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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.
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