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Why is ‘6174’ so magical?

 Why is ‘6174’ so magical?


Let's do some magic today. The special number for this is ‘6174’. Yes, you heard it correctly. You may be asking what makes this number so significant when it appears to be just another number. Let me tell you that this is a magical number since it connects virtually all four-digit numbers. You can easily understand this if you follow the simple steps of subtraction.


Let's unravel the mystery:


  • Step 1: 

Choose any four-digit numbers, using at least two different digits (1111,7777 are not allowed). Numbers having leading digits (like 0321,0045) are also allowed.

        I take the current year: 2021


  • Step 2: 

Arrange the digits in ascending and descending order, which can have leading zeros if necessary.

           Ascending order: 0122

           Descending order: 2210


  • Step 3:

 Subtract the smaller number from the larger number.

           2210 - 0122 = 2088


  • Step 4:

 Repeat step 2.

           8820 - 0288 = 8532

           8532 - 2358 = 6174

           7641 - 1467 = 6174


The above process will always reach a fixed number ‘ 6174’, in at most 8 iterations. Once ‘6174’ is reached, this process will continue giving ‘6174’(7641 - 1467 = 6174).


Isn't it fascinating? I'm certain it is. 


You might be wondering about a magician who discovered this. D.R. Kaprekar, an Indian mathematician, discovered the unique properties of the four-digit number ‘6174,' also known as Kaprekr's constant. The procedure we used here is known as Kaprekr's process.


Similarly, there is a three-digit number ‘495’. This is also known as Kaprekr’s constant which means when you take a three-digit number and follow the same process which we have done here will always end at ‘495’ in at most six iterations.


-Diamond GC

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