A LODGING-HOUSE DIFFICULTY.
(
Moving Counter Problem)
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.
Answer:
The shortest possible way is to move the articles in the following
order: Piano, bookcase, wardrobe, piano, cabinet, chest of drawers,
piano, wardrobe, bookcase, cabinet, wardrobe, piano, chest of drawers,
wardrobe, cabinet, bookcase, piano. Thus seventeen removals are
necessary. The landlady could then move chest of drawers, wardrobe, and
cabinet. Mr. Dobson did not mind the wardrobe and chest of drawers
changing rooms so long as he secured the piano.
