Math Problem 5: Dividing the Inheritance
A man has died, and his three sons must divide their inheritance according to his will. Everything was going smoothly until they came to the part regarding the man's horses. He had instructed that his oldest son would receive half the herd, his second oldest a fourth of the herd, and his youngest an eighth of the herd. The problem was that there were seven horses.
Not being particularly prone to violence, the eldest son had no wish to take his share of three and a half horses. "After all," he thought, "what could one do with half a horse?" And yet all three sons had agreed to abide strictly by their father's will.
The oldest brother asked a kindly neighbour to give them one of his horses. The three brothers rejoiced, since now the horses could be divided without an unnecessarily messy situation taking place. The oldest brother took his half, being four horses. The second oldest took his fourth, being two horses. The youngest took his eighth, being one horse.
However, four horses plus two horses plus one horse only equals seven horses - there was one left over! This horse, of course, went back to the kindly neighbour. So it wasn't really necessary after all.
The youngest brother that night thought long and hard about the matter. He could not understand how half of seven was a whole number; and suspected that his oldest brother may have fooled them, tricking them into giving him an extra half horse.
Where's the problem? Did the oldest brother swindle his siblings?
The problem is not that there were seven horses. The total number of horses has nothing to do with it.
The easiest way to solve this is to consider the will, not how it was resolved.
The father's will does not account for his entire herd. In particular, 1/2 + 1/4 + 1/8 is 7/8, not 1!
The oldest brother was not a swindler. In resolving the will as he did, they simply divided the remaining 1/8 of the herd not accounted for in the will among the brothers.
Strictly applying the will, the oldest brother received 3 1/2 horses, the second oldest 1 3/4 horses, and the yongest 7/8 of a horse. This left 7/8 of a horse not accounted for in the will. Dividing the fractional horse, the oldest brother got half a horse (bringing his total to 4), the second oldest a quarter (bringing his total to 2), and the youngest an eighth (bringing his total to 1).