Here is a little puzzle culled from the traditions of an old monastery in the west of England. Abbot Francis, it seems, was a very worthy man; and his methods of equity extended to those little acts of charity for which he was noted for miles round.
The Abbot, moreover, had a fine taste in wines. On one occasion he sent for the cellarman, and complained that a particular bottling was not to his palate.
"Pray tell me, Brother John, how much of this wine thou didst bottle withal."
"A fair dozen in large bottles, my lord abbot, and the like in the small," replied the cellarman, "whereof five of each have been drunk in the refectory."
"So be it. There be three varlets waiting at the gate. Let the two dozen bottles be given unto them, both full and empty; and see that the dole be fairly made, so that no man receive more wine than another, nor any difference in bottles."
Poor John returned to his cellar, taking the three men with him, and then his task began to perplex him. Of full bottles he had seven large and seven small, and of empty bottles five large and five small, as shown in the illustration. How was he to make the required equitable division?
He divided the bottles into three groups in several ways that at first sight seemed to be quite fair, since two small bottles held just the same quantity of wine as one large one. But the large bottles themselves, when empty, were not worth two small ones.
Hence the abbot's order that each man must take away the same number of bottles of each size.
Finally, the cellarman had to consult one of the monks who was good at puzzles of this kind, and who showed him how the thing was done. Can you find out just how the distribution was made?
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