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For example, let the number be 3165. D.R. Kaprekar
Arranging the digits in ascending order gives 1356. Dattatreya Ramchandra Kaprekar
Arranging the digits in descending order gives (1905-1986) was an Indian
6531. recreational mathematician
Subtract the smaller number from the larger one who discovered many interesting
and repeat. numbers such as – Harshad
Step 1: 6531 – 1356 = 5175 Numbers, Kaprekar numbers,
Step 2: 7551 – 1557 = 5994 Self-Numbers, Kaprekar constants, etc. He was
born in Dahanu (Maharashtra). After completing
Step 3: 9954 – 4599 = 5355 his graduation from Fergusson College, Pune he
Step 4: 5553 – 3555 = 1998 joined as a school teacher in 1929 at Devlali. He
Step 5: 9981 – 1899 = 8082 was so fascinated by number theory that he
Step 6: 8820 – 0288 = 8532 once said – ‘A drunkard wants to go on drinking
wine to remain in that pleasurable state. The
Step 7: 8532 – 2358 = 6174 (Kaprekar constant) same is the case with me, as far as numbers are
Example 12: How many rounds does 5683 take to concerned’.
reach the Kaprekar constant?
Solution. Let us proceed to reach the Kaprekar constant taking the given number 5683 as follows:

Step 1: 8653 Step 2: 8550 Step 3: 9972 Step 4: 7731 Step 5: 6543 Step 6: 8730 Step 7: 8532
– 3568 – 0558 – 2799 – 1377 – 3456 – 0378 – 2358
= 5085 = 7992 = 7173 = 6354 = 3087 = 8352 = 6174
Hence, the number 5683 takes 7 rounds to reach the Kaprekar constant.

Project

Take the help from internet and answer the following:
1. D.R. Kaprekar spent most of his life in Devlali Village. He also named a number as Devlali number. What is
a devlali number?
2. Write 8 numbers which are Harshad number. Why is it named Harshad number?
3. What is a Kaprekar number? What is the difference between the Kaprekar number and the Kaprekar constant?

Practice Time 3D

1. Given below are some numbers arranged in some patterns. Find out the sum of the numbers in
each of the below figures.

(a) (b)

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