Question 1096519
<br>(1) All the digits must be either 0, 1, or 8.<br>
(2) Since you are rotating the whole 7-digit number 180 degrees and you want to end up with the same number, the 1st and 7th digits must be the same; the 2nd and 6th must be the same, and the 3rd and 5th must be the same.  The 4th digit, being in the middle, can be any one of the 3 allowable digits.<br>
...there are 2 choices for the 1st digit (it can't be 0); and then there is only 1 choice for the 7th digit.
...there are 3 choices for the 2nd digit, and then only 1 choice for the 6th.
...There are 3 choices for the 3rd digit, and then only 1 choice for the 5th.
...there are 3 choices for the 4th digit.<br>
The total number of choices, and therefore the number of 7-digit numbers that satisfy the requirements, is
{{{2*3*3*3*1*1*1 = 54}}}