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Makes magic squares.

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These programs make magic squares and rectangles using "Constraint-Based Local Search".
(For non-square rectangles, input the order as two numbers.)
There are 3 similar programs: CompleteSquare, CompleteSquareSteps, and MagicSquares.

Given an input square with some cell values between 1 and NxN specified,
(and other cell values 0), CompleteSquare attempts to complete a magic square by
placing the remaining values. The square type can be input as semimagic, magic,
or associative.

For successful solutions, CompleteSquareSteps shows the steps of the search.
The number exchanges at each step and the intermediate squares are written to files.

MagicSquares does not require an input file.
MagicSquares (only) also supports concentric and pandiagonal. (Pandiagonal succeeds only for small orders.)


mssolutions Web Site


  • constraint-based local search
  • tabu search
  • randomly generated starting rectangles
  • user-supplied starting rectangles
  • user-supplied rectangle templates


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Additional Project Details

Intended Audience

Science/Research, Education, End Users/Desktop

Programming Language




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