THE BARREL PUZZLE.
(
Measuring, Weight, and Packing Puzzles.)
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.
Answer:
[Illustration: Figs. 1, 2, and 3]
All that is necessary is to tilt the barrel as in Fig. 1, and if the
edge of the surface of the water exactly touches the lip a at the same
time that it touches the edge of the bottom b, it will be just half
full. To be more exact, if the bottom is an inch or so from the ground,
then we can allow for that, and the thickness of the bottom, at the top.
If when the surface of the water reached the lip a it had risen to the
point c in Fig. 2, then it would be more than half full. If, as in
Fig. 3, some portion of the bottom were visible and the level of the
water fell to the point d, then it would be less than half full.
This method applies to all symmetrically constructed vessels.
