THE BARRELS OF HONEY.
(
Measuring, Weight, and Packing Puzzles.)
Once upon a time there was an aged merchant of Bagdad who was much
respected by all who knew him. He had three sons, and it was a rule of
his life to treat them all exactly alike. Whenever one received a
present, the other two were each given one of equal value. One day this
worthy man fell sick and died, bequeathing all his possessions to his
three sons in equal shares.
The only difficulty that arose was over the stock of honey. There were
exactly twenty-one barrels. The old man had left instructions that not
only should every son receive an equal quantity of honey, but should
receive exactly the same number of barrels, and that no honey should be
transferred from barrel to barrel on account of the waste involved. Now,
as seven of these barrels were full of honey, seven were half-full, and
seven were empty, this was found to be quite a puzzle, especially as
each brother objected to taking more than four barrels of, the same
description--full, half-full, or empty. Can you show how they succeeded
in making a correct division of the property?
CROSSING RIVER PROBLEMS
"My boat is on the shore."
BYRON.
This is another mediaeval class of puzzles. Probably the earliest example
was by Abbot Alcuin, who was born in Yorkshire in 735 and died at Tours
in 804. And everybody knows the story of the man with the wolf, goat,
and basket of cabbages whose boat would only take one of the three at a
time with the man himself. His difficulties arose from his being unable
to leave the wolf alone with the goat, or the goat alone with the
cabbages. These puzzles were considered by Tartaglia and Bachet, and
have been later investigated by Lucas, De Fonteney, Delannoy, Tarry, and
others. In the puzzles I give there will be found one or two new
conditions which add to the complexity somewhat. I also include a pulley
problem that practically involves the same principles.
Answer:
The only way in which the barrels could be equally divided among the
three brothers, so that each should receive his 31/2 barrels of honey
and his 7 barrels, is as follows:--
Full. Half-full. Empty.
A 3 1 3
B 2 3 2
C 2 3 2
There is one other way in which the division could be made, were it not
for the objection that all the brothers made to taking 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.
