[Illustration]
In introducing a little Commonwealth problem, I must first explain that
the diagram represents the sixtyfour fields, all properly fenced off
from one another, of an Australian settlement, though I need hardly say
that our kith and kin "dow
[Illustration:
(1)
(2)
(2)
(4) (5) (1) (6) (7)
(3) (4) (9) (5) (6)
(3)
(7)
A
(8)
(8)
B
(9)
]
278.A DORMITORY PUZZLE.
In a certain convent there were eight large dormitories on one floor,
approached by a spiral staircase in the centre, as shown in our pla
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 for
335.FARMER LAWRENCE'S CORNFIELDS.
One of the most beautiful districts within easy distance of London for a
summer ramble is that part of Buckinghamshire known as the Valley of the
Chessat least, it was a few years ago, before it was discovered by the
sp
you change the direction of your pencil it begins a new stroke. You may
go over the same line more than once if you like. It requires just a
little care, or you may find yourself beaten by one stroke.
[Illustration]
242.THE TUBE INSPECTOR'S PUZZLE.
The m
Now, in order to reduce their growing obesity, and to combine physical
exercise with mental recreation, the prisoners decided, on the
suggestion of one of their number who was interested in knight's tours,
to try to form themselves into a perfect knight's
without mutual attack. I shall give an exceedingly simple rule for
determining the number of ways for a square chequered board of any
number of squares.
300.THE EIGHT QUEENS.
[Illustration:
+++++++++
    .Q    
++++.+++++
  .Q. 
245.THE FLY ON THE OCTAHEDRON.
"Look here," said the professor to his colleague, "I have been watching
that fly on the octahedron, and it confines its walks entirely to the
edges. What can be its reason for avoiding the sides?"
"Perhaps it is trying to s
263.KING ARTHUR'S KNIGHTS.
King Arthur sat at the Round Table on three successive evenings with his
knightsBeleobus, Caradoc, Driam, Eric, Floll, and Galahadbut on no
occasion did any person have as his neighbour one who had before sat
next to him. On
There are no morals in puzzles. When we are solving the old puzzle of
the captain who, having to throw half his crew overboard in a storm,
arranged to draw lots, but so placed the men that only the Turks were
sacrificed, and all the Christians left on boa
once. How would you arrange them?
If we represent them by the first nine letters of the alphabet, they
might be grouped on the first day as follows:A B C
D E F
G H I
Then A can never walk again side by side with B, or B with C, or D with
E, and so on. Bu
+++++++++
  EVLI  
+++++++++
  LIEV  
+++++++++
]
If the reader will examine the above diagram, he will see that I have so
placed eight V's, eight E's, eight I's, and eight L's in the diagram
that no letter is in
297.BISHOPSUNGUARDED.
Place as few bishops as possible on an ordinary chessboard so that every
square of the board shall be either occupied or attacked. It will be
seen that the rook has more scope than the bishop: for wherever you
place the former, it
Once upon a time the Lord Abbot of St. Edmondsbury, in consequence of
"devotions too strong for his head," fell sick and was unable to leave
his bed. As he lay awake, tossing his head restlessly from side to side,
the attentive monks noticed that somethin
same. Only remember this: that in no case may two of you ever be
together in the same cell."
One of the prisoners, after working at the problem for two or three
days, with a piece of chalk, undertook to obtain the liberty of himself
and his fellowprisone
NONATTACKING CHESSBOARD ARRANGEMENTS.
We know that n queens may always be placed on a square board of n squared
squares (if n be greater than 3) without any queen attacking another
queen. But no general formula for enumerating the number of different
way
that this arrangement will not answer the conditions, for in the two
directions indicated by the dotted lines there are three queens in a
straight line. There is only one of the twelve fundamental ways that
will solve the puzzle. Can you find it?
301.THE
you arrange them? It will be found that of the twelve shown in the
diagram only four are thus protected by being a knight's move from
another knight.
THE GUARDED CHESSBOARD.
On an ordinary chessboard, 8 by 8, every square can be guardedthat is,
either oc
  * * 
+++++++
 *
+++

+++
In the illustration we have a somewhat curious target designed by an
eccentric sharpshooter. His idea was that in order to score you must hit
four circles in as many shots so that those four shots shall form
not enter.
Well, the captain says that if a spirited lion crosses your path in the
desert it becomes lively, for the lion has generally been looking for
the man just as much as the man has sought the king of the forest. And
yet when they meet they always
last cigar, assuming that they each will play in the best possible
manner? The size of the table top and the size of the cigar are not
given, but in order to exclude the ridiculous answer that the table
might be so diminutive as only to take one cigar, we
arises the question of how you are to make the best of your time and
other resources. You have determined to get as far as some particular
place, to include visits to suchandsuch a town, to try to see
something of special interest elsewhere, and perhaps
When Philip of Macedon, the father of Alexander the Great, found himself
confronted with great difficulties in the siege of Byzantium, he set his
men to undermine the walls. His desires, however, miscarried, for no
sooner had the operations been begun tha
board on which a reentrant tour is possible is one that is 6 by 5.
A complete knight's path (not reentrant) over all the squares of a
board is never possible if there be only two squares on one side; nor is
it possible on a square board of smaller dimen
309.THE FORTYNINE COUNTERS.
[Illustration]
Can you rearrange the above fortynine 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
li
with the white ones, no bishop ever attacking another of the opposite
colour. They must move alternatelyfirst a white, then a black, then a
white, and so on. When you have succeeded in doing it at all, try to
find the fewest possible moves.
If you leave
]
If you will look at the lettered square you will understand that there
are only ten really differently placed squares on a chessboardthose
enclosed by a dark lineall the others are mere reversals or
reflections. For example, every A is a corner square
parishes in the fewest possible moves. Of course, all the parishes
passed through on any move are regarded as "visited." You can visit any
squares more than once, but you are not allowed to move twice between
the same two adjoining squares. What are the f