386 Answers- FLIES ON WINDOW PANES
The three lively flies have taken up new positions, as indicated by the arrows,
and still no two flies are in a straight line.
Q]
i~
~
i" I~
I~
~ t
~ 1t{J
l4:)
Ii{}- CITY LUNCHEONS
If the Pilkins staff had been II in number, and the Radson staff 12, they
could have sat down differently in 165 and 495 ways respectively, which
would have solved the question. Only we were told that there happened to be
the same number of men in each staff. Therefore the answer is 15 in threes
for 455 days, and 15 in fours for 1,365 days.- THE NECKLACE PROBLEM
The number of different necklaces with eight beads under the conditions
is 30.
A general solution for any number of beads is difficult, if not impossible.
But with as few as eight beads the reader will have no difficulty in finding the
correct answer by mere trial.
[For a discussion of the general problem, with a recursive formula that
gives the number of different necklaces with n beads of m different colors, see