Find the number of children, given that the estate was divided evenly between them Problem of the Week at University of Waterloo:

A man died leaving some money in his estate. All of this money was to be
  divided among his children in the following manner:



*

*$x$ to the first born plus $1/16$ of what remains, then

*$2x$ to the second born plus $1/16$ of what then remains, then

*$3x$ to the third born plus $1/16$ of what then remains, and so on.


When the distribution of the money was complete, each child received the same amount and no money was left over. Determine the number of children.
Can anyone hint at a strategy I could use to solve this? I've tried everything I could think of. All I want is a hint, though. No solutions please.

Hint 
Let $y$ be the amount he left over. How much did the first born receive? How much did the second born receive?
Mathe them equal.
