THE MOTOR-GARAGE PUZZLE.
(
Moving Counter Problem)
The difficulties of the proprietor of a motor garage are converted into
a little pastime of a kind that has a peculiar fascination. All you need
is to make a simple plan or diagram on a sheet of paper or cardboard and
number eight counters, 1 to 8. Then a whole family can enter into an
amusing competition to find the best possible solution of the
difficulty.
The illustration represents the plan of a motor garage, with
accommodation for twelve cars. But the premises are so inconveniently
restricted that the proprietor is often caused considerable perplexity.
Suppose, for example, that the eight cars numbered 1 to 8 are in the
positions shown, how are they to be shifted in the quickest possible way
so that 1, 2, 3, and 4 shall change places with 5, 6, 7, and 8--that is,
with the numbers still running from left to right, as at present, but
the top row exchanged with the bottom row? What are the fewest possible
moves?
One car moves at a time, and any distance counts as one move. To prevent
misunderstanding, the stopping-places are marked in squares, and only
one car can be in a square at the same time.
Answer:
The exchange of cars can be made in forty-three moves, as follows: 6-G,
2-B, 1-E, 3-H, 4-I, 3-L, 6-K, 4-G, 1-I, 2-J, 5-H, 4-A, 7-F, 8-E, 4-D,
8-C, 7-A, 8-G, 5-C, 2-B, 1-E, 8-I, 1-G, 2-J, 7-H, 1-A, 7-G, 2-B, 6-E,
3-H, 8-L, 3-I, 7-K, 3-G, 6-I, 2-J, 5-H, 3-C, 5-G, 2-B, 6-E, 5-I, 6-J. Of
course, "6-G" means that the car numbered "6" moves to the point "G."
There are other ways in forty-three moves.
