(related to Problem: The Barrels Of Honey)

The only way in which the barrels could be equally divided among the three brothers so that each should receive his $3.5$ barrels of honey and his $7$ barrels is as follows:—

Full Half-full Empty
A 3 1
B 2 3
C 2 3

There is one other way in which the division could be made, were it not for the objection that all the brothers made to take more than four barrels of the same description. Except for this difficulty, they might have given $B$ his quantity in exactly the same way as $A$ above, and then have left $C$ one full barrel, five half-full barrels, and one empty barrel. It will thus be seen that in any case, two brothers would have to receive their allowance in the same way.

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Project Gutenberg

  1. Dudeney, H. E.: "Amusements in Mathematics", The Authors' Club, 1917

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