Prove the magic trick for the number \(1089
= 33^2\): if you take any \(3\)-digit number \(\overline{abc}\) with digits coming in
strictly descending order and subtract from it the number obtained by
reversing the digits of the original number \(\overline{abc} - \overline{cba}\) you get
another \(3\)-digit number, call it
\(\overline{xyz}\). Then, no matter
which number you started with, the sum \(\overline{xyz} + \overline{zyx} =
1089\).
Recall that a number \(\overline{abc}\)
is divisible by \(11\) if and only if
\(a-b+c\) also is.