Question 1173431
.


            The solution by  @ewatrrr is  ABSOLUTELY  WRONG.


            For your safety,  ignore it . . . 


            I came to bring you the correct solution.




<pre>
First digit can be any of the 8 given digits from 1 to 8 inclusive.

    (notice that 0 (zero) can not be the first digit of a two-digit number).
 


Second digit can be any of the 9 given digits from 0 to 8 inclusive.



It gives us  8*9 = 72 potential candidates for two digit numbers.



From this amount, we should exclude two-digit numbers with repeating digits.

They are  11, 22, 33, 44, 55, 66, 77, and 88 - in all, 8 numbers must be excluded from 72.


It gives the <U>ANSWER</U>  72 - 8 = 64.


<U>ANSWER</U>.  There are 64 two-digit numbers satisfying to imposed conditions.
</pre>

Solved.