Here is a puzzle that was once on sale in the London shops. It represents
a military train--an engine and eight cars. The puzzle is to reverse the
cars, so that they shall be in the order 8, 7, 6, 5, 4, 3, 2, 1, instead
of 1, 2, 3, 4, 5, 6, 7, 8, with the engine left, as at first, on the side
track. Do this in the fewest possible moves. Every time the engine or a
car is moved from the main to the side track, or _vice versa_, it counts
a move for each car or engine passed over one of the points. Moves along
the main track are not counted. With 8 at the extremity, as shown, there
is just room to pass 7 on to the side track, run 8 up to 6, and bring
down 7 again; or you can put as many as five cars, or four and the
engine, on the siding at the same time. The cars move without the aid of
the engine. The purchaser is invited to "try to do it in 20 moves." How
many do you require?
[Illustration]