[Illustration]
Set up the position shown in the diagram. Then the condition of the
puzzle is-White to play and checkmate in six moves. Notwithstanding the
complexities, I will show how the manner of play may be condensed into
quite a few lines, merely sta
depicted in the act of worrying out a pleasant little problem which I
will relate. One of her gardens is oblong in shape, enclosed by a high
holly hedge, and she is turning it into a rosary for the cultivation of
some of her choicest roses. She wants to d
179.-STEALING THE BELL-ROPES.
Two men broke into a church tower one night to steal the bell-ropes. The
two ropes passed through holes in the wooden ceiling high above them,
and they lost no time in climbing to the top. Then one man drew his
knife and cut
arm of the cross be if it is required that there shall be used just the
same quantity of red and of white bunting?
[Illustration]
186.-THE CLOTHES LINE PUZZLE.
A boy tied a clothes line from the top of each of two poles to the base
of the other. He then p
the professor the other day. The answer was certainly curious.
"If you add one quarter of the time from noon till now to half the time
from now till noon to-morrow, you will get the time exactly."
What was the time of day when the professor spoke?
58.-A T
94.-THE DIGITAL CENTURY.
1 2 3 4 5 6 7 8 9 = 100.
It is required to place arithmetical signs between the nine figures so
that they shall equal 100. Of course, you must not alter the present
numerical arrangement of the figures. Can you give a correct solu
"Variety's the very spice of life,
That gives it all its flavour."
COWPER: _The Task._
97.-THE SPOT ON THE TABLE.
A boy, recently home from school, wished to give his father an
exhibition of his precocity. He pushed a large circular table into the
corner
satisfy these conditions?
210.-THE TEN COINS.
Place ten pennies on a large sheet of paper or cardboard, as shown in
the diagram, five on each edge. Now remove four of the coins, without
disturbing the others, and replace them on the paper so that the ten
Often a dissection problem is quite easy apart from this limitation of
pieces. At the time of the publication in the _Weekly Dispatch_, in
1902, of a method of cutting an equilateral triangle into four parts
that will form a square (see No. 26, "Canterbur
station and take off nine wagons. But an ingenious stoker undertook to
pass the trains and send them on their respective journeys with their
engines properly in front. He also contrived to reverse the engines the
fewest times possible. Could you have perf
PLATO.
"There is no study," said Augustus de Morgan, "which presents so simple
a beginning as that of geometry; there is none in which difficulties
grow more rapidly as we proceed." This will be found when the reader
comes to consider the following puzzle
[Illustration: 12]
Finally, I give an example from the many curious paradoxes that one
happens upon in manipulating Tangrams. I show designs of two dignified
individuals (15 and 16) who appear to be exactly alike, except for the
fact that one has a foot a
these form the series 1 squared, 3 squared, 6 squared, 10 squared, etc. It will now be understood
when I say that one of the keys to the puzzle was the fact that these
are always the squares of triangular numbers-that is, the squares of 1,
3, 6, 10, 15, 2
the Aztec mounds of Mexico, the pyramids of Egypt, the ruins of Troy,
and the ancient lore of India and China. One might almost say there is a
curious affinity between the Greek cross and Swastika! If, however, we
require that the four pieces shall be pro
39.-THE COSTERMONGER'S PUZZLE.
"How much did yer pay for them oranges, Bill?"
"I ain't a-goin' to tell yer, Jim. But I beat the old cove down
fourpence a hundred."
"What good did that do yer?"
"Well, it meant five more oranges on every ten shillin's-worth
the purpose of some architectural decoration, when a smart schoolboy
came upon the scene.
"Look here," said the mason, "you seem to be a sharp youngster, can you
tell me this? If I placed this ball on the level ground, how many other
balls of the same siz
Most people know that if you take any sum of money in pounds, shillings,
and pence, in which the number of pounds (less than L12) exceeds that of
the pence, reverse it (calling the pounds pence and the pence pounds),
find the difference, then reverse and
The word "labyrinth" is derived from a Greek word signifying the
passages of a mine. The ancient mines of Greece and elsewhere inspired
fear and awe on account of their darkness and the danger of getting lost
in their intricate passages. Legend was afterw
The varied character of the contributions is just what we would expect
on such an occasion, for it was a gathering not of expert mathematicians
and logicians, but of quite ordinary folk.
"It is a wonderful age!" repeated Mr. Allgood. "A man has just desig
Dorset, is in a class by itself (Fig. 19). It was formed of small ridges
about a foot high, and covered nearly an acre of ground; but it was,
unfortunately, ploughed up in 1730.
[Illustration: FIG. 19.-Maze at Pimperne, Dorset.]
We will now pass to the in
bring us safely out of a maze that we have entered; it may happen to
take us through the "centre," and if we miss the centre we shall know
there must be islands. But it has to be done with a little care, and in
no case can we be sure that we have traverse
this little puzzle had not caused him to lose his mental balance some
other more or less trivial thing would in time have done so. There is no
moral in the story, unless it be that of the Irish maxim, which applies
to every occupation of life as much as t
"Let me think," said Mrs. Allgood. "Yes-yes-that is correct."
"Very well, then. As there are only nine hundred and ninety-nine
thousand nine hundred and ninety-nine _different_ ways of bearing hair,
it is clear that the millionth person must repeat one of
"Well, then, I think you will find, uncle, that Guernsey is about
twenty-six miles from France, and England is only twenty-one miles from
France, between Calais and Dover."
"My mathematical master," said George, "has been trying to induce me to
accept the
Turmitville to Wurzleton; but as it was found that a railway company was
making a deep level cutting in the same direction, they arranged to put
up the posts beside the line. Now, the posts were to be a hundred yards
apart, the length of the road over the
If we number six cards 1, 2, 4, 5, 7, and 8, and arrange them on the
table in this order:-1
4
2
8
5
7
We can demonstrate that in order to multiply by 3 all that is necessary
is to remove the 1 to the other end of the row, and the thing is done.
The answer
three times as large as the other, and (2) so as to enclose two
five-sided spaces, one exactly three times as large as the other? All
the eighteen matches must be fairly used in each case; the two spaces
must be quite detached, and there must be no loose
The above clock face indicates a little before 42 minutes past 4. The
hands will again point at exactly the same spots a little after 23
minutes past 8. In fact, the hands will have changed places. How many
times do the hands of a clock change places betw
two-cent piece, and a one-cent piece. How did the tradesman manage to
give change? For the benefit of those readers who are not familiar with
the American coinage, it is only necessary to say that a dollar is a
hundred cents and a dime ten cents. A puzzle
and you can do your share." The son was not quite satisfied as to the
proposed division of labour, and as the village schoolmaster happened to
be passing, he appealed to that person to decide the matter. He found
the farmer was quite correct, provided the
[Illustration]
In introducing a little Commonwealth problem, I must first explain that
the diagram represents the sixty-four 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
Chess-at 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