The Kaprekar number

Meet D. R. Kaprekar, a mathematics teacher at a government school in Devlali, Maharashtra. He was not a famous professor; he simply loved playing with numbers. In 1949 he found something magical about 4-digit numbers.

Pick a 4-digit number with at least two different digits, say 6382:

• A = the largest number from its digits: 8632.
• B = the smallest number from its digits: 2368.
• C = A − B = 8632 − 2368 = 6264.

Now repeat with 6264: 6642 − 2466 = 4176. And again: 7641 − 1467 = 6174.

Carry on from 6174 and you get 7641 − 1467 = 6174 again and again. Start with any suitable 4-digit number and you always end up at 6174! It is called the Kaprekar constant.

With 3-digit numbers the same steps end at a different number: 495. For 495, the largest number is 954 and the smallest is 459, and 954 − 459 = 495 again.

In the book, Pratibha makes the largest and smallest numbers from the digits 4, 7, 3 and 2: 7432 and 2347. Their difference is 7432 − 2347 = 5085, and their sum is 9779.