Hinglish

Palindromes and Kaprekar's Magic Number

Class 6 Maths · Chapter 3: Number Play · NCERT Ganita Prakash section 3.5–3.6

Learn

Some numbers are the same whether you read them forwards or backwards, like 44, 707, 383 and 2112. These numbers are called palindromes.

Reverse and add: take a 2-digit number, add it to its reverse, and keep going until you get a palindrome. 57 + 75 = 132, then 132 + 231 = 363.

Kaprekar's steps: pick a 4-digit number. Arrange its digits to make the biggest number A and the smallest number B, then find A − B. Repeat with the answer. (The Indian maths teacher D. R. Kaprekar discovered what happens.)

5432 − 2345 = 3087

Try any 4-digit number (not all digits the same). You always reach 6174, the Kaprekar constant!

Remember

  • A palindrome reads the same both ways: 575, 1221.
  • Kaprekar: largest − smallest from the digits, repeat: 4-digit numbers always reach 6174.

Quick check

Which of these numbers is a palindrome?

  1. 1231
  2. 4554
  3. 4545
  4. 1223
Answer

4554. 4554 backwards is 4554.

Think about it

Puzzle: I am a 4-digit palindrome. My first digit is 2 and all my digits add up to 10. Who am I?

One answer

A 4-digit palindrome looks like 2 _ _ 2 with the two middle digits the same. 2 + 2 = 4, so the middle digits add to 6: 3 and 3. I am 2332.

Practice

Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.