Saturday, December 17, 2016

Independent and Dependent Variables for a Magic Cube

The sums found in the last blog can be used to eliminate dependent variables from the magic square. The remaining independent variables can be reduced to the following set.

The magic square can be reconstructed with the following formulas.

In a similar manner the known sums can be used to fill in the unknown boxes if one initially fills in the magic square with some arbitrary numbers. The selections that can be made are limited by the known sums.

Supplemental (Dec 17): The set of independent variables is ordered so there are
16·15·14·13·12·11 = 16!/10! = 5,765,760 ways of assigning 6 out of the 16 possible numbers to them. Not all combinations will yield a magic square consistent with the rules.

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