Make a simple plan or diagram on a sheet of paper
or cardboard and number eight counters, 1 to 8.
The illustration represents the plan of a motor garage, with
accommodation for twelve cars.
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
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.