S = 46  Magic Stars are
normally considered to be figures of 4 numbers in a row that add to the
magic constant. The magic hexagram is such a pattern, and consists of the
numbers 1 to 12 arranged in 6 lines of 4 numbers such that each line sums
to the constant S. The sum of the series 1 to 12 is 78, there are 6 lines
with each cell appearing in 2 lines, so the magic constant (S) is (2 x
78)/6 = 26. [1]
In 1989, Harold Reiter and David Richie considered an elaboration of this
figure [2]. They found that the answer was affirmative. Their algorithm and the resulting computer search program found all possible solutions. There are actually 9 separate magic constants, ranging from 46 to 54. This search problem was made manageable by using several shortcuts.
Their search involved only 18,264,704 checks instead of the 19! that would have been required if all combinations were checked. The number of basic solutions are:
[1]
http://www.geocities.com/~harveyh/order6.htm


S=47  
S = 48 
The S = 51 solution below is the complement of the S = 49 solution shown.
S = 49 
S = 50 
S = 51 
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This page last updated
April 04, 2007
Copyright © 2002 by Harvey D. Heinz