A most engrossing article. I wonder, if the following premise has a particular description and if anybody would be kind enough to furnish me with an explanation? In respect of the 1089 trick; I found that any number, of two or more digits (except 'mirrored' numbers such as 11 or 89,598) where at least one number is more or less than it's adjoining digits, when reversed and the lower subtracted from the higher the answer is always divisible by 9, for example:

75 - 57 = 18 = 9 x 2
9801 - 1089 = 8712 = 9 x 968
7,324,586 - 6,854,237 = 470,349 = 9 x 52,261

I have very little academic background, simply interest and curiosity and would greatly appreciate any clarification.

Thank you in advance.

Mike.

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