Magic Square

a series of consecutive numbers from one upward written in a square table so constructed that the sum of any row crosswise or up and down shall be the same as that of any other column. The numbers one to nine and one to sixteen may be written in magic squares whose constant sum is fifteen and thirty-four, respectively:

The difficulty of arrangement is increased by shifting the columns until the sums of the diagonal rows also come within rules. The numbers 1 to 25; 1 to 36; 1 to 49; 1 to 64, etc., may all be arranged in magic squares. The numbers 3, 5, 11, 13, 14, 16, 22, 24, 25, 27, 33, 35, 36, 38, 44, and 46 may be arranged in four-square columns whose constant sum is 98. The Arabians, to whose invention we owe advance in algebra and arithmetic, constructed these squares and appear to have worn them superstitiously as amulets or writings of magic power to ward off evil influences.