>  examine the visual patterns of the
>  numbers, noting that there were arrangements of 8712 and 9801 (and
>  their
>  reverses) that repeated themselves in larger numbers. Their solutions
>  reflect this approach, yet they admit to being incomplete solutions:
>  they
>  don't find every reverse divisible number.

They may be incomplete (although I'm not so sure this is true for
marcelo's approach) but at least they find some numbers in finite
time.