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The term magic constant or '''magic sum''' is similarly applied to other "magic" figures such as Magic Star s and Magic Cube s. NORMAL MAGIC SQUARES If a magic square of order ''n'' is Normal (i.e., it contains the numbers 1 to ''n''2), then the magic constant depends only on ''n''; its value is :. This formula is a consequence of the formula for the sum of the first n integers : applied to the case ''k'' = ''n''2, yielding ''n''2(''n''2+1)/2, which is then divided by ''n'' because there are ''n'' rows, all of which sum to the same value. The magic constants of normal magic squares of order ''n'' = 3, 4, 5, … are (sequence in OEIS ): : 15 , 34 , 65 , 111 , 175 , 260 , 369, 505, 671, 870 The numbers in any row, column, or diagonal of a normal magic square form a Magic Series . EXTERNAL LINK |
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