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Read Ebook: Twentieth Century Standard Puzzle Book Three Parts in One Volume by Pearson A Cyril Arthur Cyril Editor
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Ebook has 2438 lines and 141647 words, and 49 pages
HALLAM'S UNSOLVED ENIGMA
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 nod To 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.
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 unusual ways:--
+--+--+--+--+--+--+--+--+ |18|63| 4|61| 6|59| 8|41| +--+--+--+--+--+--+--+--+ |49|32|51|14|53|12|39|10| +--+--+--+--+--+--+--+--+ | 2|47|36|45|22|27|24|57| +--+--+--+--+--+--+--+--+ |33|16|35|46|21|28|55|26| +--+--+--+--+--+--+--+--+ |31|50|29|20|43|38| 9|40| +--+--+--+--+--+--+--+--+ |64|17|30|19|44|37|42| 7| +--+--+--+--+--+--+--+--+ |15|34|13|52|11|54|25|56| +--+--+--+--+--+--+--+--+ |48| 1|62| 3|60| 5|58|23| +--+--+--+--+--+--+--+--+
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. The sum of the 4 central numbers and 4 corners. The diagonal cross of 4 numbers in the middle of the board.
On another page we 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.
RANK TREASON
BY AN IRISH REBEL, 1798
The pomps of Courts and pride of Kings I prize above all earthly things; I love my country, but the King Above all men his praise I sing. The royal banners are displayed, And may success the standard aid!
I fain would banish far from hence The "Rights of Men" and "Common Sense;" Confusion to his odious reign, That Foe to princes, Thomas Payne. Defeat and ruin seize the cause Of France, its liberties and laws!
Where does the treason come in?
The following square of numbers is interesting in connection with the year 1906.
Add the rows --ABCD, EFGH, IJKL, MNOP. or the squares --ABEF, CDGH, IJMN, KLOP. or semi-diagonals--AFIN, BEJM, CHKP, DGLO, AFCH, BEGD, INKP, MJOL.
and the sum, in every case, is 1906.
Here is quite a curious nest of clustered Magic Squares, which is worth preserving:--
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.
AN ENIGMA FOR CHRISTMAS HOLIDAYS
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.
A very interesting method of constructing a Magic Square is shown in these three diagrams:--
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 night To dart across the way. Sometimes you see me climb a wall As nimble as a cat, Then down into a pit I fall Like any frightened rat. Catch me who can--woman or man-- None have succeeded who after me ran.
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.
WHAT MOVED HIM?
I grasped it, meaning nothing wrong, And moved to meet my friend, When lo! the stalwart man and strong At once began to bend. The biped by the quadruped No longer upright stood, But bowed the knee and bent his head Before the carved wood.
These are two interesting Magic Squares found on an antique gong, at Caius College, Cambridge:--
+--+--+--+ +--+--+--+ | 6|13| 8| | 7|14| 9| +--+--+--+ +--+--+--+ |11| 9| 7| |12|20| 8| +--+--+--+ +--+--+--+ |10| 5|12| |11| 6|13| +--+--+--+ +--+--+--+
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.
RINGING THE CHANGES
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!
Among Moorish Mussulmans 78 is a mystic number.
+--+--+--+--+ |40|10|20| 8| +--+--+--+--+ | 7|21| 9|41| +--+--+--+--+ |12|42| 6|18| +--+--+--+--+ |19| 5|43|11| +--+--+--+--+
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 singular charm:--
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.
CANNING'S ENIGMA
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.
There is an old-world charm about this Enigma:--
In the ears of young and old I repeat what I am told; And they hear me, old and young, Though I have no busy tongue. When a thunder-clap awakes me Not a touch of terror takes me; Yet so tender is my ear That the softest sound I fear. Call me not with bated breath, For a whisper is my death.
Here is an arrangement of fractions which form a perfect Magic Square:--
"DOUBLE, DOUBLE, TOIL AND TROUBLE!"
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.
Two brothers wisely kept apart, Together ne'er employed; Though to one purpose we are bent Each takes a different side.
We travel much, yet prisoners are, And close confined to boot, Can with the fleetest horse keep pace, Yet always go on foot.
On similar lines to Magic Squares, but as a distinct variety, we give below a specimen of a Magic Oblong.
+--+--+--+--+--+--+--+--+ | 1|10|11|29|28|19|18|16| +--+--+--+--+--+--+--+--+ | 9| 2|30|12|20|27| 7|25| |--+--+--+--+--+--+--+--| |24|31| 3|21|13| 6|26| 8| |--+--+--+--+--+--+--+--| |32|23|22| 4| 5|14|15|17| +--+--+--+--+--+--+--+--+
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