I was born in the year 1971. Let us play with this number.  

If we arrange the digits of this number in descending and ascending order we get two numbers 9711 and 1179. Let us now subtract the number we get by arranging the digits in ascending order from the number we get by arranging the digits in descending order. 

1) 9711 – 1179 = 8532 

Now let us arrange the digits of the result, 8532, in descending and ascending order. This will give us two numbers 8532 and 2358. Subtracting 2358 from 8532 we get:  

2) 8532 – 2358 = 6174 

Let us repeat the same procedure with this new result, 6174. 

3) 7641 – 1467 = 6174 

Lo behold. We get the same result. 

Let us do the same operations on the number of the current year, say 2020. 

1) 2020 - 0022 = 2178

2) 8721 - 1278 = 7443

3) 7443 - 3447 = 3996

4) 9963 - 3699 = 6264

5) 6642 - 2466 = 4176

6) 7641 - 1467 = 6174 

Again we get the same result, 6174. 

Now, let us do the same operations on the number of the year our country gained independence, 1947. 

1) 9741 – 1479 = 8262

2) 8622 – 2268 = 6354

3) 6543 – 3456 = 3087

4) 8730 – 0378 = 8352

5) 8532 – 2358 = 6174 

Lo behold, again we get the same number, 6174. 

If you do these operations on any four-digit number in which all the digits are not the same (a four-digit number consisting at least two different digits), then you will get the result as 6174 in not more than seven steps.  

This amazing discovery was made by the Indian mathematician Shri Dattatreya Ramchandra Kaprekar (1905 – 1986) in the year 1949. In honour of Shri Kaprekar, the number 6174 is called Kaprekar’s constant and the above procedure is called Kaprekar’s operations. 

As a child, Kaprekar lost his mother early in his life. He was brought up by his father, a clerk who was interested in astrology. Indian Astrology, as we know, relies a lot on mathematics, and Kaprekar’s father imparted to his child a love for numbers. When he was young, Kaprekar is said to have spent a lot of time just solving mathematical problems. After finishing school, he completed his higher education at Pune’s famed Fergusson College. Naturally, he was a great student there and even won the Wrangler R P Paranjpe Mathematical Prize for best original mathematical work.  

Kaprekar then went on to become a mathematics teacher in a school at Deolali near Nasik. His entire career was dedicated to teaching children, concepts he so passionately loved. He once said: “A drunkard wants to go on drinking wine to remain in that pleasurable state. The same is the case with me in so far as numbers are concerned.” 

Apart from teaching in school, he was also invited to give lectures on mathematics to college students. Number theory (study of properties of integers) was his favourite subject. Due to his passion for mathematics he was also called Ganitanand (one who derives happiness by doing mathematics). After many years of teaching, Kaprekar retired in 1962, when he was 58.  

Kaprekar had made many amazing discoveries in number theory. But his work was initially ignored by Indian mathematicians. In 1975, Martin Gardner, the world famous mathematics writer, wrote an article on Kaprekar’s constant in his popular column on recreational mathematics in Scientific American. This made Kaprekar and his work world famous. 

Now, you must be wondering what if you try Kaprekar's operations on a three-digit number where all the digits are not the same? 

Let us apply Kaprekar's operations on 628, the year Brahmagupta wrote Brahmasphutasiddhanta. 

1) 862 - 268 = 594

2) 954 - 459 = 495 

Now, let us apply Kaprekar's operations on 850, the year Mahaviracharya wrote Ganitasarasangraha. 

1) 850 - 058 = 792

2) 972 - 279 = 693

3) 963 - 369 = 594

4) 954 - 459 = 495

 Now, let us try Kaprekar's operations on 443.

1) 443 - 344 = 099

2) 990 - 099 = 891

3) 981 - 189 = 792

4) 972 - 279 = 693

5) 963 - 369 = 594

6) 954 - 459 = 495

We always get the number 495 when we carry out Kaprekar's operations on any three digit number where all the digits are not the same in at most 6 steps. The number 495 is the three digits Kaprekar's constant.

 Lastly as a tribute to this great mathematician let us perform Kaprekar’s operations on a new four-digit number, 3133.

 1) 3331 – 1333 = 1998

2) 9981 – 1899 = 8082

3) 8820 – 0288 = 8532

4) 8532 – 2358 = 6174 

Till today, numerous mathematicians and students of numbers remain fascinated by Kaprekar and his work. A math teacher from India captured the minds of mathematicians around the world with his sheer love and passion for numbers.

Reference:

https://mathshistory.st-andrews.ac.uk/Biographies/Kaprekar/

 

 

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