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?
See answer
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