To exchange the cars and return the engine to its initial position 16 moves are required. Within the moves six* couplings and uncouplings are performed. A move is either a coupling/uncoupling or moving of an engine alone/with car(s) till the moment it reverses its direction. The moves are shown in the illustration.

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The improvement on the number of required couplings and uncouplings, decreased from 8 to 6, has been sent to us by Japhet Stevens. Many thanks!