Henry Ernest Dudeney/Modern Puzzles/48 - Railway Shunting/Solution

Modern Puzzles by Henry Ernest Dudeney: $48$

Railway Shunting

How are the trains in our illustration to pass one another, and proceed with their engines in front?

The small side track is large enough to hold one engine or one carriage at a time, and no tricks, such as ropes and flying-switches, are allowed.

Every reversal -- that is, change of direction -- of an engine is counted as a move in the solution.

What is the smallest number of moves necessary?

Solution

Refer to the following diagram, in which:

the engines are $L$ and $R$

$L$'s carriages, never separated in the solution, are denoted by $X$

$R$'s carriages are $A$ and $B$

$S$ is the siding.

Make the following moves:

\(\ds \)

\(\)

\(\ds \)

$R$ moves left without $A$ and $B$ (continuation of existing motion, so not a move as such)

\(\text {(1)}: \quad\)

\(\ds \)

\(\)

\(\ds \)

$R$ to $S$

\(\ds \)

\(\)

\(\ds \)

$X L$ to right (continuation of existing motion, so not a move as such)

\(\text {(2)}: \quad\)

\(\ds \)

\(\)

\(\ds \)

$R$ to left

\(\text {(3)}: \quad\)

\(\ds \)

\(\)

\(\ds \)

$X L A$ to left

\(\text {(4)}: \quad\)

\(\ds \)

\(\)

\(\ds \)

$L$ takes $A$ to $S$

\(\text {(5)}: \quad\)

\(\ds \)

\(\)

\(\ds \)

$L$ to left

\(\text {(6)}: \quad\)

\(\ds \)

\(\)

\(\ds \)

$X L$ to right

\(\text {(7)}: \quad\)

\(\ds \)

\(\)

\(\ds \)

$R$ to $A$

\(\text {(8)}: \quad\)

\(\ds \)

\(\)

\(\ds \)

$R A$ to left

\(\text {(9)}: \quad\)

\(\ds \)

\(\)

\(\ds \)

$X L B$ to left

\(\text {(10)}: \quad\)

\(\ds \)

\(\)

\(\ds \)

$L$ takes $B$ to $S$

\(\text {(11)}: \quad\)

\(\ds \)

\(\)

\(\ds \)

$L$ to left

\(\text {(12)}: \quad\)

\(\ds \)

\(\)

\(\ds \)

$X L$ to right, and away

\(\text {(13)}: \quad\)

\(\ds \)

\(\)

\(\ds \)

$R A$ to $B$

\(\text {(14)}: \quad\)

\(\ds \)

\(\)

\(\ds \)

$R A B$ to right and away

$\blacksquare$

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Solutions: $48$. -- Railway Shunting
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $374$. Railway Shunting