Hello MaplePrime users,

Yesterday, I posted my MagicPuzzles package to the MapleCloud. It is a collection of tools I have written for manipulating, solving, and visualizing puzzles like Magic Squares and Magic Stars. Here's a sample solution for each:

For the Magic Square, the numbers on each horizontal and vertical line, along with the numbers on each of the two diagonals, add up to 65.

The inaugural version has separate sub-packages for:

  • Magic Annulai (my own name)
  • Magic Hexagons
  • Magic Squares
  • Magic Stars

Moreover, each sub-package contains these commands:

  • Equations(), to return the linear equations for the variables based on the Magic Sum;
  • Constraints(), to return the conditions that prevent redundant solutions found by reflections and rotations;
  • VerifySolution(), to confirm if a list of numbers is a solution;
  • EquivalentSolutions(), to determine solutions equivalent to a given solution;
  • PrimarySolution(), which takes a solution and returns the associated primary solution;
  • Reflection() and Rotation(), to reflect and rotate a solution; and
  • Draw(), to provide a visualization (like the ones above).

There is also a command, MagicSolve(), which is used to find solutions, which take the form of permutations of [1,...n] for some positive integer n, to the equations. Essentially, it solves the linear equations, and cycles through all permutations for the free variables, and selects those that give "magic" solutions.

In future versions, I intend to add:

  • Other specific classes of problems;
  • More sample solutions; and
  • Known algorithms for finding particular solutions.

To install the package, you can do so from here, or just execute the following within Maple 2017+:

PackageTools:-Install( 5755630338965504, 'overwrite' );

There are many examples in the help pages.

I think others will find this package interesting and useful, and I encourage you to check it out.

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