Form the greatest six-digit odd number and smallest six-digit even number using the digits from $1$ to $9$ only once. What will be the sum of these numbers?

Find the greatest and the smallest numbers and their sum:

The given digits are $1,2,3,4,5,6,7,8$ and $9$.

A condition is given that each digit can be used only once while forming the two six-digit numbers.

So, the greatest six-digit odd number $=987653$

Here, $4$ is not used as the unit digit because an odd number is required.

And, the smallest six-digit even number $=123456$

Now, the difference between the greatest six-digit odd number and the smallest six-digit even number can be calculated as,

The required sum $=$ greatest number $+$ smallest number

$\Rightarrow$the required sum $=987653+123456$

$\Rightarrow$the required sum $=1111109$

Hence, the required sum is $1111109$.