Question

A $\textit{palindrome}$ is a positive integer which reads the same forward and backward, like $12321$ or $4884$. How many $4$-digit palindromes are there

Answer 1

There are 90 4-digit palindromes

What are palindromes?

Palindromes are numbers whose reverse is the same as the original number

How to determine the count of 4-digit palindromes

Since the digit is 4, then

• The first digit of the palindrome can be any of 1 to 9 (i.e. 9 digits)
• The second digit can be any of 0 - 9 (i.e. 10 digits)
• The third digit must be the second digit (i.e. 1 digit)
• The last digit must be the first digit (i.e. 1 digit)

So, the total number of digits is:

$n =9 * 10 * 1 * 1$

Evaluate the product

$n =90$

Hence, there are 90 4-digit palindromes.

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