Test of the Sharing Problem

In Abgammon, a father had gone away leaving 38 Gazzam to be divided among his three sons. Murharzarm at Buserian's request, added one of his own to the herd, divided the herd and cam away with his beast and another.

Commentary: Obviously the first son must receive a larger portion, the second son a smaller portion and so on. But since the altered size of the herd is an odd number, the first son's fraction cannot be a half. If he has two thirds of the herd, the remainder left is 13 gazzam. No other common fraction fits because the other factor of 39 is 13, a prime number.

At this point Murharzarm must have taken away the gazzam that he had added to leave behind 12. From that, the second son receives 9 gazzam and the third son 3 (implying that he received three quarters of what was left behind) with the remaining gazzam being given to Murharzarm. Other solutions are possible but they require more complex fractions.