1. What are Palindromic Numbers?
Palindromic numbers are those that have the same forward and backward reading. In other words, they are symmetrical and can be read from left to right as well as right to left. For example, the numbers 121 and 1331 are palindromic.
1.1 How Do You Identify Palindromic Numbers?
To find palindromic numbers, students should look for numbers that read the same forward and backwards. For example, 11, 22, 121, 1221, and 12321. It's important to note that palindromic numbers can have an odd or even number of digits.
- The first useful strategy for identifying palindromic numbers is to look at a number's first and last digits. If they are identical, the number could be a palindrome. The number 1221, for example, has the same first and last digit, indicating that it is most likely a palindrome.
- Another method is to reverse the digits of the number to see if the result remains the same. For example, the number 12321 is a palindrome because it remains the same when its digits are reversed. Hence 12321 is a palindromic number.
2. Types of Palindromic Numbers:
There are several types of palindromic numbers, as follows:
2.1 Single-digit Palindromes:
- These are palindromic numbers that have only one digit.
- Examples: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
2.2 Even-digit Palindromes:
- These are palindromic numbers that have an even number of digits.
- They are symmetrical around their centre, which is the midpoint between the two middle digits.
- Examples: 22, 3333, 2442, and 1221.
2.3 Odd-digit Palindromes:
- These are palindromic numbers that have an odd number of digits.
- They are symmetrical around their middle digit.
- Examples: 121, 33333, 24442, and 12321.
2.4 Prime Palindromes:
- These are palindromic numbers that are also prime numbers.
- Examples: 11, 101, 131, and 929.
2.5 Square Palindromes:
- These are palindromic numbers that are also perfect squares.
- Examples: 1, 4, 9, 121, and 484.
Students can more easily recognise palindromic numbers and use them in math problems and puzzles if they are aware of the various types of palindromic numbers. They can also apply this knowledge to solve palindromic number problems in the 11+ exams.
