Maths for a sense of wonder

1089 and All That

Think of a three-figure number.
Any three-figure number will do, so long as the first
and last figures differ by 2 or more.
Now reverse it, and subtract the smaller number from
the larger. So, for example,
782 - 287 = 495.

Finally, reverse the new three-figure number, and add:

495 - 594 = 1089.

At the end of this procedure, then, we have a final answer
of 1089, though we have to expect, surely, that this final
answer will depend on which three-figure number we
start with.

But it doesn’t.

The final answer always turns out to be 1089.

It was the element of mystery and surprise, I think,
that put this result into a different league from some of
the work we were doing in school.

David Acheson, 1089 and all That, Published by Oxford University Press 2002
Reprinted 2003, 2004 (twice), 2005, 2006