Take any pair of two digit numbers $ ab $ and $ cd $ where,
without loss of generality, $ ab> cd $. Form two 4 digit
numbers $ abcd $ and $ cdab $ and calculate:
\[\frac{abcd^2-cdab^2}{ab^2-cd^2}\] Repeat this with other
choices of $ab$ and $cd$. There is a common feature of all the
answers. What is it? Why does this occur? Generalise this to $n$
digits for other values of $n$.