king had eccentric ideas on the subject of military
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
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
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
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
Remember that they must form five straight lines
with four castles in every line.