220.—­A LODGING-HOUSE DIFFICULTY.

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The Dobsons secured apartments at Slocomb-on-Sea.  There were six rooms on the same floor, all communicating, as shown in the diagram.  The rooms they took were numbers 4, 5, and 6, all facing the sea.  But a little difficulty arose.  Mr. Dobson insisted that the piano and the bookcase should change rooms.  This was wily, for the Dobsons were not musical, but they wanted to prevent any one else playing the instrument.  Now, the rooms were very small and the pieces of furniture indicated were very big, so that no two of these articles could be got into any room at the same time.  How was the exchange to be made with the least possible labour?  Suppose, for example, you first move the wardrobe into No. 2; then you can move the bookcase to No. 5 and the piano to No. 6, and so on.  It is a fascinating puzzle, but the landlady had reasons for not appreciating it.  Try to solve her difficulty in the fewest possible removals with counters on a sheet of paper.

221.—­THE EIGHT ENGINES.

The diagram represents the engine-yard of a railway company under eccentric management.  The engines are allowed to be stationary only at the nine points indicated, one of which is at present vacant.  It is required to move the engines, one at a time, from point to point, in seventeen moves, so that their numbers shall be in numerical order round the circle, with the central point left vacant.  But one of the engines has had its fire drawn, and therefore cannot move.  How is the thing to be done?  And which engine remains stationary throughout?

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222.—­A RAILWAY PUZZLE.

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Make a diagram, on a large sheet of paper, like the illustration, and have three counters marked A, three marked B, and three marked C. It will be seen that at the intersection of lines there are nine stopping-places, and a tenth stopping-place is attached to the outer circle like the tail of a Q. Place the three counters or engines marked A, the three marked B, and the three marked C at the places indicated.  The puzzle is to move the engines, one at a time, along the lines, from stopping-place to stopping-place, until you succeed in getting an A, a B, and a C on each circle, and also A, B, and C on each straight line.  You are required to do this in as few moves as possible.  How many moves do you need?

223.—­A RAILWAY MUDDLE.

The plan represents a portion of the line of the London, Clodville, and Mudford Railway Company.  It is a single line with a loop.  There is only room for eight wagons, or seven wagons and an engine, between B and C on either the left line or the right line of the loop.  It happened that two goods trains (each consisting of an engine and sixteen wagons) got into the position shown in the illustration.  It looked like a hopeless deadlock, and each engine-driver wanted the other to go back to the next station and