Part 3
A market gardener who has a large square plot of ground wishes to reserve a fourth of it in the shape of a triangle for himself, as is shown in the diagram--
[Illustration]
and to divide the remainder among his four sons, so that each shares equally, with plots of similar shape. How did he mark it out for them?
This appears in a less perfect form in “The Twentieth Century Standard Puzzle Book.”
No. LVII.--USE YOUR PENCIL
Here is a simple little puzzle which may amuse anyone who has paper and pencil at hand:--
[Illustration]
Can you combine three figures similar to Fig. A with two similar to Fig. B, so that a perfect Latin cross is formed?
It is, of course, an easier matter to cut out five such pieces in paper or cardboard, and arrange them in the form required.
45. MISSING WORDS
I love strolling ....... that wander around, Each ....... a ....... in versatile skill; Each ....... so quaint, each idea so profound, My barn’s at their service, whenever they will. A company played there last night, but to-day Ducks ......., and poultry have vanished away!
The missing words are spelt with the same seven letters.
No. LVIII.--SUBTLE SELFISHNESS
Four poor men were living in the cottages shown in this diagram, round a central lake well stocked with fish. Four rich men built their houses further afield, and selfishly determined to exclude their neighbours from access to the water.
[Illustration]
How could they do this effectually without cutting themselves off from the lake?
46. AN ARITHMOREM
150 hat robe or tent
Can you form from this the name of a famous British author, treating the 150 as Roman numerals?
No. LIX.--FOR THE CHILDREN
Cut out in cardboard four pieces of the shape and size of each of the large patterns, and two pieces of the small one:--
[Illustration]
Now arrange these ten pieces so that they form a perfect square.
47. SHEDDING LETTERS
I’m a worker most active, most useful, most known, Of all that are busy in country and town. Take from me one letter, and yet my good name In spite of this loss will continue the same. Take from me two letters, and still you will see That precisely the same in effect I shall be. Take from me three letters, or even take more, Yet still I continue as sound as before.
No. LX.
The dotted lines in this diagram show how the figure can be divided into nine parts by four straight cuts
[Illustration]
which can be reunited to form a perfect cross.
48. A SHARP BOY
Tom Larkins, proud of his prize for arithmetic, challenged his sisters to show on a blackboard that if 50 is subtracted from the sum of the nine digits, the result is equal to the number obtained by dividing their sum by 3. How did he prove his point?
No. LXI.--AN EASY ONE
Take in paper or cardboard a figure made up of a square and half of a similar square, thus:--
[Illustration]
How can you, in the simplest way, divide it into four equal and similar parts by four straight cuts?
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.”
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?
[Illustration]
Each line must be at right angles to another.
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?
No. LXIII
[Illustration: _Cut up this triangle into 5 parts_,]
[Illustration: _which can be reassembled to form this triangle_.]
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│ └───┴───┴───┴───┴───┴───┴───┴───┘
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.
^ ╱│╲ 2╱ │ ╲5 ╱ │ ╲ ╱ 1 │ 0 ╲ ╱│╲ │ ╱│╲ 4╱ │ ╲ │ ╱ │ ╲3 ╱ │ ╲│╱ │ ╲ ╱ 2 │ 0 ╳ 0 │ 6 ╲ ╱│╲ │ ╱│╲ │ ╱│╲ 3╱ │ ╲ │ ╱ │ ╲ │ ╱ │ ╲4 ╱ │ ╲│╱ │ ╲│╱ │ ╲ │ 1 │ 5 ╳ 1 │ 2 ╳ 0 │ 8 │ ╲ │ ╱│╲ │ ╱│╲ │ ╱ ╲ │ ╱ │ ╲ │ ╱ │ ╲ │ ╱ ╲│╱ │ ╲│╱ │ ╲│╱ ╲ 0 │ 9 ╳ 1 │ 6 ╱ ╲ │ ╱│╲ │ ╱ ╲ │ ╱ │ ╲ │ ╱ ╲│╱ │ ╲│╱ ╲ 1 │ 2 ╱ ╲ │ ╱ ╲ │ ╱ ╲│╱ v ───────────────────────── 1 8 2 6 2 8 ─────────────────────────
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.
* ╱ ╲ ╱ ╲ ╱ ╲ * * ╱ ╲ ╱ ╲ ╱ ╲ ╱ ╲ ╱ ╲ ╱ ╲ ╱ * ╲ ╱ ╱ ╲ ╲ ╱ ╱ ╲ ╲ ╱ ╱ ╲ ╲ *───────*───────*───────*───────*───────* ╲ ╱ ╱ ╲ ╲ ╱ ╲ ╱ ╱ ╲ ╲ ╱ ╲ ╱ ╱ ╲ ╲ ╱ * ╱ ╲ * ╱ ╲ ╱ ╲ ╱ ╲ ╱ ╲ ╱ ╲ ╱ ╲ ╱ ╲ ╱ ╲ ╱ ╲ ╱ * * ╲ ╱ ╱ ╲ ╱ ╲ ╲ ╱ ╱ ╲ ╱ ╲ ╲ ╱ ╱ ╲ ╱ ╲ ╲ *───────*───────*───────────────*───────*───────* ╱ ╱ ╲ ╱ ╲ ╲ ╱ ╱ ╲ ╱ ╲ ╲ ╱ ╱ ╲ ╱ ╲ ╲ *───────*───────────────*───────*───────────────*───────* ╲ ╱ ╲ ╱ ╲ ╱ *
Can you rearrange them so that with similar conditions they all fall within the borders of one equilateral triangle?
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?
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 │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ ♠ │ │ ♡ │ │ ♣ │ │ ♢ │ │ ♣ │ │ ♢ │ │ ♣ │ │ ♡ │ └───┘ └───┘ └───┘ └───┘ └───┘ └───┘ └───┘ └───┘
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.
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.
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.
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│ ║ ║ └───────────────┘└───────────────┘└───────────────┘ ║ ╚════════════════════════════════════════════════════════════════════╝
You can then in a moment, and at a glance, pick out the number that is chosen.
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.
●┅┅┅● ●┅┅┅● ●┅┅┅●┅┅┅●┅┅┅● ┇ ┇ ┇ ┇ ┇ ┇ ● ● ● ● ● ●┅┅┅● ● ┇ ┇ ┇ ┇ ┇ ┇ ┇ ┇ ● ● ● ● ● ● ● ● ┇ ┇ ┇ ┇ ┇ ┇ ┇ ┇ ● ● ● ● ○ ● ● ● ┇ ┇ ┇ ┇ ┇ ┇ ┇ ┇ ● ● ● ●┅┅┅● ● ● ● ┇ ┇ ┇ ┇ ┇ ┇ ● ● ●┅┅┅●┅┅┅● ● ● ● ┇ ┇ ┇ ┇ ┇ ┇ ● ●┅┅┅●┅┅┅●┅┅┅● ● ● ● ┇ ┇ ┇ ┇ ●┅┅┅●┅┅┅●┅┅┅●┅┅┅●┅┅┅● ●┅┅┅●
Can he take a course which involves fewer turnings?
No. LXX.--TRANSFORMATIONS
Here is an ingenious paper and scissors puzzle:--
[Illustration: 1.]
[Illustration: 2.]
[Illustration: 3.]
Divide a square card into three pieces, so that these can be reunited to form No. 2 or No. 3 of this diagram.
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?
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.
No. LXXI.--A PUZZLE WITH CHESS PIECES
┏━━━┯━━━┯━━━┯━━━┯━━━┯━━━┯━━━┯━━━┓ ┃ │###│ │###│ │###│ │###┃ ┠───┼───┼───┼───┼───┼───┼───┼───┨ ┃###│ │###│ │###│ │###│ ┃ ┠───┼───┼───┼───┼───┼───┼───┼───┨ ┃ │###│ │###│ │###│ │###┃ ┠───┼───┼───┼───┼───┼───┼───┼───┨ ┃###│ │###│ │#♚#│ │###│ ┃ ┠───┼───┼───┼───┼───┼───┼───┼───┨ ┃ │###│ │###│ │###│ │###┃ ┠───┼───┼───┼───┼───┼───┼───┼───┨ ┃###│ │###│ │###│ │###│ ┃ ┠───┼───┼───┼───┼───┼───┼───┼───┨ ┃ │###│ │###│ │###│ │###┃ ┠───┼───┼───┼───┼───┼───┼───┼───┨ ┃#♖#│ │###│ │###│ │#♘#│#♖#┃ ┗━━━┷━━━┷━━━┷━━━┷━━━┷━━━┷━━━┷━━━┛
Leaving the Black King in his position, place the three white men so that he stands checkmated.
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?
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.
[Illustration]
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”:--
[Illustration]
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.
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?
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.
[Illustration]
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.
[Illustration]
How did he accomplish this?
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.
[Illustration]
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.
No. LXXVII.--AN EASY MATCH PUZZLE
This is a simple arrangement of eight matches, by which two squares and four similar triangles are formed.
[Illustration]
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.
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.
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.
[Illustration]
What was his shortest course?
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 ‖.
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?
╔═══╤═══╤═══╤═══╤═══╤═══╗ ║ │ │ │ │ │ ║ ╟───┼───┼───┼───┼───┼───╢ ║ │ │ │ │ │ ║ ╟───┼───┼───┼───┼───┼───╢ ║ ◎ │ ◎ │ ◎ │ ◎ │ ◎ │ ◎ ║ ╟───┼───┼───┼───┼───┼───╢ ║ ◎ │ ◎ │ ◎ │ ◎ │ ◎ │ ◎ ║ ╟───┼───┼───┼───┼───┼───╢ ║ │ │ │ │ │ ║ ╟───┼───┼───┼───┼───┼───╢ ║ │ │ │ │ │ ║ ╚═══╧═══╧═══╧═══╧═══╧═══╝
There must not be more than these two counters in the same straight line.
63. A CHARADE
What ho, my jolly _second!_ never say my _first_ While my final you can find in Amsterdam. Think how a sound _whole_ stays your hunger and your thirst, Deftly readjusting bread and meat and jam.
No. LXXX.--THE QUEEN’S TOUR
This is a course by which the queen on a chessboard, starting from K R sq., passes over every square in fourteen moves.
[Illustration]
64. AFTER THE MATCH
“Did you score a score?” said Funniman to his schoolboy nephew, after a local cricket match. “No, uncle,” said the youngster, “but if I had made as many more runs, half as many more, and two runs and a half, I should have made my twenty.” How many runs did he get?
No. LXXXI.--A NEST OF TRIANGLES
In the “Twentieth Century Standard Puzzle Book” we gave a figure similar to this, in which there were 653 interlacing triangles in four tiers of this character.
[Illustration]
We now add a fifth tier at the base, and ask our solvers to determine how many triangles of all shapes and sizes can be counted within its enlarged borders.
65. AN ENIGMA
Six letters spell the happy state Of two in love made one. The same six letters tell the fate Of marriage ties undone.
No. LXXXII.--A SIMPLE MATCH PUZZLE
Place eight matches in a row, about an inch apart, as indicated in the diagram.
║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║
The puzzle is to form these into four pairs in four moves, by moving one match clear over two matches every time.
66. A TOPICAL RIDDLE
My First’s a bond, my Seconds weigh; These own the Rest of all my lay; Busy my Third; Fourth like the Pole, Whose opposite my Fifth makes goal.
67. MISSING WORDS
For two months at the .... we played, Ere we were .... to Lord’s; Alas! the score our champion made Was what a .... affords! The crowd in .... of thousands came But took scant notice of the game.
No. LXXXIII.--A MATCH PUZZLE
Place twelve matches, as is shown in the diagram, so that they form four squares.
══════ ══════ ║ ║ ║ ║ ║ ║ ║ ║ ║ ═══════ ══════ ║ ║ ║ ║ ║ ║ ║ ║ ║ ══════ ══════
Now remove three of the matches, and readjust the nine that remain so that they represent three squares.
68. MARCONIGRAMS
Edwin and Angelina were far apart, when this message, with its touch of jealous resentment, reached her on the wings of a Marconigram--
“No fickle girl is bonnie to my mind!”
Quite equal to the occasion, she flashed back the reply--
“In love inconstant I no pleasure find!”
How did these messages reveal the places from which they were despatched?
No. LXXXIV.--MATHEMATICS WITH MATCHES