[Illustration]
In attempting to solve this problem it is first necessary to take the
two distinctive compartments of twenty and twelve squares respectively
and analyse them with a view to determining where the necessary points
of entry and exit lie. In the case of the larger compartment it will be
found that to complete a tour of it we must begin and end on two of the
outside squares on the long sides. But though you may start at any one
of these ten squares, you are restricted as to those at which you can
end, or (which is the same thing) you may end at whichever of these you
like, provided you begin your tour at certain particular squares. In the
case of the smaller compartment you are compelled to begin and end at
one of the six squares lying at the two narrow ends of the compartments,
but similar restrictions apply as in the other instance. A very little
thought will show that in the case of the two small compartments you
must begin and finish at the ends that lie together, and it then
follows that the tours in the larger compartments must also start and
end on the contiguous sides.
In the diagram given of one of the possible solutions it will be seen
that there are eight places at which we may start this particular tour;
but there is only one route in each case, because we must complete the
compartment in which we find ourself before passing into another. In any
solution we shall find that the squares distinguished by stars must be
entering or exit points, but the law of reversals leaves us the option
of making the other connections either at the diamonds or at the
circles. In the solution worked out the diamonds are used, but other
variations occur in which the circle squares are employed instead. I
think these remarks explain all the essential points in the puzzle,
which is distinctly instructive and interesting.