Question 1204708
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        My understanding is different, and therefore my solution and my answer are different.


        As I understand from the problem's description, we should look in each 5-digit number (ZIP-code)

        and compare it with another ZIP-code, as if we look "upside-down".


        "Upside-down" means that every digit is rotated 180 degrees about its center {{{highlight(highlight(AND))}}} the order of digits 

        is opposed to the original order (reversed).


        Non-ambiguous codes are those that look the same when we look at them as they are written 
        and as we look at them "upside-down".



<pre>
I consider two categories of digits.

First category are those digits, that transform to themselves (with no change)
under the rotation 180 degrees about their center.

This set of digits is T = { 0, 1, 5, 8 }.         (T originates from word "Themselves").



Second set are those digits, that transform to some (other or the same) digit 
under the rotation 180 degrees about their center.

This set of digits is D = { 0, 1, 5, 6, 8, 9 }.   (D originates from word "Digits").


Notice that set D contains set T as a sub-set.



Now, non-ambiguous numbers are the numbers of the form

    {{{d[1]}}} {{{d[2]}}} {{{t}}} {{{(d[2])^t}}} {{{(d[1])^t}}}

where a digit {{{(d[i])^t}}} designates the image  of a digit {{{d[i]}}} from the set D

under rotation 180 degrees about their center; "t" is from set T.



In the first  (leftmost) position,                    we       have 6 possible digits from set D.

In the next,  second position from leftmost position, we again have 6 possible digits from set D.

In the next,  third position from leftmost position,  we       have 4 possible digits from set T.



These 6*6*4 = 144 digits are our "independent variables".

In the 4-th and 5-th position, we have "derivative" digits, so they are not "independent variables".



Thus, the total number of all possible 5-digit zip-codes is 10,000.

Of them,  6*6*4 = 144  codes are non-ambiguous: they remain the same when we look at them upside-down.


<U>ANSWER</U>.  The number of non-ambiguous zip-codes is 144.
</pre>

Solved.