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.
[Illustration]
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?