Amusements in Mathematics
every box and sack, and assaying every piece of gold) to give any assurance on the
subject. In presenting the following little puzzle, I wish it to be also understood that I do
not guarantee the real existence of the gold, and the point is not at all material to our
purpose. Moreover, if the reader says that gold is not usually "put up" in slabs of the
dimensions that I give, I can only claim problematic licence.
Russian officials were engaged in packing 800 gold slabs, each measuring 12½ inches
long, 11 inches wide, and 1 inch deep. What are the interior dimensions of a box of equal
length and width, and necessary depth, that will exactly contain them without any space
being left over? Not more than twelve slabs may be laid on edge, according to the rules of
the government. It is an interesting little problem in packing, and not at all difficult.
372.—THE BARRELS OF HONEY.
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?