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.
Solutions: 1
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