178 Combinatorial & Topological Problemsarranged them so that the numbers in
the three sides added up alike-that
is, to 16.
Can you rearrange them so that the
three sides shall sum to the smallest
number possible? Of course the cen-
tral barrel (which happens to be 7 in
the illustration) does not come into
the count.- LAMP SIGNALLING
Two spies on the opposite sides of a
river contrived a method for signalling
by night. They each put up a stand,
like our illustration, and each pos-
sessed three lamps which could show
either white, red, or green light. They
constructed a code in which every
different signal meant a sentence. You
will, of course, see that a single lamp
hung on anyone of the hooks could
only mean the same thing, that two
lamps hung on the upper hooks 1
and 2 could not be distinguished
from two on 4 and 5. Two red lamps
on 1 and 5 could be distinguished
from two on 1 and 6. And two on
1 and 2 would be different from two
on 1 and 3.
Remembering the variations of
color as well as of position, what is
the greatest number of signals that
could be sent?- THE HANDCUFFED PRISONERS
Once upon a time there were nine prisoners of particularly dangerous
character who had to be carefully watched. Every weekday they were taken
out for exercise, handcuffed together, as shown in the sketch made by one
of their guards. On no day in anyone week were the same two men to