is a piece of card; _b b_ a narrow slip divided from its bottom edge, the
whole breadth of the card, except just sufficient to hold it on at each
side; _c c_ is another small slip of card with two large square ends, _e
e_; _d_ is a bit of tobacco-pipe, through which _c c_ is passed, and which
is kept on by the two ends _e e_. The puzzle consists in getting the pipe
off without breaking it or injuring any other part of the puzzle. This,
which appears to be impossible, is done in the most simple manner. On a
moment's consideration it will appear plainly that there must be as much
difficulty in getting the pipe in its present situation, as there can be
in taking it away. The way to put the puzzle together is as follows: The
slip _c c e e_ is cut out of a piece of card in the shape delineated in
Fig. 3. The card in the first figure must then be gently bent at A, so as
to allow of the slip at the bottom of it being also bent sufficiently to
pass double through the pipe, as in Fig. 2. The detached slip with the
square ends (Fig. 3) is then to be passed half way through the loop _f_ at
the bottom of the pipe; it is next to be doubled in the center at _a_, and
pulled through the pipe, double; by means of the loop of the slip to the
card. Upon unbending the card the puzzle will be complete, and appear as
represented in Fig. 1.
20. THREE SQUARE PUZZLE.
[Illustration]
Cut seventeen slips of cardboard of equal lengths, and place them on a
table to form six squares, as in the diagram. It is now required to take
away five of the pieces, yet to leave but three perfect squares.
21. THE CYLINDER PUZZLE.
[Illustration]
Cut a piece of cardboard about four inches long, of the shape of the
diagram, and make three holes in it, as represented. The puzzle is, to
make one piece of wood to pass through, and also exactly to fill, each of
the three holes.
22. PUZZLE OF THE FOUR TENANTS.
[Illustration]
I have a square plot of ground, in one quarter of which I have built a
house, which I have let to four tenants. I tell them that if they can
divide the remaining ground into four equal plots, alike in shape, and
each containing one of the four apple trees I have planted, they shall
have it without any increase of rent. How may they succeed?
23. THE PUZZLE WALL.
Suppose there was a pond, around which four poor men built their houses,
thus:
[Illustration]
Suppose four evil-disposed rich men afterwards built houses around the
poor people, thus:
[Illustration]
and wished to have all the water of the pond to themselves. How could they
build a high wall, so as to shut out the poor people from the pond?
24. THE NUNS.
[Illustration]
Twenty-four nuns were arranged in a convent by night, by a sister, to
count nine each way, as in the diagram. Four of them went out for a walk
by moonlight. How were the remainder placed in the square so as still to
count nine each way? The four who went out returned, bringing with them
four friends; how were they all placed still to count nine each way, and
thus to deceive the sister, as to whether there were 20, 24, 28, or 82, in
the square?
25. THE HORSE SHOE PUZZLE.
[Illustration]
Cut a piece of apple or turnip into the shape of a horse shoe, stick six
pins in it for nails, and then, by two cuts, divide it into six parts,
each to contain one pin.
26. THE CARD SQUARE.
[Illustration]
With eight pieces of card or paper, of the shape of Fig. _a_, four of Fig.
_b_, and four of Fig. _c_, and of proportionate sizes, form a perfect
square.
27. THE DOG PUZZLE.
[Illustration]
The dogs are, by placing two lines upon them, to be suddenly aroused to
life and made to run. Query, How and where should these lines be placed,
and what should be the forms of them?
28. PUZZLE OF THE TWO FATHERS.
Two fathers have each a square of land. One father divides his so as to
reserve to himself one fourth; thus--
[Illustration:
+----------------+
| |
| |
| |
+------+ |
| | |
| | |
| | |
+------+---------+
]
The other father divides his so as to reserve to himself one fourth in the
form of a triangle; thus--
[Illustration:
+--------+
| |
| |
| /\ |
| / \ |
| / \ |
|/ \|
+--------+
]
They each have four sons, and each divides the remainder among his sons
in such a way that each son will share equally with his brother, and in
similar shape. How were the two farms divided?
29. THE TRIANGLE PUZZLE.
Cut twenty triangles out of ten square pieces of wood; mix them together,
and request a person to make an exact square with them.
30. CUTTING OUT A CROSS.
[Illustration]
How can be cut out of a single piece of paper, and with one cut of the
scissors, a perfect cross, and all the other forms as shown in the cuts?
31. ANOTHER CROSS PUZZLE.
[Illustration]
With three pieces of cardboard of the shape and size of No. 1, and one
each of No. 2 and 3, to form a cross.
32. THE FOUNTAIN PUZZLE.
A is a wall, B C D three houses, and E F G three fountains or canals.
[Illustration]
It is required to bring the water from E to D, from G to B, and from F to
C, without one crossing the other, or passing outside of the wall A.
33. THE PUZZLE OF THE STARS.
Friends one and all, I pray you show
How you _nine stars_ would so bestow,
_Ten_ rows to form--in each row _three_--
Tell me, ye wits, how this can be?
34. THE COUNTER PUZZLE.
[Illustration]
Place eight counters or coins, as in the diagram; it is then required to
lay them in four couples, removing only one at a time, and in each removal
passing the one in the hand over _two_ on the table.
35. THE JAPAN SQUARE PUZZLE.
[Illustration]
Cut out ten pieces of card or wood of the same sizes and shapes as in the
diagram, and then form a square with them.
36. THE CABINET MAKER'S PUZZLE.
A cabinet-maker has a circular piece of veneering with which he has to
veneer the tops of two oval stools; but it so happens that the area of
the stools, exclusive of the hand-holes in the center, and that of the
circular piece, are the same. How must he cut his stuff so as to be
exactly sufficient for his purpose?
37. THE STRING AND BALLS PUZZLE.
Get an oblong strip of wood or ivory, and bore three holes in it, as shown
in the cut. Then take a piece of twine, passing the two ends through the
holes at the extremities, fastening them with a knot, and thread upon it
two beads or rings, as depicted above. The puzzle is to get both beads on
the same side, without removing the string from the holes, or untying the
knots.
[Illustration]
38. THE DOUBLE-HEADED PUZZLE.
[Illustration]
Cut a circular piece of wood as in the cut No. 1, and four others, like
No. 2. The puzzle consists in getting them all into the cross-shaped slit,
until they look like Fig. 3.
39. ARITHMETICAL PUZZLE.
The sum of four figures in value will be.
Above seven thousand nine hundred and three;
But when they are halved, you'll find very fair
The sum will be nothing, in truth I declare.
40. GRAMMATICAL PUZZLE.
Let the rich, great, and noble, banquet in the festal halls,
And pass the hours away, as the most thoughtless revel;
Then seek the poor man's dreary home, whose very dingy walls
Proclaim full well to all how low his rank and level.
Take away one letter from a word in the above stanza, and substitute
another, leaving the word so metamorphosed still a word of the English
language; and, by that change, totally after the syntactical construction
of the whole sentence, changing the moods and tenses of verbs, turning
verbs into nouns, nouns into adjectives, and adjectives into adverbs, &c.,
and so make the entire stanza bear quite a different meaning from that
which it has as it stands above.
41. THE TREE PUZZLE.
Plant an orchard of twenty-one trees, so that there shall be nine straight
rows, with five trees in each row, the _outline_ a regular geometrical
figure, and the trees all at unequal distances from each other.
42. AN EPITAPH ON ELLINOR BACHELLOR, AN OLD PYE WOMAN.
Bene A. Thin Thed Ustt HEMO. Uld yo
L.D.C. RUSTO! Fnel L.B.
Ach El Lor. Lat. ELY,
Wa. S. shove N. W. How--Ass! kill'd I. N. T. H.
Ear T. Sofp, I, Escu Star.
D. San D T Art. San D K. N E. W. E
Ver----Yus E.--Oft He ove N W. Hens He
'Dli V'DL. on geno
Ug H S hem A.D.E. he R. la Stp. Uf----fap
Uf. F. B Y he. R hu
S. Ban D. M.
Uch pra is 'D. No. Wheres Hedot
HL. i. e. Tom. A kead I.R.T.P. Yein hop Esthathe
R. C. RUSTWI,
L L B. Era is '----D!
43. A CURIOUS LETTER.
Friends Sir, friends,
stand your disposition;
I bearing
a man the world
is whilst the
contempt,
ridicule.
are
ambitious.
44. A PUZZLING INSCRIPTION.
P R S V R Y P R F C T M N
V R K P T H S P R C P T S T N.
The two lines above were affixed to the communion table of a small church
in Wales, and continued to puzzle the learned congregation for several
centuries, but at length the inscription was deciphered. What was it?
45. THE PUZZLING RINGS.
This perplexing invention is of great antiquity, and was treated on by
Cardan, the mathematician, at the beginning of the sixteenth century.
It consists of a flat piece of thin metal or bone, with ten holes in
it; in each hole a wire is loosely fixed, beaten out into a head at one
end, to prevent its slipping through, and the other fastened to a ring,
also loose. Each wire has been passed through the ring of the next wire,
previously to its own ring being fastened on; and through the whole of
the rings runs a wire loop or bow, which also contains, within its oblong
space, all the wires to which the rings are fastened; the whole presenting
so complicated an appearance, as to make the releasing the rings from the
bow appear an impossibility. The construction of it would be found rather
troublesome to the amateur, but it may be purchased at most of the toy
shops very lightly and elegantly made. It also exists in various parts of
the country, forged in iron, perhaps by some ingenious village mechanic,
and aptly named "The Tiring Irons." The following instructions will show
the principle on which the puzzle is constructed, and will prove a key to
its solution.
Take the loop in your left hand, holding it at the end, B, and consider
the rings as being numbered 1st to 10th. The 1st will be the extreme ring
to the right, and the 10th the nearest your left hand.
[Illustration]
It will be seen that the difficulty arises from each ring passing round
the wire of its right-hand neighbor. The extreme ring at the right hand,
of course, being unconnected with any other wire than its own, may at any
time be drawn off the end of the bow at A, raised up, dropped through
the bow, and finally released. After you have done this, try to pass the
second ring in the same way, and you will not succeed, as it is obstructed
by the wire of the first ring; but if you bring the first ring on again,
by reversing the process by which you took it off, viz., by putting it
up through the bow, and on to the end of it, you will then find that by
taking the first and second rings together, they will both draw off, lift
up, and drop through the bow. Having done this, try to pass the third ring
off, and you will not be able; because it is fastened on one side to its
own wire, which is within the bow, and on the other side to the second
ring, which is without the bow. Therefore, leaving the third ring for the
present, try the fourth ring, which is now at the end all but one, and
both of the wires which affect it being within the bow, you will draw it
off without obstruction; and, in doing this, you will have to slip the
third ring off, which will not drop through for the reasons before given;
so, having dropped the fourth ring through, you can only slip the third
ring on again. You will now comprehend that (with the exception of the
first ring) the only ring which can at any time be released is that which
happens to be second on the bow, at the right-hand end; because both the
wires which affect it being within the bow, there will be no impediment to
its dropping through. You have now the first and second rings released,
and the fourth also--the third still fixed; to release which we must make
it last but one on the bow, and to effect which pass the first and second
rings together through the bow, and on to it; then release the first ring
again by slipping it off and dropping it through, and the third ring will
stand as second on the bow, in its proper position for releasing, by
drawing the second and third off together, dropping the third through, and
slipping the second on again. Now to release the second, put the first up,
through and on the bow; then slip the two together off, raise them up,
and drop them through. The sixth will now stand second, consequently in
its proper place for releasing; therefore draw it toward the end, A, slip
the fifth off, then the sixth, and drop it through; after which replace
the fifth, as you cannot release it until it stands in the position of a
second ring; in order to effect this you must bring the first and second
rings together, through and on to the bow; then in order to get the third
on, slip the first off and down through the bow; then bring the third up,
through and on to the bow; then bring the first ring up and on again,
and, releasing the first and second together, bring the fourth through
and on to the bow, replacing the third; then bring the first and second
together on, drop the first off and through, then the third the same,
replace the first on the bow, take off the first and second together,
and the fifth will then stand second, as you desired; draw it toward the
end, slip it off and through, replace the fourth, bring the first and
second together up and on again, release the first, bring on the third,
passing the second ring on to the bow again, replace the first, in order
to release the first and second together; then bring the fourth toward
the end, slipping it off and through, replace the third, bring the first
and second together up and on again, release the first, then the third,
replacing the second, bring the first up and on, in order to release the
first and second together, which having done, your eighth ring will then
stand second, consequently you can release it, slipping the seventh on
again. Then to release the seventh, you must begin by putting the first
and second up and on together, and going through the movements in the same
succession as before, until you find you have only the tenth and ninth
on the bow; then slip the tenth off and through the bow, and replace the
ninth. This dropping of the tenth ring is the first effectual movement
toward getting the rings off, as all the changes you have gone through
were only to enable you to get at the tenth ring. You will then find that
you have only the ninth left on the bow, and you must not be discouraged
on learning, that in order to get that ring off, all the others to the
right hand must be put on again, beginning by putting the first and second
together, and working as before, until you find that the ninth stands as
second on the bow, at which time you can release it. You will then have
only the eighth left on the bow; you must again put on all the rings to
the right hand, beginning by putting up the first and second together,
till you find the eighth standing as second on the bow, or in its proper
position for releasing; and so you proceed until you find all the rings
finally released. As you commence your operations with all the rings
ready fixed on the bow, you will release the tenth ring in one hundred
and seventy moves; but as you then have only the ninth on, and as it
is necessary to bring on again all the rings up to the ninth, in order
to release the ninth, and which requires fifteen moves more, you will,
consequently, release the ninth ring in two hundred and fifty-six moves;
and, for your encouragement, your labor will diminish, by one half, with
each following ring which is finally released. The eighth comes off in
one hundred and twenty-eight moves, the seventh in sixty-four moves, and
so on, until you arrive at the second and first rings, which come off
together, making six hundred and eighty-one moves, which are necessary to
take off all the rings. With the experience you will by this time have
acquired, it is only necessary to say, that to replace the rings, you
begin by putting up the first and second together, and follow precisely
the same system as before.
46. MOVING THE KNIGHT OVER ALL THE SQUARES ALTERNATELY.
[Illustration: EULER'S METHOD.]
The problem respecting the placing the knight on any given square, and
moving him from that square to any house on the board, has not been
thought unworthy the attention of the first mathematicians. Euler, Ozanam,
De Montmart, De Moivre, De Majron, and others, have all given methods by
which this feat might be accomplished. It was reserved, however, for the
present century to lay this down on a general plan; and the only English
writer who has noticed this is Mr. George Walker, in his _Treatise on
Chess_. The plan is this: Let the knight be placed on any square, and
move him from square to square, on the principle of always playing him to
that point, from which, in actual play, he would command the fewest other
squares; observing, that in reckoning the squares commanded by him you
must omit such as he has already covered. If, too, there are two squares,
on both of which his powers would be equal, you may move him to either.
Try this on the board, with some counters or wafers, placing one on
every square; and, when you clearly understand it, you may astonish your
friends by inviting them to station the knight on any square they like,
and engaging to play him, from that square, over the remaining sixty-three
in sixty-three moves. When the automaton Chessplayer was last exhibited
in England, this was made part of the wonders he accomplished, though as
the above plan was not then known here, he could not adopt it, but used
something like the method laid down by Euler, and which we subjoin.
Our young Chess-players must remember that it does not matter on which
square the knight is placed at starting; as, by acquiring the plan by
heart, which is soon done, he can play him over all the squares from any
given point, his last square being at the distance of a knight's move from
his first. It is obvious that this route may be varied many ways, and we
have often amused ourselves by trying to work it on a slate.
ANOTHER METHOD.
The problem of the knight's covering successively each square of
the board, has, in all ages, attracted the attention of the first
mathematicians; it is only lately, however, that this very ingenious
system for performing the feat without seeing the board, has been invented
by an Edinburgh gentleman. We well recollect the surprise occasioned
among chess-amateurs when it was first performed; indeed it was generally
considered a greater mental effort than that of playing three games of
chess at the same time, without seeing the board.
The general rule for moving the Knight upon all the squares of the board,
is to commence by moving him to that square which commands the fewest
points of attack, and by continuing this principle he will occupy all
the squares in rotation, observing, that if on any two or more squares
his power would be equal, he may be placed indifferently on either
of such squares. Thus we see, that there are different routes which
the Knight-errant may take in his progress over all the board; still,
whichever of these routes for covering the sixty-four squares may be
adapted, each move forms, if we may so express ourselves, a link in an
endless chain, so that whatever square we start from, by taking one known
route, we are sure to arrive at a square, the last link of the chain,
a Knight's move distant from the square of our departure. Consequently,
if any person could commit to memory the consecutive moves of any one
route over the board, he would be able to start from any one square in
that route, in the same manner that any of us, if required to mention the
numerals up to sixty-four, could as easily start at thirty and end at
twenty-nine, as if we started at one and ended at sixty-four.
+------+------+------+------+------+------+------+------+
| | | | | | | | |
| Met. | Let. | Ket. | Het. | Get. | Fet. | Det. | Bet. |
+------+------+------+------+------+------+------+------+
| | | | | | | | |
| Men. | Len. | Ken. | Hen. | Gen. | Fen. | Den. | Ben. |
+------+------+------+------+------+------+------+------+
| | | | | | | | |
| Mix. | Lix. | Kix. | Hix. | Gix. | Fix. | Dix. | Bix. |
+------+------+------+------+------+------+------+------+
| | | | | | | | |
| Miv. | Liv. | Kiv. | Hiv. | Giv. | Fiv. | Div. | Biv. |
+------+------+------+------+------+------+------+------+
| | | | | | | | |
| Mor. | Lor. | Kor. | Hor. | Gor. | For. | Dor. | Bor. |
+------+------+------+------+------+------+------+------+
| | | | | | | | |
| Mee. | Lee. | Kee. | Hee. | Gee. | Fee. | Dee. | Bee. |
+------+------+------+------+------+------+------+------+
| | | | | | | | |
| Moo. | Loo. | Koo. | Hoo. | Goo. | Foo. | Doo. | Boo. |
+------+------+------+------+------+------+------+------+
| | | | | | | | |
| Mun. | Lun. | Kun. | Hun. | Gun. | Fun. | Dan. | Bun. |
+------+------+------+------+------+------+------+------+
M L K H G F D B
These considerations greatly reduce the apparent impossibility of
performing the feat; but the reader will exclaim, "What an immense
undertaking it would be, to commit to memory the moves forming a Knight's
route over the sixty-four squares!" and we reply, "Certainly it would be,
if we used the language of Chess to designate the squares;" and herein
lies the beauty of the invention. A set of names, whose application can be
understood at a glance, are invented for the squares, and the performer
of the feat, having learned a route of the Knight, expressed by these
invented names, thinks in the new language which he directs the moves in
the terms of chess--just as many of us _think_ in English, when we are
writing or speaking French.
The diagram given above represents the chess-board; the distinction of
white and black squares is not necessary for our purpose. The files,
commencing from the right hand are distinguished by the consonants in
alphabetical succession (C and J are, for obvious reasons, omitted.)
Thus, the King's rook's file is known as B, the King's Knight's as D,
the King's Bishops as F, the King's as G, the Queen's as H, the Queen's
Bishop's as K, the Queen's Knight's as L, and the Queen's Rook's as M.
This is all that has to be learned, in this system of Chess notation; for
the lines of squares tell their own numbers--one being _un_, two _oo_,
three _ee_, four _or_, six _ix_, seven _en_, eight _et_--being, in fact,
the terminal sounds of the first eight numerals. Bun being B _one_, or
King's Rook's square; Gix, G _six_, or King's sixth square. We consider
it quite unnecessary to say another word in explanation of this system;
its ingenious simplicity causes it to be understood and learned at a
glance. All that is required now is, to select a Knight's route over all
the squares of the board, and commit it to memory, not in the complicated
terms of Chess, but in these simple equivalents. Suppose we start from the
Queen's Knights seventh square, _len_, the route will be as follows:
Len het fen bet. Dix bor doo gun
Koo mun lee kun. Moo kee goo dun.
Bee div ben fet. Hen let mix lor.
Hee kiv gor hix. Liv men ket gen.
Kix giv fee hor. Gix for hiv gee.
Fiv den biv dee. Bun foo hun loo.
Mor lix met ken. Get fix det bix.
Dor boo fun hoo. Lun mee kor miv
The only trouble is to commit this cabalistical-looking table to memory,
which may be all accomplished in half an hour; the process will be greatly
facilitated by the learner frequently playing the route over on the
chess-board. He will be amply rewarded by the astonishment he will cause
to the _natives_ of his locality, who may have the great misfortune of
being unacquainted with our book's enlightening pages; and, if not quite
a first-rate player, he will acquire an intimate knowledge of the peculiar
powers and perplexing peregrinations of the eccentric _Caballeros_, who
"----fiery coursers guide
With headlong speed throng wars empurpled tide;
Alert and brave they spring amidst the fight,
From white to black, from black to candid white."
[Illustration]
ANOTHER METHOD.
Let Black Queen's Rook's Square count 1, (as in the diagram,) Black King's
Rook 8, and count all the other Squares in the same way from 9 to 64.
Place the Knight upon Black King's Rook's Square, 8, and move as follows:
23, 40, 55, 61, 51, 57, 42, 25, 10, 4, 14, 24, 39, 56, 62, 52, 58, 41, 26,
9, 3, 13, 7, 22, 32, 47, 64, 54, 60, 50, 33, 18, 1, 11, 5, 15, 21, 6, 16,
31, 48, 63, 53, 59, 49, 34, 17, 2, 12, 27, 44, 38, 28, 43, 37, 20, 35, 45,
30, 36, 18, 29, and 46. It may be well to chalk the figures on the board,
as a guide, until the feat is well understood.
47. ROSAMOND'S BOWER.
The subjoined cut represents, it is said, the Maze at Woodstock, in
which King Henry placed Fair Rosamond to protect her from the Queen. It
certainly is a most ingenious contrivance, and may be made productive of
much amusement. The puzzle consists in getting, from one of the numerous
outlets, to the bower in the center, without crossing any of the lines.
ROSAMOND'S BOWER.
[Illustration]
48. A MAZE OR LABYRINTH.
[Illustration]