Henry Ernest Dudeney/Modern Puzzles/89 - The Seventeen Horses/Solution

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Modern Puzzles by Henry Ernest Dudeney: $89$

The Seventeen Horses
"I suppose you all know this old puzzle," said Jeffries.
"A farmer left seventeen horses to be divided among his three sons in the following proportions:
To the eldest, one-half;
to the second, one-third;
and to the youngest, one-ninth.
How should they be divided?
"Yes; I think we all know that," said Robinson, "but it can't be done.
The answer always given is a fallacy."
(Considerable pointless argument ensues.)
... The terms of the will can be exactly carried out, without any mutilation of a horse.
... How should the horses be divided in strict accordance with the directions?


Solution

In Seventeen Horses, this is analysed in some detail.


The telling point is:

The fact that the ratios do not add up to $1$ tells us straight away that those ratios are not in fact the actual fractions of the inheritance that each will receive.
It is noted that the question carefully does not state that one son receives $\dfrac 1 2$, the next son $\dfrac 1 3$ and the third $\dfrac 1 9$, because that is not what actually happens here.


This, effectively, is how Dudeney himself answers the question.


Sources

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