Chapter V: Hand Shadows and how to work them. Illustrated (4)

Another finds in _K_ the key, as that letter with _no ar_ is alone in _ark_. With much ingenuity he shows that the last line calls for a second letter, and that the letters _K_ and _G_ can be traced throughout almost all Hallam’s “lights;” _Kilogram_ being nearly 3 lbs., and _Knot_ a mile; while either _K.G._ (Knight of the Garter) or _King_ would fit the final line.

7. The lines become “rank treason” if the corresponding lines of the two stanzas are read together, thus:--

The pomps of Courts and pride of Kings
I fain would banish far from hence,

and so on throughout.

8. A pair of skates.

9. A shadow.

10. A chair.

11. The changes that are rung are one, eno, Noe, neo, eon, on, none.

12. Cares, caress.

13. Echo.

14. Strike.

15. A pair of spurs.

16. A.D.A.M.; Adam; a dam; Adam; a damson; a dam.

17. The CID, the Castilian hero whose fame was at its height in the middle of the eleventh century.

18. A sigh.

19. Coxcomb.

20. Jack and Jill.

21. A man’s felt hat.

22. Measurable.

23. Chair, char, arch.

24. Sala (G.A.S.), which reversed is _alas_.

25. Page, (p)age.

26. C (sea), A (hay), T (tea).

27. A BROKEN TALE

The deil jumped over the clouds so high
That he bounded almost right over the sky.
Over gates and fields, and under the trees
He dodged, with his tail dragging over all these,
But, alas! made a terrible blunder,
For a twist in his tail hooked under a rail,
And broke that appendage asunder.

28. Yesterday. _Most_ excludes Adam, and _ter_ is half of _terror_.

29. Donkey.

30. Mental, lament, mantle.

31. His heels.

32. Tares, tears, a rest.

33. Connecticut.

34. Grate, rate, rat, ate.

35. Mary, in fanciful mood, on her thirty-sixth birthday, decorated her pincushion thus--XXXVI.

36. Opinionist.

37. Violin (LVII + on).

38. Trout (tr--out).

39. Post--stop.

40. A pair of scissors in a case.

41. Dog.

42. Mainland.

43. Changed.

44. The name of the Russian nobleman’s third son, the boy who went to sea, was Yvan. As the name of the eldest, Rab, who became a lawyer, was Bar reversed, and that of the soldier son Mary was Army as an anagram, so Yvan’s name resolves itself into Navy, his profession.

45. VIVID.

46. Nothing.

47. London.

48. Rock, cork.

49. Place, lace, ace, lac.

50. a, e, i, o, u, y.

51. The solution of the enigma which begins:--

“Twice six is six, and so
Six is but three;
Three is just five you know,
What can we be?”

is the number of letters of the alphabet used in spelling a number. Thus twice six, or _twelve_, is composed of six letters, and so on.

52. A button.

53. LEVEL--MADAM.

54. An egg.

55. Vague.

56.

A headless man had a letter to write,
(The letter O, i.e. _nothing_.)
He who read it had lost his sight,
(He read _nothing_.)
The dumb repeated it word for word,
(He said _nothing_.)
And deaf was he who listened and heard.
(He heard _nothing_.)

57. Highway.

58. A set of false teeth.

59. The “fearful fate” enigma is slaughter; cut off its head and we have laughter; lop off its shoulders and we find aught.

60. Speculation--peculations.

61. The word “united” is “of fellowship the token,” and the requirement “reverse it, and the bond is broken” refers only to the two central letters. When this is reversed the word “untied” is formed.

62. Average.

63. German--manger.

64. Corkscrew.

65. _Tar_ is transformed by _Art_, and as a sailor is fond of port, and blisters in the sun. When it turns to run it becomes _Rat_, and when it doubles it is _Tartar_, and is caught.

66.

A man with one eye two plums must have seen,
One perfectly ripe, the other quite green.
The former he took, and ate it with pleasure,
The other he left to ripen at leisure.

67. A widower who has lost two wives.

68. The grape-vine on the Marquis of Breadalbane’s estate, Killin, N.B., which bears more than 5000 bunches of grapes, of which only 500, properly thinned out, are allowed to mature, so that the fewer and smaller bunches bear finer fruit.

69. Poe, poet, poetry.

70. Theatres. The articles _the_ and _a_ lead on to the other four letters _tres_, and these form the word _rest_, if the _t_ is transferred to the end.

71. Scold, cold, old.

72. Justice, (_just_--_ice_).

73. A shadow.

74. VI., IV., I.

75. The letter I.

76. The letter V.

77. An army.

78. _A rich table_; _chair_, _table_; _charitable_.

79. High-low.

80. Orange, pear, date, banana, peach, plum, lime, lemon, mango, apple.

81. Innuendo.

82. Snipe, of which _pines_ is an exact anagram.

83.

None can locate the subject of my riddle,
For all the world would seek its place in vain,
Cut it asunder almost in the middle,
And in our very midst its place is plain

is solved by _nowhere_, _now here_.

CHARADES

1. Good-night (knight).

2. Grandson.

3. Oyster.

4. Stay-lace.

5. Ann--ounce.

6. VOID, OVID.

7. Disconsolate (disc--on--so--late).

8. Ginger--Nigger. (G.E.R. Great Eastern Railway).

9. Honesty (hone, below the razor).

10. Nutmeg.

11. Waterloo.

12. Whether (whet--her).

13. Mendicant (mend I can’t).

14. Campbell.

15. Foxglove.

16. Anglesea.

17. Shewed.

18. Sparrow, often a gutter percher!

19. Dishonest (dish--one--st).

20. Dogmatism.

21. Anthem.

22. Gigantic (gig--antic).

23. Toad (_ad_ is Latin for _to_).

24. Cineraria (sinner--area).

25. Ignis--fatuus, or Will-o’-the-wisp (ignis, fire--fatuus, a fool).

26. Isis (sis in Latin, _thou mayest be_).

27. Capacity.

28. Scarcity.

29. Pardon.

30. Humbug.

31. Ramrod.

32. Dumpling.

33. Into.

34. Herring.

35. Dublin (bud--nil).

36. Peerless.

37. Beatrice.

38. Beam--_be_ is half of the word _verb_, _am_ is half of _same_, and _be_ and _am_ are similar in sense.

39. Pulpit.

40. Spare--rib.

41. Usher.

42. The ship _Carmania_.

43. Candid.

44. Husbandman.

45. Hamlet.

46. Handcuff.

47. Sinecure.

48. Infancy.

49. Teachest.

50. Hippodrome.

51. Invalid.

52. Woman.

53. Kensington.

54. Benjamin.

55. Stipendiary.

56. Wonder.

57. Cabin.

58. Falstaff.

59. Periwinkle.

60. Nameless.

61. Fourscore.

62. Hatred.

63. Catsup.

64. Molestation.

65. Omen.

66. Isinglass.

67. Muffin.

68. Footman.

69. Sparrow-grass.

70. Matchless.

71. Planted.

72. Toast-rack.

73. Half-and-half, if properly punctuated.

RIDDLES AND CONUNDRUMS

1. Washerwoman.

2.

“Call me an uncle, then you speak me fair,
Call me an _uncle_-_an_ uncle if you dare!”

3. Pluck the goose.

4. Also.

5. A lawsuit.

6. Because they are bargains.

7. A pair of shoes.

8. Because whenever he goes out he can put his portmanteaux (Portman toes) into his boots.

9. FIVE.

10. Rail--liar.

11. Because it slopes with a flap!

12. In California they eat all the peaches they can, and can all they can’t!

13. The utmost effort ever made by a piebald (or by any) horse at a high jump is _four feet from the ground_!

14. Insatiate (in--sat--I--ate).

The clever couplet--

Under my first my second stood.
That’s your riddle: mine’s as good!

was intended to point out that the enigma

In my first my second sat,
Then my third and fourth I ate

was _understood_, and to frame at the same time a fresh one of similar sort.

15. A gardener minds his peas, a billiard-marker his cues, a precise man his p’s and q’s, and a verger his keys and pews.

16. A man with one eye can see more than a man with two, for in addition to all else he can see the other man’s two eyes, which can only see his one.

17. When you ask a policeman what o’clock it is, you are like the Viceroy of India, because you are _as king for the time_.

18. “What does Y E S spell?” is the question to which “yes” is the only possible reply.

19. An umbrella.

20. London for many years was a wonderful place for sound, for you could laugh at 5 p.m. at Waterloo Junction, and by walking briskly across the river be in time for the late Echo at Charing Cross.

21. Because it may be smelt!

22. The full reading of “1s. 6d. me a bloater” is “Bob Tanner sent me a bloater.”

_Note._--If any solver should ask, “But where is the ‘sent’?” we reply, “The scent was in the bloater!”

23. The solution of the prime conundrum “Why is a moth flying round a candle like a garden gate?” is--Because if it keeps on it singes its wings (its hinges it swings).

24. (Twe)lve--twe(nty) = twenty.

25. Because it would be my newt (minute).

26. The steps by which, in paying my debt to a lawyer, a threepenny piece swells to the needed six and eightpence are these:--

Three pence is one and two pence;
One and two pence is fourteen pence;
Fourteen pence is six and eight pence!

27. When the Vickers Maxim (vicar smacks him).

28. Children should go to bed soon after tea because when “t” is taken away _night_ is _nigh_.

29. Scottish may be lighter than Irish men, for while Irishmen may be men of Cork, Scotsmen may be men of Ayr.

30. Because barbers do not cut hair any longer!

31. Colenso.

32. This is Archbishop Whately’s riddle, and a solution, suggested long after his offer of £50 had expired:--

When from the Ark’s capacious round
Mankind came forth in pairs,
Who was it that first heard the sound
Of boots upon the stairs?

To him who cons the matter o’er,
A little thought reveals,
He heard it first who went before
Two pairs of soles and eels!

33. If Moses was the son of Pharaoh’s daughter, _he_ was the daughter of Pharaoh’s son.

34. The word of three syllables which represents woman or man alternately by three contractions is heroine--hero--her--he.

35. Solution to-morrow!

36. Wholesome.

37. They were jolly well tired!

38. The stocks.

39. Because it makes a far--thing present.

40. If I were in the sun, and you were out of it, it would be a _sin_.

41. COLD.

42. Take _off_--_ice_.

43. Enduring.

44. Uncross the “t” of “a foot,” and it becomes “a fool.”

45. A rabbit can run into a square wood with sides that each measures a mile, keeping always in a straight line, _until it reaches the middle of the wood_, when it must begin to run out of it!

46. To-morrow.

47. Scar--bo--rough.

48.

Though I in time for lunch may be,
U cannot come till after T.

49. A wig.

50. Because _we_ cannot be _wed_ without it.

51. A spit.

52. Wit (double you--I--tea).

53. Holding up your hand you will see what you never have seen, never can see, and never will see--namely, the little finger as long as the finger next to it!

54. The Emperor of Russia issues manifestoes. An ill-shod beggar manifests toes without his shoes!

55. To show Walsham How a good bishop is made.

56. There was certainly a tribe of Man--asses.

57. L. s. d.

58. A pillow.

59. Abused (a--b--used).

60. A settler.

61. Because John Burns.

62. It looks round!

63. A minute.

64. A deaf and dumb man cannot tickle nine persons, because he can only gesticulate (just tickle eight!).

65. London always began with an _l_, and end always began with an _e_!

66. Season.

67. The new moon, for the full moon is much lighter.

68. Island (_la_ is the middle, _is_ is the beginning, _and_ is the end!).

69. Because! (_bee caws_).

70. The reading of the Dark Rebus

O
B =e= D

is--a little blackie in bed with nothing over him.

71. If a monkey is placed before a cross it at once gets to the top, for APE is then APEX.

72. The answer to this riddle, defined as “two heads and an application,” is _a kiss_.

73. The Latin expression of encouragement “macte” may be applied in its English equivalent _in-crease_ to a batsman when an umpire says of him “not out” after a risky run.

74. The place which answers to the description “Half an inch (ch) before the trees (elms), half a foot (fo), and half a yard (rd) after them leads us to an English town,” is _Chelmsford_.

75. The subject of the riddle, which none can locate, is _nowhere_. Cut asunder almost in the middle, it breaks into the opposite extreme, and becomes _now here_!

76. The two letters which in nine letters describe the position of one who has been left alone in his extremity are a _b_ and one _d_. _Abandoned._

77. Usher (us--her).

78. You can make a Maltese cross with less than twelve unbent and unbroken matches, by striking only one match and dropping it down his back. If the first fails, try another!

79. We may suppose that there were less vowels than we have now in the early days of _Noe_, when _u_ and _i_ were not there.

80. An orange (or--ange).

81. The moral taught to us by the old emblem of a weathercock in the shape of a fish on a church near Lewes is, “It is vain to aspire!”

82. FIDDLE.

83. The words “for the want of water we drank water, and if we had had water we should have drank wine,” were spoken by the crew of a vessel that could not cross the harbour bar for want of water, and who had no wine on board.

84.

The poor have two, the rich have none,
Millions have many, you have one,

is solved by O.

85. Money.

86. Had _I_ been in Stanley’s place when Marmion cried “On, Stanley, on!” the resulting word _on_-_i_-_on_ would have made the Scottish fray seem more like Irish stew.

87. The figure O.

88.

Let her be, or beat her,
Give her little ease;
Then in safety seat her
All among the bees,

is solved by _A Queen Bee_. The _Bee_ is made up of the letter _b_, in Greek called _beta_, and two little _e_s.

89. Its.

90. Inch--chin.

NUTS TO CRACK

1. CRAZY LOGIC

Can you prove that madman = madam is solved thus:--

A madman is a man beside himself. Therefore a madman = two men.

Madam is a woman. Woman is double you O man (w-o-man). Therefore madam = two men.

And as things which are equal to the same are equal to one another, therefore madman = madam.

Q. E. D.
(_Quite easily Done._)

2. A BIT OF BOTANY

The water-plant is the _Frogbit_, which floats and spreads on the surface of ponds and pools.

3. The six islands buried in the lines--

He set down the answer to that sum at random.

By bold policy Prussia became a leading power.

A great taste for mosaic has arisen lately.

The glad news was swiftly borne over England.

At dusk, year after year, the old man rambled home.

The children cried, hearing such dismal tales.

are Sumatra, Cyprus, Formosa, Borneo, Skye, Malta.

4. The seven geographical names “buried” in the sentence, “We could hide a light royal boat with a man or two; the skipper, though, came to a bad end,” are Deal, Troy, Witham, Esk, Perth, Baden, Aden.

5. The jumbled letter lines read thus:--

Let those who deal in mystic rhymes
This transposition trace;
And to _The Standard_ send betimes
Each letter in its place.

6.

Three little articles all in a line
Lead to a thousand, expressing,
If with another all these you combine,
What can be never a blessing--

is solved by ANATHEMA (an-a-the-M-a).

7.

Ask a policeman, possibly he knows
In uniformed array
If not, an added letter plainly shows
How little he can say--

is solved by adding n _to uniformed_--_uninformed_.

8. The Ruling letters in:--

We rule the world, we letters five,
We rule the world, we do!
And of our number three contrive
To rule the other two--

are B. U. T. (beauty), and Y. Z. (wise head).

9. Many might punctuate the sentence, “Maud like the pretty girl that she was went for a walk in the meadows” by merely putting a full stop at the end of it. But why not make a _dash after Maud_?

10. The answer by Echo to

What were they who paid three guineas
To hear a tune of Paganini’s

is _Pack o’ ninnies_!

11. The verse in which only five different letters are used is--

It is nineteen tennis nets,
Nine in tents in tints intense.
Ten sent in inset in sets,
See it, test it, it is sense!

12. The catch sentence: “If is is not is and is not is is what is it is not is and what is it is is not if is not is is?” becomes intelligible if it is punctuated thus: If “is” is not “is,” and “is not” is “is,” what is it “is not” is, and what is it “is” is not, if “is not” is “is?”

13. The words on the placard were PALE ALE, and these through the steps described become PA-LE AP-LE, APPLE.

14. The reading of “Time flies you cannot they pass at such irregular intervals,” is as though it ran “You cannot time flies, they pass at such irregular intervals.”

ROYAL MEMORIES

15. I was reminded of Queen Victoria as I entered the South Kensington Museum at _five minutes to one_, because I noticed that the hands of my watch were so placed as to represent a very perfect V.

When I left the building it was _twenty-five minutes and forty-five seconds to six_, and then the hands, with the help of the seconds hand which crossed it, formed a very perfect A, and so reminded me of Prince Albert.

16. The solution of

CCC
---
SAW

is “the season was backward.”

17. THE OLD LATIN LEGEND

+------------------+
| AMANS TAM ERAT |
| HI DESINT HERO |
|AD DIGITO UT MANDO|
+------------------+

reads off into excellent English thus:--

“A man’s tame rat hides in the road; dig it out man, do!”

18. The statement “I know that roseate hues preserve” does not imply that there is any curative virtue in rose-coloured rays, but asserts “I know that Rose ate Hugh’s preserve!”

19. The following exception was taken to Dr Fell’s diet for the sick of all sops:--

“Sure the doctor’s wits are failing,”
Cried a saucy wag.
“Allsopp’s ale the sick and ailing
To their bier will drag.”

20. The English dislocated sentence formed by these thirty-six letters:--

SAR BAB SAR BAB SAR BAB
SAR BAB SAR BAB SAR ARA

is, “A bar as a barb bars Barbara’s Barabbas.”

21. The Wiltshire farmer’s sentence--

“Igineyvartydreevriswutts”

when interpreted runs, “I gave him forty-three for his oats.”

22. Here is a tolerable rhyme to Chrysanthemum:--

Through gardens where appear
Beds of chrysanthemum,
We pass at eve to hear
Our choir their anthem hum.

23. This was, in brief, the pathetic tale of the three eggs--“_Two bad!_”

24. THE ANCIENT LEGEND

+--------------+
|Doun tooth ers|
| A sy |
| Ouw ould bed |
| One by |
+--------------+

reads thus:--“Do unto others as you would be done by.”

25. There were but six persons in the vault which contained two grandmothers and their two grand-daughters; two husbands and their two wives; two fathers and their two daughters; two mothers and their two sons; two maidens and their two mothers; two sisters and their two brothers. Two widows had each one son, and each married the son of the other, and had a daughter by the marriage.

26. The supposed charm--

ground
turn evil star

given by the wise woman to a nervous couple, to counteract their evil star, and account for mysterious noises, is merely “Rats live underground,” _turn_ being a direction to the solver.

27. The word composed of five varied vowels of foreign sound, with but one consonant between them, is oiseau, the French for bird. The three letters which flow in four are eau, water, which flows in the River Oise, and the other trio spell oie, a goose, which is found therein.

28. The Paradox--

What in his mind no man can find
Four symbols will display;
But only one remains behind
If one we take away--

is solved by _Bone_.

29. The barber who had placed in his window the notice--

“What do you think
I will shave you for nothing and give you a drink”

explained, to the man who expected a free shave and a cool drink, that the interpretation was really this:--“What? Do you think I will shave you for nothing, and give you a drink?”

30. The curious Latin label--

+-------------------------+
| G E N U I N E J A M |
| A |
| I C A R U M. |
+-------------------------+

has no reference to Icarus, or to flying machines. Its proper place was on a cask of “Genuine Jamaica Rum.”

31. The puzzle word is ipecacuanha.

32.

Johnson’s cat went up a tree,
Which was sixty feet and three;
Every day she climbed eleven,
Every night she came down seven.
Tell me, if she did not drop,
When her paws would touch the top--

is solved thus:--As each day and night the cat climbed up eleven feet, and came down seven, the daily upward gain was four feet, and thirteen days would bring her fifty-two feet up the tree. Then on the fourteenth day she mounted the remaining eleven feet, and was at the top, so that no coming down seven feet is to be taken into account, and she attains her place _in fourteen days_.

33.

A third of six behind them fix,
A third of six before;
Thus makes two nines, when all combines,
Exactly fifty-four--

is solved:--

IX NINE (the two nines.)
(S is a third of six) SIX NINES = 54.

34. To bridge the moat, or space between the two squares which one match cannot span, place one match across one of the corners of the outer square, and the other from this to the inner square.

35.

We start when the ninth hour is past,
Then there’s an end of you.
A vengeful goddess shows at last
What Antifat will do--

is solved by _attenuate_ (at ten-u-Ate, goddess of vengeance).

36. Mrs P.W. had only one guest to provide for. Her husband had invited his father’s brother-in-law, Jones, who was his brother’s father-in-law, because Mr P.W.’s brother had married Jones’ daughter, and his father-in-law’s brother, because he had himself married Jones’ niece, and also his brother-in-law’s father, as Mr P.W.’s sister married Jones’ son.

37. This sharp customer started with _fivepence farthing_, and gradually extracted from the landlord’s pocket a shilling and three farthings towards the eighteenpence which he spent in refreshments.

38. To form four triangles of equal size with six similar matches, place three of them in a triangle on the table, and hold or balance the other three above these, so as to form the skeleton of a pyramid.

39. The following couplet solves this question:--

Forty-five-years I had seen
When my bride was but fifteen

40. The lad gave tenpence each to a grandfather, his son, and his grandson.

41. Nell’s reply to Tom, when he said, with a yawn, “I wish we could play lawn-tennis!” “Odioso ni mus rem. Moto ima os illud nam,” was not Latin, but good sound English. Read each word in its order _backwards_, and you have-- “Oh! so do I in summer. Oh, Tom! am I so dull, I man?”

42. The policeman who was looking up the road for motor-car scorchers was able to see that his mate, who was looking down the road, was smiling, because they stood face to face.

43.

Twenty-seven with three nines
You and I can score;
Anyone on other lines
Can extend them more.
Who can write them to be seen
Equal only to sixteen?--

is solved thus:--Two of the three nines are reversed, and then

96
-- = 16.
6

44. The trying sentence, “that that is is that that is not is not is not that it it is,” is cleared thus by proper punctuation:--That that is, is; that that is not, is not. Is not that it? It is.

45. A L L O is “Nothing after all.”

46. The proverb with missing consonants is--Give a dog a bad name and hang him.

47. If to the thirteen upright strokes--

| | | | | | | | | | | | |

thirteen more are added, the word HOTTENTOT may be formed.

48. A coroner could, after signing his name, write down his official position with _c or one r_.

=PART II.=

CONTENTS

PAGE

OPTICAL ILLUSIONS II-1

FREAKS OF FIGURES II-20

CHESS CAMEOS II-26

SCIENCE AT PLAY II-58

CURIOUS CALCULATIONS II-114

WORD AND LETTER PUZZLES II-147

SOLUTIONS II-167

OPTICAL ILLUSIONS

No. I.--SWALLOWED!

Take a small card and place it on its longer edge upon the dotted line. Now set the picture in a good light on the table, and let your head drop gradually towards the card until you almost touch it with your nose. You will see the bird fly into the jaws of the snake!

AMUSING PROBLEMS

THE CARPENTER’S PUZZLE

1. A carpenter was called in to mend a hole in a wooden floor. The gap was two feet wide, and twelve feet long, while the only board at hand was three feet wide, and eight feet long.

+----------------+
| Fig. 1. |
| |
| |
+----------------+

+------------------------+
| Fig. 2. |
| |
+------------------------+

This had been put aside as useless, but, on catching sight of it, the carpenter ran his rule over it and said that he could make a perfect fit, and cover all the hole by cutting the board into two pieces. How did he do this?

No. II.--AN ILLUSION OF ROTATION

This most interesting optical illusion was devised by Professor Thompson some years ago:--

If the illustration is moved by hand in a small circle on the level, with such motion as is given in rinsing out a bowl, the circles of the larger diagram will seem to revolve in the direction in which the paper is moved, while the cogs of the smaller diagram will apparently turn slowly in the opposite direction.

No. III.--WHIRLING WHEELS

Here is another combination of the clever illusion of the whirling wheels.

If a rapid rotating motion is given to the diagram, each circle will seem to revolve, and the cog wheel in the centre will appear to move slowly round in the opposite direction.

GOLDEN PIPPINS

2. A man leaves an orchard of forty choice apple trees to his ten sons. On the first tree is one apple, on the second there are two, on the third three, and so on to the fortieth, on which there are forty.

Each son is to have four of the trees, and on them an equal number of the apples. How can they thus apportion the trees, and how many apples will each son have? Here is one way:--

1 2 3 4 5 6 7 8 9 10
20 19 18 17 16 15 14 13 12 11
21 22 23 24 25 26 27 28 29 30
40 39 38 37 36 35 34 33 32 31
-----------------------------
82 82 82 82 82 82 82 82 82 82

Can you find another perfect solution?

No. IV.--AN ILLUSION OF MOTION

We call very particular attention to this fascinating illustration of the fact that the mind and eye may receive and register false impressions under quite simple conditions:--

Hold this at rather more than reading distance, upright, and move it steadily up and down. The dark line will soon seem to slide up and down upon the perpendicular line. It will be better seen if drawn to pattern on a card.

No. V.--ARE THEY PARALLEL?

As the eye falls upon the principal lines of this interesting diagram, an immediate impression is formed that they are not parallel.

This, however, is a most curious illusion, created in the mind entirely by the short sloping lines, as is found at once by the simple test of measurement.

AN AWKWARD FIX

3. With no knowledge of the surrounding district, I was making my way to a distant town through country roads, guided by the successive sign-posts that were provided.

Coming presently to four cross-roads I found to my dismay that some one had in mischief uprooted the sign-post and thrown it into the ditch. In this perplexing fix how could I find my way? A bright thought struck me. What was it?

LINKED SWEETNESS LONG DRAWN OUT

4. As I stood on the platform at a quiet country station, an engine, coming along from my left at thirty miles an hour, began to whistle when still a mile away from me. The shrill sound continued until the engine had passed a mile and a half to my right. For how long was I hearing its whistle?

No. VI.--ILLUSION OF LENGTH

In this curious optical illusion the lines are exactly equal in length.

\ /
\ /
>--------------------<
/ \
/ \

/ \
/ \
<-------------------->
\ /
\ /

The eye is misled by the effect which the lines drawn outward and inward at their ends produce upon the mind and sight.

ELASTIC QUARTERS

5.

In room marked A two men were placed,
A third he lodged in B;
The fourth to C was next assigned,
The fifth was sent to D.
In E the sixth was tucked away,
F held the seventh man;
For eighth and ninth were G and H,
Then back to A he ran.
Thence taking one, the tenth and last,
He lodged him safe in I;
Thus in nine rooms ten men found place,
Now can you tell me why?

EXCLUDED DAYS

6. Are there any particular days of the week with which no new century can begin?

No. VII.--ILLUSION OF HEIGHT

These straight lines, at right angles to each other, are, though they do not seem to be, exactly equal in length.

This and similar illusions are probably due to the variation of the vague mental standard which we unconsciously employ, and to the fact that the mind cannot form and adhere to a definite scale of measurement.

DRIVING POWER

7. Why has a spliced cricket bat such good driving power? and why is the “follow through” of the head of a golf club so telling in a driving stroke?

THE BUSY BOOKWORM

8. On my bookshelf in proper order stand two volumes. Each is two inches thick over all, and each cover is an eighth of an inch in thickness. How far would a bookworm have to bore in order to penetrate from the first page of Vol. I. to the last page of Vol. II.?

No. VIII.--ILLUSION OF DIRECTION

Can you decide at a glance which of the two lines below the thick band is a continuation of the line above it?

Make up your mind quickly, and then test your decision with a straight edge.

A TERRIBLE TUMBLE

9. From what height must a man fall out of an airship--screaming as he goes overboard--so as to reach the earth before the sound of his cry?

_N.B._--Resistance of the air, and the acoustical fact that sound will not travel from a rare to a dense atmosphere, are to be disregarded.

IN A PREDICAMENT

10. Imagine a man on a perfectly smooth table surface of considerable size, in a vacuum, where there is no outside force to move him, and there is no friction. He may raise himself up and down, slide his feet about, double himself up, wave his arms, but his centre of gravity will be always vertically above the same point of the surface.

How could he escape from this predicament, if it was a possible one?

No. IX.--THINGS ARE NOT WHAT THEY SEEM

It is difficult, even after measurement, to believe that these figures are of the same size.

But they will stand the test of measurement.

A CLIMBING MONKEY

11. A rope passes over a single fixed pulley. A monkey clings to one end of the rope, and on the other end hangs a weight exactly as heavy as the monkey. The monkey presently starts to climb up the rope. Will he succeed?

GAINING GROUND

12. Seeing that the tension on a pair of traces tends as much to pull the horse backward as it does to pull the carriage forward, why do the traces move on at all?

No. X.--THE SHIFTING BRICK

A very curious and interesting form of optical illusion is well illustrated by what may be called “the shifting brick.”

The central brick, drawn to show all its edges, as though it were made of glass, will assume the form indicated by one or other of the smaller bricks at its right and left, according to the way in which the eyes accommodate themselves for the moment to one pattern or to the other. If you do not see this at first, look steadily for awhile at the pattern you desire.

ASK A CYCLIST

13. Why does a rubber tyre leave a double rut in dust, and a single one in mud?

TODHUNTER’S UNIQUE PUZZLE PROBLEM

14. If two cats, on opposite sides of a sharply sloping roof, are on the point of slipping off, which will hold on the longest?

No. XI.--AN ILLUSION WITH COINS

If you place four coins in the positions shown at the top of this diagram, and attempt, or challenge some one to attempt, without any measuring, to move the single coin down in a straight line until the spaces from C to D on either side exactly equal the distance from A to B--

It must drop as far as is shown here, which seems to the unaided eye to be too far.

This excellent illusion can be shown as an after-dinner trick with four napkin-rings.

No. XII.--THE FICKLE BARREL

Here is another excellent optical illusion. Look attentively at the diagram below, and notice in which direction you apparently look into it, as though it were an open cask.

Now shake the paper, or move it slightly, and you will find, more often than not, that you seem to see into it in quite the opposite direction.

HEADS I WIN!

15. I hold a penny level between my finger and thumb, and presently let it fall from the thumb by withdrawing my finger. It makes exactly a half-turn in falling through the first foot. If it starts “heads,” how far must it fall to bring it “heads” to the floor?

HE DID IT!

16. “They call these safety matches,” said Funnyboy at his club one day, “and say that they strike only on the box. Don’t believe it! I can strike them quite easily on my boot.”

No sooner said than done. He took out a match, struck it on his boot, and--phiz!--it was instantly alight. The box was handed round, and match after match was struck by the bystanders on their boots, but not one of them could succeed.

“You don’t give the magic touch,” said Funnyboy, as he gaily struck another. How did he do it?

No. XIII.--A STRANGE OPTICAL ILLUSION

How many cubes can you see as you look at the large diagram? The two smaller ones should be looked at first alternately, and they will assist the eye to see at one time six, and at another time seven, very distinct cubes.

No. XIV.--A CIRCULAR ILLUSION

This curious optical illusion is not easily followed by eye to the finish of the several lines.

Each short line is, in fact, part of the circumference of a circle, and the circles when completed will be found to be accurately concentric. It would seem at first sight that the lines are taking courses which would eventually meet at some point common to them all.

A CYCLE SURPRISE

17. We commend this curious point to the special attention of cyclists:--

A bicycle is stationary, with one pedal at its lowest point. If this bicycle is lightly supported, and the bottom pedal is pulled backward, what will happen?

No. XV.--THE GHOST OF A COIN

A most remarkable optical illusion is produced by the blending of the dark and light converging rays of this diagram. Stand with your back to the light, hold the page, or better still, the diagram copied on a card, by the lower right-hand corner, give it a continuous revolving movement in either direction, and the visible ghost of a silver coin, sometimes as large as sixpence, sometimes as large as a shilling, will appear! Where can it come from?

ROUGH AND READY

18. A merchant has a large pair of scales, but he has lost his weights, and cannot at the moment replace them. A neighbour sends him six rough stones, assuring him that with them he can weigh any number of pounds, from 1 to 364. What did each stone weigh?

No. XVI.--A TAME GOOSE

Here is a pretty form of our first illusion:--

Place the edge of a card on the dotted line, look down upon it in a good light, and, as you drop your face till it almost touches the card, you will see the goose _move towards the sugar_ in the little maiden’s hand.

REJECTED ADDRESSES

19. A wheel is running along a level road, and a small clot of mud is thrown from the hindermost part of the rim. What happens to it? Does it ever renew its acquaintance with the wheel that has thus rejected it?

No. XVII.--ILLUSION OF LENGTH

Here is another method by which an optical illusion of length is very plainly shown:--

A B
+--------------+
/ \
/ \
/ \
/ \
+------------------------+

A B
+--------------+
\ /
\ /
\ /
\ /
+----+

Judged by appearances, the line A B in the larger figure is considerably longer than the line A B below it, but tested by measurement they are exactly equal.

THE CARELESS CARPENTER

20. A village carpenter undertook to make a cupboard door. When he began to put it in its place it was too big, so he took it back to his workshop to alter it. Unfortunately he now cut it too little. What could he do? He determined to cut it again, and it at once became a good fit. How was this done?

No. XVIII.--PERPENDICULAR LINES

Here is another excellent illustration that seeing is not always believing.

No one could suppose at first sight that these four lines are perfectly straight and parallel, but they will stand the test of a straight edge. The divergent rays distract the vision.

BY THE COMPASS

21. If from the North Pole you start sailing in a south-westerly direction, and keep a straight course for twenty miles, to what point of the compass must you steer to get back as quickly as possible to the Pole?

No. XIX.--ILLUSION OF PERSPECTIVE

The optical illusion in the picture which we reproduce is due to the defective drawing of the two men on the platform. In actual size upon the paper the further man looks much taller than the other.

Measurement, however, shows the figures to be exactly of a height. This illusion is due to the fact that the head of the further man is quite out of perspective. If he is about as tall as the other, and on level ground, both heads should be about on the same line. As drawn, he is, in fact, a monster more than eight feet high.

DICK IN A SWING

22. If Dick, who is five feet in height, stands bolt-upright in a swing, the ropes of which are twenty feet long, how much further in round numbers do his feet travel than his head in describing a semi-circle?

No. XX.--OUR BLIND SPOT

Here is an excellent and very simple illustration of a well-known optical curiosity:--

Hold this picture at arm’s length in the right hand, hold the left hand over the left eye, and draw the picture towards you gradually, looking always at the black cross with the right eye. The black disc will presently disappear, and then come into sight again as you continue to advance the paper.

A POSER

23. Can you name nine countries in Europe of which the initial letters are the same as the finals?

FREAKS OF FIGURES

A HANDY SHORT CUT

Here is a delightfully simple way in which market gardeners, or others who buy or sell weighty produce, can check their invoices for potatoes or what not.

Say, for example, that a consignment weighs 6 tons, 10 cwts., 1 qr. Then, since 20 cwts. are to a ton as 20s. are to a pound, and each quarter would answer on these lines to 3d., we can at once write down £6 10s. 3d., as the price at £1 the ton. On this sure basis any further calculation is easily made.

No. XXI.--THE PERSISTENCE OF VISION

Look steadily, in a good light, for thirty seconds at the cross in the eye of the pictured skull; then look up at the wall or ceiling, or look fixedly at a sheet of paper for another thirty seconds, when a ghost-like image of the skull will be developed.

NOT SO FAST!

A gardener, when he had planted 100 trees on a line at intervals of 10 yards, was able to walk from the first of these to the last in a few seconds, for they were set _on the circumference of a circle_!

No. XXII.--THE PERSISTENCE OF VISION

Here is another example of what is known as the persistence of vision:--

Look fixedly for some little time at this grotesque figure, then turn your eyes to the wall or ceiling, and you will in a few seconds see it appear in dark form upon a light ground.

A PUZZLE NUMBER

The sum of nine figures a number will make,
Of which just a third will remain
If fifty away from the whole you should take,
Thus turning a loss to a gain.

It needs something more than mere arithmetic to discover that the solution to this puzzle is XLV, the sum of the nine digits, for if the L is removed, XV, the third of XLV, remains.

No. XXIII.--ANOTHER PARALLEL FREAK

Here is another curious illusion:--

The four straight lines are perfectly parallel, but the contradictory herring-bones disturb the eye.

THE MAGIC OF FIGURES

If our penny had been current coin in the first year of the Christian era, and had been invested at compound interest at five per cent., it would have amounted in 1905 to more than £132,010,000,000,000,000,000,000,000,000,000,000,000.

This gigantic sum would afford an income of £101,890,000,000,000,000,000 every second to every man, woman, and child in the world, if we take its population to be 1,483,000,000 souls!

Absurdly small in contrast to these startling figures is the modest eight shillings which the same penny would have yielded in the same time at simple interest.

No. XXIV.--ILLUSION OF LENGTH

Here in another form is shown the illusion of length.

At first sight it seems that the two upright lines are distinctly longer than the line that slopes, but it is not so.

WHAT IS YOUR AGE?

Here is a neat method of discovering the age of a person older than yourself:--

Subtract your own age from 99. Ask your friend to add this remainder to his age, and then to remove the first figure and add it to the last, telling you the result. This will always be the difference of your ages. Thus, if you are 22, and he is 35, 99 - 22 = 77. Then 35 + 77 = 112. The next process turns this into 13, which, added to your age, gives his age, 35.

No. XXV.--THE HONEYCOMB ILLUSION

In this diagram one hundred and twenty-one circular spots are grouped in a diamond.

If we half close our eyes, and look at this through our eye-lashes, we find that it takes on the appearance of a section of honeycomb, with hexagonal cells.

MULTIPLICATION NO VEXATION

Here is a ready method for multiplying together any two numbers between 12 and 20.

Take one of the two numbers and add it to the unit digit of the other. Beneath the sum thus obtained, but one place to the right, put the product of the unit digits of the two original numbers.

The sum of these new numbers is the product of the numbers that were chosen. Thus:--

19 × 13. (19 + 3) = 22
(9 × 3) = 27
---
247

No. XXVI.--CHESS CAMEO

By Dr GOLD

_A Chess Joke_

BLACK
+---+---+---+---+---+---+---+---+
| |.b.| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| p |...| k |...| |.K.| |
+---+---+---+---+---+---+---+---+
| |.n.| |.P.| |...| |...|
+---+---+---+---+---+---+---+---+
|.P.| |...| p |...| |...| |
+---+---+---+---+---+---+---+---+
| |...| N |...| N |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| B |...| |...| |
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
WHITE

Black has made an illegal move. He must replace this, and move his king as the penalty. White then mates on the move.

[1]SHOT IN A PYRAMID

Here is a method for determining the total number of balls in a solid pyramid built up on a square base:--

Multiply the number of shot on one side of the base line by 2, add 3, multiply by the number on the base line, add 1, multiply again by the number on the base, and finally divide by 6. Thus, if the base line is 12--

12 × 2 + 3 = 27; 27 × 12 + 1 = 325; 325 × 12 = 3900; and 3900 ÷ 6 = 650, which is the required number.

[1] _N.B._--This title does not imply a tragedy.

No. XXVII.--CHESS CAMEO

By A. CYRIL PEARSON

_A Chess Puzzle_

BLACK
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |.p.| |...| |.p.| p |
+---+---+---+---+---+---+---+---+
| |.P.| |.P.| |.k.| |...|
+---+---+---+---+---+---+---+---+
|...| |.p.| K |.N.| P |...| |
+---+---+---+---+---+---+---+---+
| |...| |...| p |...| R |...|
+---+---+---+---+---+---+---+---+
|...| |...| |.N.| |...| |
+---+---+---+---+---+---+---+---+
| |.q.| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
WHITE

White might have given mate on the last move. White now to retract his move, and mate at once.

_Show by analysis the mating position._

No. XXVIII.--CHESS CAMEO

By J. G. CAMPBELL

_A very Clever Device_

BLACK
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| p |...| |...| |...| |
+---+---+---+---+---+---+---+---+
| |.P.| |.p.| |...| |...|
+---+---+---+---+---+---+---+---+
|...| K |...| p |...| |.B.| |
+---+---+---+---+---+---+---+---+
| P |...| |.P.| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |.p.| p |
+---+---+---+---+---+---+---+---+
| |.P.| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| K |...| |
+---+---+---+---+---+---+---+---+
WHITE

White to play and draw.

COMIC ARITHMETIC

“Now, boys,” said Dr Bulbous Roots to class, “you shall have a half-holiday if you prove in a novel way that 10 is an even number.”

Next morning, when the doctor came into school, he found this on the blackboard:--

SIX = 6
IX = 9
---------
By subtraction S = -3

SEVEN = 7
S = -3
------------
Therefore EVEN = 10

Q. E. D.
(_Quite easily done!_)

The half-holiday was won.

No. XXIX.--CHESS CAMEO

By E. B. COOK

_A Fine Example_

BLACK
+---+---+---+---+---+---+---+---+
| |.k.| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|.R.| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
| K |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
| |...| p |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
WHITE

White to play, and draw.

No. XXX.--CHESS CAMEO

By A. F. MACKENZIE

_A Prize Problem_

BLACK
+---+---+---+---+---+---+---+---+
| |...| |.r.| |...| |.b.|
+---+---+---+---+---+---+---+---+
|.p.| |...| |...| |.P.| |
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |.q.|
+---+---+---+---+---+---+---+---+
|.N.| b |...| |...| |...| K |
+---+---+---+---+---+---+---+---+
| p |.P.| |.k.| P |...| R |...|
+---+---+---+---+---+---+---+---+
|...| |.p.| P |.p.| |.B.| R |
+---+---+---+---+---+---+---+---+
| |...| n |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |.N.| |...| |
+---+---+---+---+---+---+---+---+
WHITE

White to play, and mate in two moves.

There are twelve variations in this beautiful problem.

MAGIC MULTIPLICATION

It will interest all who study short cuts and contrivances to know that a novice at arithmetic who has mastered simple addition, and can multiply or divide by 2, but by no higher numbers, can, by using all these methods, multiply any two numbers together easily and accurately.

This is how it is done:--

Write down the numbers, say 53 and 21, divide one of them by 2 as often as possible, omitting remainders, and multiply the other by 2 the same number of times; set these down side by side, as in the instance given below, and wherever there is an _even_ number on the division side, strike out the corresponding number on the multiplication side. Add up what remains on that side, and the sum is done. Thus:--

53 21
26 (42)
13 84
6 (168)
3 336
1 672
------
1113

which is 53 multiplied by 21.

No. XXXI.--CHESS CAMEO

BY A. W. GALITZKY

_A Prize Problem_

BLACK
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
| |.B.| q |.n.| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| p |
+---+---+---+---+---+---+---+---+
| |...| N |...| R |...| P |.P.|
+---+---+---+---+---+---+---+---+
|...| |...| |...| k |...| |
+---+---+---+---+---+---+---+---+
| |...| b |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| n |...| |...| |.K.| |
+---+---+---+---+---+---+---+---+
WHITE

White to play, and mate in two moves.

No. XXXII.--CHESS CAMEO

BY S. LOYD

BLACK
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
| |.N.| |.p.| |.p.| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |.p.| |...| |
+---+---+---+---+---+---+---+---+
| |...| |.k.| N |.q.| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |.n.| |...| |
+---+---+---+---+---+---+---+---+
| |.K.| |...| |.B.| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
WHITE

White to play, and mate in two moves.

No. XXXIII.--CHESS CAMEO

BY B. G. LAWS

_A Prize Problem_

BLACK
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |.q.| |
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| n |.p.| |.p.| p |...| k |
+---+---+---+---+---+---+---+---+
| N |...| P |...| k |.b.| |.R.|
+---+---+---+---+---+---+---+---+
|...| n |...| |.B.| |...| R |
+---+---+---+---+---+---+---+---+
| |...| |.r.| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
WHITE

White to play, and mate in two moves.

PERFECT NUMBERS

The following particulars about a very rare property of numbers will be new and interesting to many of our readers:--

The number 6 can only be divided without remainder by 1, 2, and 3, excluding 6 itself. The sum of 1 + 2 + 3 is 6. The only exact divisors of 28 are 1, 2, 4, 7, and 14, and the sum of these is 28; 6 and 28 are therefore known as perfect numbers.

The only other known numbers which fulfil these conditions are 496; 8128; 33,550,336; 8,589,869,056; 137,438,691,328; and

2,305,843,008,139,952,128.

This most remarkable rarity of perfect numbers is a symbol of their perfection.

No. XXXIV.--CHESS CAMEO

BY EMIL HOFFMANN

BLACK
+---+---+---+---+---+---+---+---+
| |...| |...| q |...| |.B.|
+---+---+---+---+---+---+---+---+
|.R.| |...| |...| |.Q.| n |
+---+---+---+---+---+---+---+---+
| |...| |...| k |...| |...|
+---+---+---+---+---+---+---+---+
|.b.| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
| |...| |.R.| |...| |...|
+---+---+---+---+---+---+---+---+
|.p.| |...| B |...| n |...| b |
+---+---+---+---+---+---+---+---+
| K |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
WHITE

White to play, and mate in two moves. There are no less than twelve variations!

No. XXXV.--CHESS CAMEO

BY J. POSPICIL

_A Prize Problem_

BLACK
+---+---+---+---+---+---+---+---+
| |...| |...| |.N.| |...|
+---+---+---+---+---+---+---+---+
|...| N |...| |...| |...| p |
+---+---+---+---+---+---+---+---+
| |...| n |...| B |.p.| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |.k.| |...| |
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|.K.| |...| |...| P |...| |
+---+---+---+---+---+---+---+---+
| |...| |...| P |.n.| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |.Q.| |
+---+---+---+---+---+---+---+---+
WHITE

White to play, and mate in two moves.

AMICABLE NUMBERS

Somewhat akin to perfect numbers are what are known as amicable numbers, of which there is a still smaller quantity in the realm of numbers.

The number 220 can be divided without remainder only by 1, 2, 4, 5, 10, 11, 22, 44, 55, and 110, and the sum of these divisors is 284. The only divisors of 284 are 1, 2, 4, 71, and 142, and the sum of these is 220.

The only other pairs of numbers which fulfil this curious mutual condition, that the sum of the divisors of each number exactly equals the other number, are 17,296 with 18,416, and 9,363,584 with 9,437,056. No other numbers, at least below ten millions, are in this way “amicable.”

No. XXXVI.--CHESS CAMEO

BY H. J. C. ANDREWS

_A Prize Problem_

BLACK
+---+---+---+---+---+---+---+---+
| |...| K |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |.Q.| |
+---+---+---+---+---+---+---+---+
| |.B.| |...| |...| |.R.|
+---+---+---+---+---+---+---+---+
|...| |...| k |.N.| |.b.| R |
+---+---+---+---+---+---+---+---+
| P |...| |...| |...| P |...|
+---+---+---+---+---+---+---+---+
|...| k |...| p |...| |...| |
+---+---+---+---+---+---+---+---+
| B |...| |.P.| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
WHITE

White to play, and mate in two moves.

No. XXXVII.--CHESS CAMEO

BY ALFRED DE MUSSET

_A Gem of the First Water_

BLACK
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| n |
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
| |...| |...| N |...| |.k.|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
| |...| |.N.| |...| |.K.|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |.R.| |
+---+---+---+---+---+---+---+---+
WHITE

White to play, and mate in three moves.

A SWARM OF ONES