Here is a little puzzle culled from the traditions
of an old
the west of England. Abbot Francis, it seems, was a very worthy man;
his methods of equity extended to those little acts of charity for
he was noted for miles round.
The Abbot, moreover, had a fine taste in wines.
occasion he sent
for the cellarman, and complained that a particular bottling was not to
"Pray tell me, Brother John, how much of this wine
"A fair dozen in large bottles, my lord abbot, and
the like in
small," replied the cellarman, "whereof five of each have been drunk in
"So be it. There be three varlets waiting at the
bottles be given unto them, both full and empty; and see that the dole
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
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
How was he to make the required equitable division?
He divided the bottles into three groups in
several ways that
sight seemed to be quite fair, since two small bottles held just the
quantity of wine as one large one.
But the large bottles themselves,
empty, were not worth two small ones.
Hence the abbot's order that each man must take
away the same
bottles of each size.
Finally, the cellarman had to consult one of the
monks who was
puzzles of this kind, and who showed him how the thing was done.
find out just how the distribution was made?