Seventeen Horses/General Problem 2/Examples/77
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Example of Seventeen Horses Problem
Suppose $77$ horses are to be divided between $4$ sons in the ratio $\dfrac 1 2 : \dfrac 1 3 : \dfrac 1 4 : \dfrac 1 5$.
We have that:
- $\dfrac 1 2 + \dfrac 1 3 + \dfrac 1 4 + \dfrac 1 5 = \dfrac {30 + 20 + 14 + 12} {60} = \dfrac {77} {60}$
of which the numerator is seen to equal the total number of horses to be divided.
So we lend $17$ horses to someone, leaving $60$ horses.
The fourth son takes $\dfrac 1 5$ of these $60$, that is, $12$.
The third son takes $\dfrac 1 4$ of these $60$, that is, $15$.
The second son takes $\dfrac 1 3$ of these $60$, that is, $20$.
The first son takes the remaining $13$ horses, then goes and hunts down the $17$ horses that were lent, and so has his share of $30$ horses.
Sources
- 1992: David Wells: Curious and Interesting Puzzles ... (previous) ... (next): Exchanging the Knights: $103$ (solution)