A father in his will left all his money to his children in the following manner:

\($1000\) to the first born and \(\frac{1}{10}\) of what then remains, then \($2000\) to the second born and \(\frac{1}{10}\) of what then remains, then \($3000\) to the third born and \(\frac{1}{10}\) of what then remains, and so on.

When this was done each child had the same amount. How many children were there?

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