Question

How many palindromes between 1000 and 9999 inclusive are divisible by 9?

Answer 1

Palindromes are numbers that remain the same, when reversed.

There are 10 palindromes divisible by 9 between 1000 and 9999

To do this, we list the numbers divisible by 9 between 10 and 99.

The numbers are:

$\mathbf{A = 09,\ 18,\ 27,\ 36,\ 45.\ 54,\ 63,\ 72,\ 81,\ 90,\ 99}$

Flip these numbers

$\mathbf{B =90,\ 81,\ 72,\ 63,\ 54.\ 45,\ 36,\ 27,\ 18,\ 09,\ 99}$

Combine corresponding numbers

$\mathbf{AB =0990,\ 1881,\ 2772,\ 3663,\ 4554,\5445,\ 6336,\ 7227,\ 8118,\ 9009,\ 9999}$

Rewrite as:

$\mathbf{AB =990,\ 1881,\ 2772,\ 3663,\ 4554,\5445,\ 6336,\ 7227,\ 8118,\ 9009,\ 9999}$

990 is less than 1000.

So, we have:

$\mathbf{AB =1881,\ 2772,\ 3663,\ 4554,\5445,\ 6336,\ 7227,\ 8118,\ 9009,\ 9999}$

Count the numbers

$\mathbf{n(AB) =10}$

Hence, there are 10 palindromes divisible by 9 between 1000 and 9999

Read more about palindromes at:

brainly.com/question/14076732