d the Post Office how it was
to be done; but they sent him to the Customs and Excise officer, who
sent him to the Insurance Commissioners, who sent him to an approved
society, who profanely sent him--but no matter.

309.--THE FORTY-NINE COUNTERS.

[Illustration]

Can you rearrange the above forty-nine counters in a square so that no
letter, and also no number, shall be in line with a similar one,
vertically, horizontally, or diagonally? Here I, of course, mean in the
lines parallel with the diagonals, in the chessboard sense.

310.--THE THREE SHEEP.

[Illustration]

A farmer had three sheep and an arrangement of sixteen pens, divided off
by hurdles in the manner indicated in the illustration. In how many
different ways could he place those sheep, each in a separate pen, so
that every pen should be either occupied or in line (horizontally,
vertically, or diagonally) with at least one sheep? I have given one
arrangement that fulfils the conditions. How many others can you find?
Mere reversals and reflections must not be counted as different. The
reader may regard the sheep as queens. The problem is then to place the
three queens so that every square shall be either occupied or attacked
by at least one queen--in the maximum number of different ways.

311.--THE FIVE DOGS PUZZLE.

In 1863, C.F. de Jaenisch first discussed the "Five Queens Puzzle"--to
place five queens on the chessboard so that every square shall be
attacked or occupied--which was propounded by his friend, a "Mr. de R."
Jaenisch showed that if no queen may attack another there are ninety-one
different ways of placing the five queens, reversals and reflections not
counting as different. If the queens may attack one another, I have
recorded hundreds of ways, but it is not practicable to enumerate them
exactly.

[Illustration]

The illustration is supposed to represent an arrangement of sixty-four
kennels. It will be seen that five kennels each contain a dog, and on
further examination it will be seen that every one of the sixty-four
kennels is in a straight line with at least one dog--either
horizontally, vertically, or diagonally. Take any kennel you like, and
you will find that you can draw a straight line to a dog in one or other
of the three ways mentioned. The puzzle is to replace the five dogs and
discover in just how many different ways they may be placed in five
kennels _in a straight row_, so that every kennel shall always be in
lin