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Amusements in Mathematics

"A curious little point occurred to me in my dispensary this morning," said a doctor. "I
had a bottle containing ten ounces of spirits of wine, and another bottle containing ten
ounces of water. I poured a quarter of an ounce of spirits into the water and shook them
up together. The mixture was then clearly forty to one. Then I poured back a quarter-
ounce of the mixture, so that the two bottles should again each contain the same quantity
of fluid. What proportion of spirits to water did the spirits of wine bottle then contain?"
The men in the illustration are disputing over the liquid contents of a barrel. What the
particular liquid is it is impossible to say, for we are unable to look into the barrel; so we
will call it water. One man says that the barrel is more than half full, while the other
insists that it is not half full. What is their easiest way of settling the point? It is not
necessary to use stick, string, or implement of any kind for measuring. I give this merely
as one of the simplest possible examples of the value of ordinary sagacity in the solving
of puzzles. What are apparently very difficult problems may frequently be solved in a
similarly easy manner if we only use a little common sense.
Here is a new poser in measuring liquids that will be found interesting. A man has two
ten-quart vessels full of wine, and a five-quart and a four-quart measure. He wants to put
exactly three quarts into each of the two measures. How is he to do it? And how many
manipulations (pourings from one vessel to another) do you require? Of course, waste of
wine, tilting, and other tricks are not allowed.
An honest dairyman in preparing his milk for public consumption employed a can
marked B, containing milk, and a can marked A, containing water. From can A he poured
enough to double the contents of can B. Then he poured from can B into can A enough to
double its contents. Then he finally poured from can A into can B until their contents
were exactly equal. After these operations he would send the can A to London, and the
puzzle is to discover what are the relative proportions of milk and water that he provides
for the Londoners' breakfast-tables. Do they get equal proportions of milk and water—or
two parts of milk and one of water—or what? It is an interesting question, though,
curiously enough, we are not told how much milk or water he puts into the cans at the
start of his operations.
Mr. Goodfellow has adopted a capital idea of late. When he gives a little dinner party and
the time arrives to smoke, after the departure of the ladies, he sometimes finds that the
conversation is apt to become too political, too personal, too slow, or too scandalous.
Then he always manages to introduce to the company some new poser that he has
secreted up his sleeve for the occasion. This invariably results in no end of interesting
discussion and debate, and puts everybody in a good humour.