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## 'Our Ages' printed from http://nrich.maths.org/

Many thanks to Robert Simons for this question:

"I am exactly $n$ times my daughter's age. In $m$ years I shall
be exactly $(n-1)$ times her age. In $m^2$ years I shall be exactly
$(n-2)$ times her age. After that I shall never again be an exact
multiple of her age. Ages, $n$ and $m$ are all whole numbers. How
old am I?

Now suppose there is some wishful thinking in the above
assertion and I have to admit to being older, and indeed that I
will be an exact multiple of her age in $m^3$ years. How old does
this make me?"