Miscellaneous Combinatorial Puzzles 175that the counters must always be disposed in a straight line. It will be found
an entertaining little puzzle.- FLIES ON WINDOW PANES
Here is a window with eighty-one
panes. There are nine flies on as many
panes, and no fly is in line with an-
other one horizontally, vertically, or
diagonally. Six of these flies are very
torpid and do not move, but each of
the remaining three goes to an adjoin-
ing pane. And yet, after this change
of station, no fly is in line with an-
other.
Which are the three lively flies, and
to which three panes (at present un-
occupied) do they pass?~
~
~
- CITY LUNCHEONS
~
~.
f&~
~r&
The clerks attached to the finn of Pilkins and Popinjay arranged that three
of them would lunch together every day at a particular table so long as they
could avoid the same three men sitting down twice together. The same num-
ber of clerks of Messrs. Radson, Robson, and Ross decided to do precisely
the same, only with four men at a time instead of three. On working it out
they found that Radson's staff could keep it up exactly three times as many
days as their neighbors.
What is the least number of men there could have been in each staff?
- THE NECKLACE PROBLEM
How many different necklaces can be made with eight beads, where each
bead may be either black or white, the beads being indistinguishable except
by color?
We may have eight white or eight black, or seven white and one black, or
six white and two black, as in our illustration on page 176. Of course, if