It is one of the best miniatures of fair distribution: it seems like elementary arithmetic, but it forces us to distinguish between what each one carried and what he really contributed to the third.
The fair counting of the loaves
Riddle statement
Two travelers cross the desert.
One carries 5 loaves.
The other carries 3 loaves.
Halfway they are joined by a third traveler, who does not bring food. The three decide to share the 8 loaves equally.
When saying goodbye, the newcomer leaves them 8 coins as a thank you.
The first proposes to distribute them according to the loaves that each one carried: 5 coins for him and 3 for the other.
Is this distribution correct? If not, how should the 8 coins actually be divided?
Show solution
Solution
The 8 loaves, distributed among 3 people, correspond to \(\frac{8}{3}\) loaves per person.
The traveler who carried 5 loaves consumed his share and contributed to the third:
The traveler who carried 3 loaves consumed his share and contributed:
The third traveler therefore received contributions in a 7:1 proportion.
The 8 coins must be distributed in that same proportion: 7 coins for the person carrying 5 loaves and 1 coin for the person carrying 3.