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