Figure

How can you, in the simplest way, divide it into four equal and similar parts by four straight cuts?

Solution

49. GEESE TO MARKET

B drove a goodly flock of geese,
 And met with Farmer A;
 Said Farmer A, “How much apiece
 For this lot did you pay?”
 Said B, “I paid for all I drive
 Just six pounds and a crown,
 And I am selling all but five
 At the next market town.
 If fifteen pence a head I charge
 Beyond the price I paid.
 I shall secure a sum as large
 As he who sold all made.”

Solution

No. LXII

Can you draw twenty-two straight lines within this circle so that they divide it into four similar parts, each having three of the dots within its borders?

Circle

Each line must be at right angles to another.

Solution

50. A QUAINT CHARADE

When second held first
 For best or for worst,
 I thought myself happy to win her.
 But what could I say
 When the very next day
 She gave me the whole for my dinner?

Solution

No. LXIII

Triangle

Cut up this triangle into 5 parts,

Triangle

which can be reassembled to form this triangle.

Solution

No. LXIV.—ARITHMETICAL TRIANGLE

The peculiar series of numbers, as arranged in this triangular form, is said to have been perfected by Pascal.

1  
2 1  
3 3 1  
4 6 4 1  
5 10 10 5 1  
6 15 20 15 6 1  
7 21 35 35 21 7 1  
8 28 56 70 56 28 8 1

Image

It has the property of showing, without calculation, how many selections or combinations can be made at a time out of a larger number. Thus to find how many selections of 3 at a time can be made out of 8 we look for the third number on the horizontal row that commences with 8, and find the answer 56.

The series is formed thus: Set down the numbers 1, 2, 3, etc., as far as you please, in a vertical row. To the right of 2 place 1, add them together, and set 3 under the 1. Then add 3 to 3, and set the result below, and so on, always placing the sum of two numbers that are side by side below the one on the right.

No. LXV.—MULTIPLICATION NO VEXATION

This diagram shows an ancient and curious method of multiplication, which will be novel to most of our readers.

Multiplication

In this instance 534 is multiplied by 342. Draw a square of nine cells with diagonals, fill the three top cells, as is shown, by multiplying the 5 by the 3, the 4 and the 2. Then multiply in similar way the 3 and the 4 by these same figures. Turn the square round so that the diagonals are upright, and add. Of course, placing the numbers thus is the same practically as carrying them by our ordinary rule.

No. LXVI

In this diagram 27 counters are arranged in 9 rows, with 6 in each row.

Puzzle

Can you rearrange them so that with similar conditions they all fall within the borders of one equilateral triangle?

Solution

51. A BURIED ADAGE

The bees’ blithe vernal love-songs softly hum,
 Blending so sweetly with the restful air;
 The noiseless, deep-laced twilight shadows come,
 And well I ken the lass who meets me there.

Can you discover a very familiar saying that is buried in these lines?

Solution

No. LXVII.—AN EIGHT-CARD PUZZLE

Place eight cards of two different colours alternately in one row, then with four moves bring all of one colour together.

A
♠		   2
♡		   3
♣		   4
♢		   5
♣		   6
♢		   7
♣		   8
♡

Image

Two cards (without altering their relative position) are to be moved at a time, and placed somewhere in the same line, one of them at least touching another card.

Solution

52. MUTILATIONS

A little beast without its head
 Becomes a mighty beast instead;
 But then the subject of my riddle
 Is cut asunder in the middle;
 And nothing this division gains,
 Though unknown quantity remains.

Solution

53. MISSING WORDS

Mary sat with ..... in hand
 Writing ..... dramatic.
 Did she ..... the plots she planned?
 Negative emphatic!
 ..... to us the ..... may be
 But at ..... they’re new to she!

The missing words are spelt with the same five letters.

Solution

No. LXVIII.—THOUGHT READING

Cut out this diagram, and paste it on a card. Hand it to anyone, and ask him to fix upon whichever number he pleases, and merely to tell you in which columns this appears.

I.   II.   III.   IV.
1 33 65 97   2 34 66 98   4 36 68 100   8 40 72 104
3 35 67 99   3 35 67 99   5 37 69 101   9 41 73 105
5 37 69 101   6 38 70 102   6 38 70 102   10 42 74 106
7 39 71 103   7 39 71 103   7 39 71 103   11 43 75 107
9 41 73 105   10 42 74 106   12 44 76 108   12 44 76 108
11 43 75 107   11 43 75 107   13 45 77 109   13 45 77 109
13 45 77 109   14 46 78 110   14 46 78 110   14 46 78 110
15 47 79 111   15 47 79 111   15 47 79 111   15 47 79 111
17 49 81 113   18 50 82 114   20 52 84 116   24 56 88 120
19 51 83 115   19 51 83 115   21 53 85 117   25 57 89 121
21 53 85 117   22 54 86 118   22 54 86 118   26 58 90 122
23 55 87 119   23 55 87 119   23 55 87 119   27 59 91 123
25 57 89 121   26 58 90 122   28 60 92 124   28 60 92 124
27 59 91 123   27 59 91 123   29 61 93 125   29 61 93 125
29 61 93 125   30 62 94 126   30 62 94 126   30 62 94 126
31 63 95 127   31 63 95 127   31 63 95 127   31 63 95 127
V.   VI.   VII.
16 48 80 112   32 48 96 112   64 80 96 112
17 49 81 113   33 49 97 113   65 81 97 113
18 50 82 114   34 50 98 114   66 82 98 114
19 51 83 115   35 51 99 115   67 83 99 115
20 52 84 116   36 52 100 116   68 84 100 116
21 53 85 117   37 53 101 117   69 85 101 117
22 54 86 118   38 54 102 118   70 86 102 118
23 55 87 119   39 55 103 119   71 87 103 119
24 56 88 120   40 56 104 120   72 88 104 120
25 57 89 121   41 57 105 121   73 89 105 121
26 58 90 122   42 58 106 122   74 90 106 122
27 59 91 123   43 59 107 123   75 91 107 123
28 60 92 124   44 60 108 124   76 92 108 124
29 61 93 125   45 61 109 125   77 93 109 125
30 62 94 126   46 62 110 126   78 94 110 126
31 63 95 127   47 63 111 127   79 95 111 127

Image

You can then in a moment, and at a glance, pick out the number that is chosen.

Solution

No. LXIX.—FROM PILLAR TO POST

Let us suppose that these black dots represent a succession of pillar boxes. It will be seen that a postman, starting from the circle, and going along the dotted lines, turns round 18 corners.

Route

Can he take a course which involves fewer turnings?

Solution

No. LXX.—TRANSFORMATIONS

Here is an ingenious paper and scissors puzzle:—

Puzzle

Divide a square card into three pieces, so that these can be reunited to form No. 2 or No. 3 of this diagram.

Solution

54. COUNTING THE GEESE

(From an old Sanscrit source, quoted by Longfellow in his “Kavanagh.”)

Ten times the square root of a flock of geese, seeing the clouds collect, flew to the Manus lake. One-eighth of the whole flew from the edge of the water among a tangle of water lilies, and three couples were seen playing in the water. Tell me, my young girl with beautiful locks, what was the whole number of geese?

Solution

55. A THIRD IS A HALF

Six hundred and sixty so ordered may be
 That if you divide the whole number by three
 You find the result will exactly express
 The half of six hundred and sixty, no less.

Solution

No. LXXI.—A PUZZLE WITH CHESS PIECES

               
               
               
        ♚      
               
               
               
♖           ♘ ♖

Image

Leaving the Black King in his position, place the three white men so that he stands checkmated.

Solution

56. PRESS PARODIES

An American paper published the following:—

There was a young damsel, oh, bless her!
 It cost very little to dress her;
 She was sweet as a rose
 In her everyday clothes,
 But had no young man to caress her.

Next day this parody appeared in a rival paper:—

There was a young ......, oh, bless her!
 It cost very little to dress her;
 Some ........... and .....
 About Thanksgiving time,
 And they ... the last bit from the ........

Can you fill in the missing words?

Solution

No. LXXII.—HEXAGONAL ILLUSIONS

If we look with one eye only, or with eyes half-closed, at these groups of circular dots, they assume the appearance familiar to us in honeycomb. This is an effect of the contrast and opposition of the black and white in the sensation of the retina.

Faux hexagons

Although the black and the white circles are of the same diameter the irradiation is in their case so intense that the white circles appear to be larger than the black.

No. LXXIII.—AN ILLUSION OF ARCHES

This excellent illusion appeared in a recent number of the “Strand Magazine”:—

Illusion

Most persons will at first see the passages under these arches as running upwards from left to right, but presently, as their line of vision shifts, the arches will take a downward course from right to left. This very curious effect will well repay a little patience, if it is not realised at once.

57. WHERE WAS THE WEDDING?

She loses her head when she joins the brides,
 He joins them after tea;
 But both are swept by ruthless tides
 Away on the western sea.

Solution

58. ON A BANANA BARROW

I have 91 bananas on my barrow, of two qualities; some I sell at four a penny, and the better sort at three a penny. If I had sold them in mixed lots at seven for twopence, I should have made a penny more. How many were there of each quality?

Solution

No. LXXIV.—IN THE TRAIN

The Puzzle Problem—

A passenger in a first-class railway carriage notices that the top of a factory window due S.W. of him coincides with a mark on the carriage window, and does not move from it while the train is running five and a half miles.

At the end of that distance the compass bearing of the chimney is due N.W. How far was the passenger from the chimney when he first noticed it?

is solved by 31⁄2 miles.

We give a diagram to make the points clear.

As the chimney top does not move from its place on the window, it is clear that the train is running on a segment of a circle having the chimney for its centre. It follows that the observer’s distance throughout is equal to the radius of that circle, and the radius of a circle of which the quadrant measures 51⁄2 miles is 31⁄2 miles within about 11 ft.

No. LXXV.—MENDING THE FLAG

The cross had been taken out from the centre of this flag, and its owner, who had an ingenious turn of mind, found that by cutting what remained into two pieces, and rejoining them, he could make it into a perfect flag without any waste of material.

Flag

How did he accomplish this?

Solution

No. LXXVI.—FOR THE CHILDREN

Add two more pieces similar in shape and size to that marked A, and one similar to B, C, and D respectively, and then readjust the eleven parts so that they form a perfect square.

Puzzle

Solution

59. MISSING WORDS

How does the sluggard’s garden grow?
 When ..... are high results are low.
 His borders ..... and bindweed spoil,
 No careful culture ..... the soil;
 But weeds that ..... are all alive
 Where ..... pink or rose should thrive.

The missing words are spelt with the same letters.

Solution

No. LXXVII.—AN EASY MATCH PUZZLE

This is a simple arrangement of eight matches, by which two squares and four similar triangles are formed.

Matches

60. WHAT AM I?

Correctly drawn results I yield.
 Varied, but welcome everywhere;
 But met with in the open field
 I’m banned if frequent, blest if rare.
 To this peculiar difference the clue
 Is called with much significance the cue.

Solution

61. BURIED TOWNS

Wait while I think the matter over,
 On holiday intent;
 The best I’ve seen is surely Dover,
 That pretty port of Kent.

Three towns are buried in these lines.

Solution

No. LXXVIII.—WALKING THE ROUNDS

A hospital was built in six detached blocks, and it was the duty of the night watchman to go completely round every block at fixed hours to see that all was safe.

Hospital grounds

What was his shortest course?

Solution

62. THE ARAB AND HIS ASS

An Arab came to the river side
 With a donkey bearing an obelisk,
 But he did not venture to ford the tide,
 For he had too good an *.
So he camped all night by that river side,
 Secure till the tide had ceased to swell,
 For he knew that whenever the donkey died
 No other could be its ‖.

Solution

No. LXXIX

Can you rearrange the twelve counters on this board of 36 squares so that there are two counters on each row, column, and diagonal?

           
           
◎ ◎ ◎ ◎ ◎ ◎
◎ ◎ ◎ ◎ ◎ ◎
           
           

Image

There must not be more than these two counters in the same straight line.

Solution

63. A CHARADE