+a) = 111a/3a ---------- equation-1

                                     = 111/3               

                                     = 37. 

It's always 37 for such types of patterns of the problem.

Putting a = 1, in equation-1, we get 111/3 = 37.

Similarly, putting a = 2, we get 222/6 = 37, and so on.

These are simply the basics and everyone knows these basics of numbers. Now we will see some different patterns of numbers.

2 digits form:

If we take the same pattern for 2 digits, it will look like the following figure.

For any positive integer "a" 

(10a+a)/(a+a) = 11a/2a ---------- equation-2

                       = 11/2               

                       = 5.5. 

It's always 5.5 for such types of patterns of the problem.

Putting a = 1, in equation-2, we get 11/2 = 5.5.

Similarly, putting a = 2, we get 22/4 = 5.5, and so on.

4 digits form:

For any positive integer "a" 

(1000a+100a+10a+a)/(a+a+a+a) = 1111a/4a ---------- equation-3

                       = 1111/4               

                       = 277.75. 

It's always 277.75 for such types of patterns of the problem.

Putting a = 1, in equation-3, we get 1111/4 = 277.75.

Similarly, putting a = 2, we get 2222/8 = 277.75, and so on.

Note: The same explanation is there for all the following figures.

5 digits form:

6 digits form:

7 digits form:

8 digits form:

9 digits form:

The same concept can be applied to any number of digits. This is only the beauty of numbers.

There is nothing new. It is a well-known fact and the basics of numbers.

ANIL SATPUTE