### A palindrome number is the same either read from left to right or right to left, for example, $121.$ How many $5-$digit palindrome numbers are there altogether$?$

$900$

Step by Step Explanation:
1. We need to find the total number of $5-$ digit palindrome numbers.
2. $10$ digits $(0, 1, 2, \ldots, 9)$ can be used to fill in the places in the number.
The first digit cannot be zero in order to make it a $5$ digit number.
Therefore, We have $9$ choices for the first place.
For the $2^{ nd }$ and the $3^{ rd }$ place, we have $10$ choices each.
3. For a $5-$digit number to be a palindrome number the $1^{ st }$ and the $5^{ th }$ , the $2^{ nd }$ and the $4^{ th }$ digit of the number needs to be the same.
Therefore, the total number of $5$ digit palindrome numbers $= 9 \times 10 \times 10 = 900$
4. Hence, there are $900$ $\space 5-$digit palindrome numbers altogether.