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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
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MAGIC SQUARES, PUZZLES, TRICKS, ENIGMAS I-1
CHARADES, ETC. I-80
RIDDLES AND CONUNDRUMS I-104
NUTS TO CRACK I-115
SOLUTIONS I-148
MAGIC SQUARES
Much time was devoted in olden days to the construction and elaboration of Magic Squares. Before we go more deeply into this fascinating subject, let us study the following pretty and ingenious method of making a Magic Square of sixteen numbers, which is comparatively simple, and easily committed to memory:--
+--+--+--+--+ | 1|15|14| 4| +--+--+--+--+ |12| 6| 7| 9| +--+--+--+--+ | 8|10|11| 5| +--+--+--+--+ |13| 3|2 |16| +--+--+--+--+
Start with the small square at the top left-hand corner, placing there the 1; then count continuously from left to right, square by square, but only insert those numbers which fall upon the diagonals--namely, 4, 6, 7, 10, 11, 13, and 16.
Then start afresh at the bottom right-hand corner, calling it 1, and fill up the remaining squares in order, from right to left, counting continuously, and so placing in their turn 2, 3, 5, 8, 9, 12, 14, and 15. Each row, column, diagonal, and almost every cluster of four has 34 as the sum of its numbers.
+--+--+--+--+--+ | 1|20|16|23| 5| +--+--+--+--+--+ |15| 7|12| 9|22| +--+--+--+--+--+ |24|18|13| 8| 2| +--+--+--+--+--+ | 4|17|14|19|11| +--+--+--+--+--+ |21| 3|10| 6|25| +--+--+--+--+--+
In this Magic Square the rows, columns, and diagonals add up to 65, and the sum of any two opposite and corresponding squares is 26.
ENIGMAS
A MYSTIC ENIGMA
He stood himself beside himself And looked into the sea; Within himself he saw himself, And at himself gazed he. Now when himself he saw himself Within himself go round, Into himself he threw himself, And in himself was drowned. Now if he had not been himself, But other beast beside, He would himself have cut himself Nor in himself have died.
+--+--+--+--+--+--+--+ |22|47|16|41|10|35| 4| +--+--+--+--+--+--+--+ | 5|23|48|17|42|11|29| +--+--+--+--+--+--+--+ |30| 6|24|49|18|36|12| +--+--+--+--+--+--+--+ |13|31| 7|25|43|19|37| +--+--+--+--+--+--+--+ |38|14|32| 1|26|44|20| +--+--+--+--+--+--+--+ |21|39| 8|33| 2|27|45| +--+--+--+--+--+--+--+ |46|15|40| 9|34| 3|28| +--+--+--+--+--+--+--+
The numbers in this Magic Square of 49 cells add up in all rows, columns, and diagonals to 175. The four corner cells of every square or rectangle that has cell 25 in its centre, and cells 1, 7, 49, 43, add up to 100.
One morning Chloe, to avoid the heat, Sat in a corner of a shady seat. Young Strephon, on the self-same errand bound, This fairest flower of all the garden found. Her peerless beauty set his heart aflame, Three monosyllables expressed his aim.
At a respectful distance he conversed About the weather; then became immersed In other topics, lessening the while The space between them, heartened by her smile. The same three simple words, now joined in one, Expressed their happy state at set of sun.
An ideal Magic Square can be constructed thus:
Place 1, 2, 3, 4, 5 in any order in the five top cells, set an asterisk over the third column, as shown in the diagram; begin the next row with this figure, and let the rest follow in the original sequence; continue this method with the other three rows.
PREPARATORY SQUARE NO. 1.
PREPARATORY SQUARE NO. 2.
Make a similar square of 25 cells with 0, 5, 10, 15, 20, as is shown in No. 2, placing the asterisk in this case over the fourth column of cells, and proceeding as before, in an unchanging sequence. Using these two preparatory squares, try to form a Magic Square in which the same number can be counted up in forty-two different ways.
Here is one of many methods by which a Magic Square of the first twenty-five numbers can readily be made.
Here is what may indeed be called a Champion Magic Square:--
Its 484 cells form, as they are numbered, a Magic Square, in which all rows, columns, and diagonals add up to 5335, and it is no easy matter to determine in how many other symmetrical ways its key-number can be found.
When the cells outside each of the dark border lines are removed, three other perfect Magic Squares remain.
Collectors should take particular note of this masterpiece.
A Magic Square of nine cells can be built up by taking any number divisible by 3, and placing, as a start, its third in the central cell. Thus:--
+--+--+--+ |28|29|24| +--+--+--+ |23|27|31| +--+--+--+ |30|25|26| +--+--+--+
Say that 81 is chosen for the key number. Place 27 in the centre; 28, 29, in cells 1, 2; 30 in cell 7; 31 in 6; and then fill up cells 3, 4, 8, and 9 with the numbers necessary to make up 81 in each row, column, and diagonal.
Any number above 14 that is divisible by 3 can be dealt with in this way.
Enriched I am with much that's fat, Yet money I possess not; Enlightening all who come to me, True wisdom I express not. I may be wicked, but protest That sinful none have found me; Though I destroy myself to be Of use to those around me.
Among the infinite number of Magic Squares which can be constructed, it would be difficult to find a more remarkable setting of the numbers 1 to 32 inclusive than this, in which two squares, each of 16 cells, are perfect twins in characteristics and curious combinations.
+--+--+--+--++--+--+--+--+ | 1| 8|29|28||11|14|23|18| +--+--+--+--++--+--+--+--+ |30|27| 2| 7||21|20| 9|16| +--+--+--+--++--+--+--+--+ | 4| 5|32|25||10|15|22|19| +--+--+--+--++--+--+--+--+ |31|26| 3| 6||24|17|12|13| +--+--+--+--++--+--+--+--+
There are at least forty-eight different ways in which 66 is the sum of four of these numbers. Besides the usual rows, columns, and diagonals, any square group of four, both corner sets, all opposite pairs on the outer cells, and each set of corresponding cells next to the corners, add up exactly to 66.
Of Spanish extraction, my hue Is as dark as a negro can be; I am solid, and yet it is true That in part I am wet as the sea, My second and first are the same In all but condition and name; My second can burst The abode of my first, And my whole from the underground came.
Here is a notable specimen of a Magic Square:--
The rows, columns, and diagonals all add up to exactly 175 in the full square. Strip off the outside cells all around, and a second Magic Square remains, which adds up in all such ways to 125.
Strip off another border, as is again indicated by the darker lines, and a third Magic Square is left, which adds up to 75.
AN OLD ENIGMA
BY HANNAH MORE
I'm a strange contradiction: I'm new and I'm old, I'm sometimes in tatters and sometimes in gold, Though I never could read, yet letter'd I'm found, Though blind I enlighten, though free I am bound.
I'm English, I'm German, I'm French, and I'm Dutch; Some love me too dearly, some slight me too much. I often die young, though I sometimes live ages, And no Queen is attended by so many pages.
Here is another example of what is called a "bordered" Magic Square:--
These 81 cells form a complete magic square, in which rows, columns, and diagonals add up to 369. As each border is removed fresh Magic Squares are formed, of which the distinctive numbers are 287, 205, and 123. The central 41 is in every case the greatest common divisor.
Can you complete this Magic Square, so that the rows, columns, and diagonals add up in every case to 505?
We have given you a substantial start, and, as a further hint, as all the numbers in the first and last columns end in 0 or 1, so in the two next columns all end in 2 or 9, in the two next in 3 or 8, in the two next in 4 or 7, and in the two central columns in 5 or 6.
HALLAM'S UNSOLVED ENIGMA
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