Let us have some fun with three digit numbers:

Choose any three digit numbers where all the digits are not the same. Let us take 850, the year Mahaviracharya wrote Ganitasarasangraha.

By arranging the digits of this number in descending and ascending order we get two numbers 850 and 058. Now let us 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) 850 - 058 = 792

Now let us arrange the digits of the result, 792, in descending and ascending order. This way we get two numbers 972 and 279. Let us subtract 279 from 972.

2) 972 - 279 = 693

Let us repeat the same procedure with this new result, 693.

3) 963 - 369 = 594

Let us repeat the same procedure with this new result, 594.

4) 954 - 459 = 495

The digits in both 594 and 495 are the same. Hence, if we repeat the same procedure we will get the same result, i.e. 495.

Let us do the same operations on 628, the year Brahmagupta wrote Brahmasphutasiddhanta.

1) 862 - 268 = 594

2) 954 - 459 = 495

Again we get the same result, 495.

Now, let us do the same operations on the number 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

Lo behold, again we get the same number, 495.

If you do these operations on any three-digit number in which all the digits are not the same (a three-digit number consisting at least two different digits), then you will get the result as 495 in not more than six steps.

This amazing discovery was made by Indian mathematician Shri Dattatreya Ramchandra Kaprekar (1905 – 1986). In honour of Shri Kaprekar the number 495 is called three-digit Kaprekar’s constant and the above procedure is called Kaprekar’s operations.

Kaprekar was a mathematics teacher in a school at Deolali (near Nasik) from 1930 to 1962. 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).

There is also a four-digit Kaprekar's constant, 6174. You can read about it in my earlier article. https://www.indictoday.com/quick-reads/kaprekar-constant/

Kaprekar had made many amazing discoveries in number theory. But his work was initially ignored by Indian mathematicians. In 1975 world famous mathematics author Martin Gardner, wrote an article on 6174, Kaprekar’s constant in his popular column on recreational mathematics in Scientific American. This made Kaprekar and his work world famous.

As a tribute to Ganitanand Kaprekar, let's carry out Kaprekar's operations on 357.

1) 753 - 357 = 396

2) 963 - 369 = 594

3) 954 - 459 = 495

 

Image Credits: Medium.com