Mother's jam puzzle
Puzzle
Mrs. Hubbard has invented a
clever system for keeping tabs on her
blackberry jam. She filled twenty-five jars and arranged the three sizes
so as to have twenty quarts on each
shelf. Can you guess her secret so
as to tell how much one of the big
jars contains?
Solution
Show solution
Alfred Merrier says: "What we
learn with pleasure we never forget,"
which is a more elegant way of expressing Josh Billings' trite saying:
"There are better ways of knocking
learning into a boy's head than with
a wormwood club."
Tommy would like to learn how to
extract unknown quantities from
those jars of jam by reduction, elimination or even by the process of sub-
stitution of empty jars for full ones.
The whole juvenile class would
speedily reduce everything to the
minimum quantities and clear off
fractions if they were not awed by
the mother's radical terms.
Like good Mother Hubbard we
will solve the problem by inspection,
and prove the quantities in the different jars. Knowing that each shelf
contains just 20 quarts, let us begin by cancelling off six little jars from
the two lower shelves. The result
proves that two big jars equal four
medium ones, or one large one equals
two medium size. Replace the jars
and cancel the two large ones from the middle shelf and equalize the top
shelf by removing the large one and
two of the medium size. This shows
that the one medium sized jar must
hold as much as three little ones.
Now multiply all the large jars by
two and they are changed to mediums, and multiply the number then
representing all the mediums by
three to reduce them to the smallest
size, and when we add them all together we find that the entire amount
could be contained in 54 of the small
size, 18 of the medium, or 9 of the
largest. As a large jar would contain one-ninth of 60 quarts, we see
that it would hold just six and two third quarts.
References
