back to the next
station and take off nine wagons. But an ingenious stoker undertook to
pass the trains and send them on their respective journeys with their
engines properly in front. He also contrived to reverse the engines the
fewest times possible. Could you have performed the feat? And how many
times would you require to reverse the engines? A "reversal" means a
change of direction, backward or forward. No rope-shunting,
fly-shunting, or other trick is allowed. All the work must be done
legitimately by the two engines. It is a simple but interesting puzzle
if attempted with counters.

[Illustration]

224.--THE MOTOR-GARAGE PUZZLE.

[Illustration]

The difficulties of the proprietor of a motor garage are converted into
a little pastime of a kind that has a peculiar fascination. All you need
is to make a simple plan or diagram on a sheet of paper or cardboard and
number eight counters, 1 to 8. Then a whole family can enter into an
amusing competition to find the best possible solution of the
difficulty.

The illustration represents the plan of a motor garage, with
accommodation for twelve cars. But the premises are so inconveniently
restricted that the proprietor is often caused considerable perplexity.
Suppose, for example, that the eight cars numbered 1 to 8 are in the
positions shown, how are they to be shifted in the quickest possible way
so that 1, 2, 3, and 4 shall change places with 5, 6, 7, and 8--that is,
with the numbers still running from left to right, as at present, but
the top row exchanged with the bottom row? What are the fewest possible
moves?

One car moves at a time, and any distance counts as one move. To prevent
misunderstanding, the stopping-places are marked in squares, and only
one car can be in a square at the same time.

225.--THE TEN PRISONERS.

If prisons had no other use, they might still be preserved for the
special benefit of puzzle-makers. They appear to be an inexhaustible
mine of perplexing ideas. Here is a little poser that will perhaps
interest the reader for a short period. We have in the illustration a
prison of sixteen cells. The locations of the ten prisoners will be
seen. The jailer has queer superstitions about odd and even numbers, and
he wants to rearrange the ten prisoners so that there shall be as many
even rows of men, vertically, horizontally, and diagonally, as
possible. At present it will be seen, as indicated by the arrows, that
there are only twelve