There was once, in ancient times, a powerful king, who had eccentric
ideas on the subject of military architecture. He held that there was
great strength and economy in symmetrical forms, and always cited the
example of the bees, who construct their combs in perfect hexagonal
cells, to prove that he had nature to support him. He resolved to build
ten new castles in his country all to be connected by fortified walls,
which should form five lines with four castles in every line. The royal
architect presented his preliminary plan in the form I have shown. But
the monarch pointed out that every castle could be approached from the
outside, and commanded that the plan should be so modified that as many
castles as possible should be free from attack from the outside, and
could only be reached by crossing the fortified walls. The architect
replied that he thought it impossible so to arrange them that even one
castle, which the king proposed to use as a royal residence, could be so
protected, but his majesty soon enlightened him by pointing out how it
might be done. How would you have built the ten castles and
fortifications so as best to fulfil the king's requirements? Remember
that they must form five straight lines with four castles in every line.
[Illustration]