"a man dies and leave his estate to his heirs. The estate is divided as follows.
1st son gets 100 crowns + 1/10 of remainder of estate
2nd son gets 200 crowns + 1/10 of remainder of estate...etc
(n)th son gets 100 x (n)th crowns
each heir recieves same amount
how many heirs, what did each receive, and what was the estate?
The original problem, and its solution, could be found in The Penguin Book of Curious and Interesting Puzzles by David Wells, Penguin Books, 1992, p. 205 and the Introduction to the History of Mathematics by H. Eves, Holt, Rinehart and Winston, 1975, p. 230.
The Wells book happens to be an outstanding source of many interesting and challenging problems.
Another variation will enable you to attack your version.
From his estate, a man left one pound to his oldest son plus one seventh of what was left; from what was left after that, he left two pounds to his next son, plus a seventh of what was left; from the remainder again, he left three pounds to the next son, plus a seventh of what was left. His wishes continued in this manner, giving each son one pound more than the previous son, plus a seventh of what remained. By way of this process, it turned out that the last son received all that was left, resulting in all the sons sharing equally. Can you determine how many sons the man had and how large was the man's estate to begin with? >>
Solution
Lets assume there were x number of sons. If the last son received all that was left at that point, by definition, there had to be no pounds left over after he first took x pounds from those remaining after the previous son's distribution. If the last son received a total N pounds + 1/7(0), the next to last son, who, by definition, also
received a total of N pounds, received (N - 1) + 1/7 of the pounds remaining at that point. Since there were no pounds left for the xth son to apply the "1/7th of the remainder" rule to, there must have been only seven pounds remaining after he had taken his (x - 1)th or (N - 1)th pounds, plus the 1/7th, or 1, leaving 6 pounds for the last son. (There were N + 6 pounds to be distributed after the previous son had received his share, and these N + 6 pounds make the two shares of N each taken by the last two sons, making N = 6.) Working backwards, the father left an estate of 36 pounds, which was divided equally between 6 sons.
