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 $n$.