I sit on a rock while I’m raising the wind,But the storm once abated I’m gentle and kind.I’ve Kings at my feet, who await but my nodTo kneel in the dust on the ground I have trod.Though seen to the world, I am known to but few,The Gentile detests me, I’m pork to the Jew.I never have passed but one night in the dark,And that was with Noah alone in the ark.My weight is three pounds, my length is a mile.And when I’m discovered you’ll say, with a smile,That my first and my last are the pride of this isle.
I sit on a rock while I’m raising the wind,But the storm once abated I’m gentle and kind.I’ve Kings at my feet, who await but my nodTo kneel in the dust on the ground I have trod.Though seen to the world, I am known to but few,The Gentile detests me, I’m pork to the Jew.I never have passed but one night in the dark,And that was with Noah alone in the ark.My weight is three pounds, my length is a mile.And when I’m discovered you’ll say, with a smile,That my first and my last are the pride of this isle.
I sit on a rock while I’m raising the wind,But the storm once abated I’m gentle and kind.I’ve Kings at my feet, who await but my nodTo kneel in the dust on the ground I have trod.Though seen to the world, I am known to but few,The Gentile detests me, I’m pork to the Jew.I never have passed but one night in the dark,And that was with Noah alone in the ark.My weight is three pounds, my length is a mile.And when I’m discovered you’ll say, with a smile,That my first and my last are the pride of this isle.
Solution
In this Magic Square, not only do the rows, columns, and diagonals add up to 260, but this same number is produced in three other and quite unusualways:—
(1) Each group of 8 numbers, ranged in a circle round the centre; there are six of these, of which the smallest is 22, 28, 38, 44, 19, 29, 35, 45, and the largest is 8, 10, 56, 58, 1, 15, 49, 63. (2) The sum of the 4 central numbers and 4 corners. (3) The diagonal cross of 4 numbers in the middle of the board.
Onanother pagewe give an interesting Magic Square of 121 cells based upon the figures of the year 1892. Here, in much more condensed form, is one more up to date.
The rows, columns, and diagonals of these nine cells add up in all cases to the figures of the year 1902.
The central 634 is found by dividing 1902 by its lowest factor greater than 2, and this is taken as the middle term of nine numbers, which are thus arranged to form a Magic Square.
The pomps of Courts and pride of KingsI prize above all earthly things;I love my country, but the KingAbove all men his praise I sing.The royal banners are displayed,And may success the standard aid!I fain would banish far from henceThe “Rights of Men” and “Common Sense;”Confusion to his odious reign,That Foe to princes, Thomas Payne.Defeat and ruin seize the causeOf France, its liberties and laws!
The pomps of Courts and pride of KingsI prize above all earthly things;I love my country, but the KingAbove all men his praise I sing.The royal banners are displayed,And may success the standard aid!I fain would banish far from henceThe “Rights of Men” and “Common Sense;”Confusion to his odious reign,That Foe to princes, Thomas Payne.Defeat and ruin seize the causeOf France, its liberties and laws!
The pomps of Courts and pride of KingsI prize above all earthly things;I love my country, but the KingAbove all men his praise I sing.The royal banners are displayed,And may success the standard aid!
I fain would banish far from henceThe “Rights of Men” and “Common Sense;”Confusion to his odious reign,That Foe to princes, Thomas Payne.Defeat and ruin seize the causeOf France, its liberties and laws!
Where does the treason come in?
Solution
The following square of numbers is interesting in connection with the year 1906.
and the sum, in every case, is 1906.
Here is quite a curious nest of clustered Magic Squares, which is worthpreserving:—
Every square of every possible combination of 25 of these numbers in their cells, such as the two with darker borders, is a perfect Magic Square, with rows, columns, and diagonals that add up in all cases to 65.
Formed half beneath and half above the earth,We owe, as twins, to art our second birth.The smith’s and carpenter’s adopted daughters,Made upon earth, we travel on the waters.Swifter we move as tighter we are bound,Yet never touch the sea, or air, or ground.We serve the poor for use, the rich for whim,Sink if it rains, and if it freezes swim.
Formed half beneath and half above the earth,We owe, as twins, to art our second birth.The smith’s and carpenter’s adopted daughters,Made upon earth, we travel on the waters.Swifter we move as tighter we are bound,Yet never touch the sea, or air, or ground.We serve the poor for use, the rich for whim,Sink if it rains, and if it freezes swim.
Formed half beneath and half above the earth,We owe, as twins, to art our second birth.The smith’s and carpenter’s adopted daughters,Made upon earth, we travel on the waters.Swifter we move as tighter we are bound,Yet never touch the sea, or air, or ground.We serve the poor for use, the rich for whim,Sink if it rains, and if it freezes swim.
Solution
A very interesting method of constructing a Magic Square is shown in these threediagrams:—
It will be noticed that each row after the first, in the two upper auxiliary squares, begins with a number from the same column in the row above it, and maintains the same sequence of numbers. When the corresponding cells of these two squares are added together, and placed in the third square, a Magic Square is formed, in which 671 is the sum of all rows, columns, and diagonals.
Here is a curious form of Magic Square. The year 1892 is taken as its basis.
Within this square 1892 can be counted up in all the usual ways, and altogether in 44 variations. Thus any two rows that run parallel to a diagonal, and have between them eleven cells, add up to this number, if they are on opposite sides of the diagonal.
The sun, the sun is my delight!I shun a gloomy day,Though I am often seen at nightTo dart across the way.Sometimes you see me climb a wallAs nimble as a cat,Then down into a pit I fallLike any frightened rat.Catch me who can—woman or man—None have succeeded who after me ran.
The sun, the sun is my delight!I shun a gloomy day,Though I am often seen at nightTo dart across the way.Sometimes you see me climb a wallAs nimble as a cat,Then down into a pit I fallLike any frightened rat.Catch me who can—woman or man—None have succeeded who after me ran.
The sun, the sun is my delight!I shun a gloomy day,Though I am often seen at nightTo dart across the way.Sometimes you see me climb a wallAs nimble as a cat,Then down into a pit I fallLike any frightened rat.Catch me who can—woman or man—None have succeeded who after me ran.
Solution
This Magic Square of 49 cells is constructed with a diagonal arrangement of the numbers from 1 to 49 in their proper order. Those that fall outside the central square are written into it in the seventh cell inwards from where they stand. It is interesting to find out the many combinations in which the number 175 is made up.
I grasped it, meaning nothing wrong,And moved to meet my friend,When lo! the stalwart man and strongAt once began to bend.The biped by the quadrupedNo longer upright stood,But bowed the knee and bent his headBefore the carved wood.
I grasped it, meaning nothing wrong,And moved to meet my friend,When lo! the stalwart man and strongAt once began to bend.The biped by the quadrupedNo longer upright stood,But bowed the knee and bent his headBefore the carved wood.
I grasped it, meaning nothing wrong,And moved to meet my friend,When lo! the stalwart man and strongAt once began to bend.The biped by the quadrupedNo longer upright stood,But bowed the knee and bent his headBefore the carved wood.
Solution
These are two interesting Magic Squares found on an antique gong, at Caius College,Cambridge:—
613811971051271491220811613
6138119710512
71491220811613
In the one nine numbers are so arranged that they count up to 27 in every direction; and in the other the outer rows total 30, while the central rows and diagonals make 40.
My figure, singular and slight,Measures but half enough at sight.I rode the waters day and night.I tell the new in Time’s quick flight,Or how old ages rolled in might.Cut off my tail, it still is on!Put on my head, and there is none!
My figure, singular and slight,Measures but half enough at sight.I rode the waters day and night.I tell the new in Time’s quick flight,Or how old ages rolled in might.Cut off my tail, it still is on!Put on my head, and there is none!
My figure, singular and slight,Measures but half enough at sight.I rode the waters day and night.I tell the new in Time’s quick flight,Or how old ages rolled in might.Cut off my tail, it still is on!Put on my head, and there is none!
Solution
Among Moorish Mussulmans 78 is a mystic number.
Here is a cleverly-constructed Magic Square, to which this number is the key.
The number 78 can be arrived at in twenty-three different combinations—namely, ten rows, columns, or diagonals; four corner squares of four cells; one central square of four cells; the four corner cells; two sets of corresponding diagonal cells next to the corners; and two sets of central cells on the top and bottom rows, and on the outside columns.
Here is a Magic Square of singularcharm:—
The 81 cells of this remarkable square are divided by parallel lines into 9 equal parts, each made up of 9 consecutive numbers, and each a Magic Square in itself within the parent square. Readers can work out for themselves the combinations in the larger square and in the little ones.
There is a noun of plural number,Foe to peace and tranquil slumber.Now almost any noun you takeBy adding “s” you plural make.But if you add an “s” to thisStrange is the metamorphosis.Plural is plural now no more,And sweet what bitter was before.
There is a noun of plural number,Foe to peace and tranquil slumber.Now almost any noun you takeBy adding “s” you plural make.But if you add an “s” to thisStrange is the metamorphosis.Plural is plural now no more,And sweet what bitter was before.
There is a noun of plural number,Foe to peace and tranquil slumber.Now almost any noun you takeBy adding “s” you plural make.But if you add an “s” to thisStrange is the metamorphosis.Plural is plural now no more,And sweet what bitter was before.
Solution
Fill each square by repeating two of its figures in the vacant cells. Then rearrange them all, so that the sums of the corresponding rows in each square are equal, and the sums of the squares of the corresponding cells of these rows are also equal; and so that the sums of the four diagonals are equal, and the sum of the squares of the cells in corresponding diagonals are equal.
Solution
There is an old-world charm about thisEnigma:—
In the ears of young and oldI repeat what I am told;And they hear me, old and young,Though I have no busy tongue.When a thunder-clap awakes meNot a touch of terror takes me;Yet so tender is my earThat the softest sound I fear.Call me not with bated breath,For a whisper is my death.
In the ears of young and oldI repeat what I am told;And they hear me, old and young,Though I have no busy tongue.When a thunder-clap awakes meNot a touch of terror takes me;Yet so tender is my earThat the softest sound I fear.Call me not with bated breath,For a whisper is my death.
In the ears of young and oldI repeat what I am told;And they hear me, old and young,Though I have no busy tongue.When a thunder-clap awakes meNot a touch of terror takes me;Yet so tender is my earThat the softest sound I fear.Call me not with bated breath,For a whisper is my death.
Solution
Here is an arrangement of fractions which form a perfect MagicSquare:—
If these fractions are added together in any one of the eight directions, the result in every case is unity. Thus3⁄8+1⁄3+7⁄24= 1,1⁄6+1⁄3+1⁄2= 1, and so on throughout the rows, columns, and diagonals.
“By hammer and handAll arts do stand”—So says an ancient saw;But hammer and handWill work or standBy my unwritten law.Behold me, as sparks from the anvils fly,But fires lie down at my bitter cry.
“By hammer and handAll arts do stand”—So says an ancient saw;But hammer and handWill work or standBy my unwritten law.Behold me, as sparks from the anvils fly,But fires lie down at my bitter cry.
“By hammer and handAll arts do stand”—So says an ancient saw;But hammer and handWill work or standBy my unwritten law.Behold me, as sparks from the anvils fly,But fires lie down at my bitter cry.
Solution
We are indebted to a friend for the following elaborate Magic Square of fractions, on the lines of that on the preceding page.
The composer claims that there are at least 160 combinations of 5 cells in which these fractions add up to unity, including, of course, the usual rows, columns, and diagonals.