Euler Fortune

A father leaves at his death several children who share in his property in the following manner:

  • The first child receives 100 crowns and a tenth part of what remains.
  • The second child receives 200 crowns and a tenth part of what remains.
  • The third child receives 300 crowns and a tenth part of what remains.
  • And so on.

Now, it is found in the end that the property has been divided equally among all the children. How much was the fortune, how many children were there, and how much did each child receive?

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