The number '6174' looks like any other ordinary number but what if I told you this is a magic number? Would you believe me?
6174 is known asKaprekar's constant as it was invented by Indian mathematician DR Kaprekar in 1949.
Even mathematicians, till date, aren't sure how to explain this magic number. Wondering, what's so unique about the number? This number is known for the following rule:
- Take any four-digit number (at least two digits should be different)
- Arrange the digits in descending and ascending order to get two new four-digit numbers
- Now, subtract the smaller number from the bigger number
- Go back to step 2 and repeat
For example, lets take the number 5432.
5432 – 2345 = 3087
8730 – 0378 = 8352
8532 – 2358 = 6174
7641 – 1467 = 6174
Now, lets follow the same method with another four-digit number for example, 2005.
5200 - 0025 = 5175
7551 - 1557 = 5994
9954 - 4599 = 5355
5553 - 3555 = 1998
9981 - 1899 = 8082
8820 - 0288 = 8532
8532 - 2358 = 6174
7641 - 1467 = 6174
You can try this out yourself. Take any four-digit number and follow the same method mentioned above and you'll see that in the end you are always left with the number 6174.
This process is called Kaprekar's routine. The routine states that you'll always reach number 6174 in at most 7 iterations and once you reach 6174, the process will continue generating the same number. How cool is that?
This procedure can be applied to any four digit numbers expect repdigits like 1111, 2222 and so on, which give the result 0000 after a single itercation.
Now, lets take you through Ramchandra Kaprekar's life story. Since childhood, Dattatreya Ramchandra Kaprekar enjoyed playing around with numbers. That's exactly how he was introduced to this mysterious number 6174.
In 1924, after completing his bachelor's degree from the University of Mumbai, he spent his entire career teaching school kids in Nashik, Maharashtra.
He was known for his intelligence and soon he was invited by other schools and colleges to solve difficult mathematical questions.
Apparently, in 1949 Kaprekar had introduced the magic number at a conference in Madras but, many mathematicians ended up making fun of him and his discovery. Most people thought the invention of 6174 was useless and baseless.
Whether the discovery of 6174 helped the world of mathematics in anyway can't be said for sure but, Kaprekar certainly discovered a unique pattern that no one has been able to explain, till date.
In addition to the Kaprekar's constant he also described self numbers or Devlali numbers, the Harshad numbers and Demlo numbers. He also constructed certain types of magic squares related to the Copernicus magic square.
It was only in 1970 that people started recognizing Kaprekar's work after America's best selling author, Martin Gardner wrote an article on Kaprekar in a magazine titled
'Scientific America'. Today, Kaprekar's contribution in the field of mathematics is known to the entire world.