A RAILWAY MUDDLE.
(
Moving Counter Problem)
The plan represents a portion of the line of the London, Clodville, and
Mudford Railway Company. It is a single line with a loop. There is only
room for eight wagons, or seven wagons and an engine, between B and C on
either the left line or the right line of the loop. It happened that two
goods trains (each consisting of an engine and sixteen wagons) got into
the position shown in the illustration. It looked like a hopeless
deadlock, and each engine-driver wanted the other to go 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.
Answer:
[Illustration: 1]
[Illustration: 2]
[Illustration: 3]
[Illustration: 4]
[Illustration: 5]
[Illustration: 6]
Only six reversals are necessary. The white train (from A to D) is
divided into three sections, engine and 7 wagons, 8 wagons, and 1 wagon.
The black train (D to A) never uncouples anything throughout. Fig. 1 is
original position with 8 and 1 uncoupled. The black train proceeds to
position in Fig. 2 (no reversal). The engine and 7 proceed towards D,
and black train backs, leaves 8 on loop, and takes up position in Fig. 3
(first reversal). Black train goes to position in Fig. 4 to fetch single
wagon (second reversal). Black train pushes 8 off loop and leaves single
wagon there, proceeding on its journey, as in Fig. 5 (third and fourth
reversals). White train now backs on to loop to pick up single car and
goes right away to D (fifth and sixth reversals).
