THE MILKMAID PUZZLE.
(
Patchwork Puzzles)
Here is a little pastoral puzzle that the reader may, at first sight, be
led into supposing is very profound, involving deep calculations. He may
even say that it is quite impossible to give any answer unless we are
told something definite as to the distances. And yet it is really quite
"childlike and bland."
In the corner of a field is seen a milkmaid milking a cow, and on the
other side of the field is the dairy where the extract has to be
deposited. But it has been noticed that the young woman always goes down
to the river with her pail before returning to the dairy. Here the
suspicious reader will perhaps ask why she pays these visits to the
river. I can only reply that it is no business of ours. The alleged milk
is entirely for local consumption.
"Where are you going to, my pretty maid?"
"Down to the river, sir," she said.
"I'll _not_ choose your dairy, my pretty maid."
"Nobody axed you, sir," she said.
If one had any curiosity in the matter, such an independent spirit would
entirely disarm one. So we will pass from the point of commercial
morality to the subject of the puzzle.
Draw a line from the milking-stool down to the river and thence to the
door of the dairy, which shall indicate the shortest possible route for
the milkmaid. That is all. It is quite easy to indicate the exact spot
on the bank of the river to which she should direct her steps if she
wants as short a walk as possible. Can you find that spot?
Answer:
[Illustration:
A
|
|
|
| B RIVER
+----+--------------
| /
| /
| /
|/ DOOR
STOOL
]
Draw a straight line, as shown in the diagram, from the milking-stool
perpendicular to the near bank of the river, and continue it to the
point A, which is the same distance from that bank as the stool. If you
now draw the straight line from A to the door of the dairy, it will cut
the river at B. Then the shortest route will be from the stool to B and
thence to the door. Obviously the shortest distance from A to the door
is the straight line, and as the distance from the stool to any point of
the river is the same as from A to that point, the correctness of the
solution will probably appeal to every reader without any acquaintance
with geometry.
