|An eccentric left a bag of gold coins to be shared amongst his children when he died. It is only known that there were less than 5,000 coins in the bag.|
The first coin was to be given to his butler, then one-fifth of the remainder to his eldest son. The butler was then to receive another coin, and now one-fifth of the remainder was to be given to the next eldest son. This was to be repeated for all his five sons. The remainding gold coins were to be divided equally among his five daughters. How many coins were there to start with, and how many did the butler, each son, and each daughter receive?