# Solution

(related to Problem: A Railway Muddle)

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 the original position with $8$ and $1$ uncoupled. The black train proceeds to the 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). The black train goes to the position in Fig. $4$ to fetch single wagon (second reversal). Black train pushes $8$ off the 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 a single car and goes right away to $D$ (fifth and sixth reversals).

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### References

#### Project Gutenberg

1. Dudeney, H. E.: "Amusements in Mathematics", The Authors' Club, 1917

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