Upon Maharaja's death all his sons (n in number) were summoned by his lawyers to get acquainted with his will. The relevant part directed them to an ornamented jewelry box filled with extremely expensive diamonds, similar in size, color and cut along with detailed, albeit peculiar instructions:
My firstborn son will pick up 1 diamond and take 1/(n+1) of the rest,
My second son will pick up 2 diamonds and 1/(n+1) of the rest,
My third son will pick up 3 diamonds and 1/(n+1) of the rest, etc.

Although there were some unresolved issues (what if some quantity will not be divisible by n+1, why not divide equally, and what happens with the rest after the youngest brother?) - there was no one to answer and the brothers acted exactly "to the selfsame tune and words" of their deceased father. Strange as may this seem, no problems of cutting occurred and none of the brothers complained about the fairness of the beloved Maharaja.

The original problem, as compiled by B.A. Kordemski, relates the above story concerning 6 brothers and asks how many diamonds were initially in the box. Out of respect to my audience, I generalized and modified the will to n sons, and now I ask how the quantity of diamonds was augmented each time another son was born?

The narrative appears in Математические завлекалки издание 1998

Posted by laxmigame on 2023-07-19 04:42:19