In one of the
outlying suburbs of London a man had
a square plot of ground on which he decided
to build eight villas, as shown in the illustration, with a common
recreation ground in the middle.
After the houses were completed, and
all or some of them let, he discovered that the number of occupants in
the three houses forming a side of the square was in every case
He did not state how the occupants were distributed, but I have shown
by the numbers on the sides of the houses one way in which it might
Discover the total number of ways in
which all or any of the houses might be occupied, so that there should
be nine persons on each side.
Although B is what we call a
reflection of A, these would count as two different arrangements, while
C, if it is turned round, will give four arrangements; and if turned
round in front of a mirror, four other arrangements.
All eight must be