How to Solve a Numbered Magic Cube

A numbered magic cube is the three-dimensional version of a magic square. Set up like a Rubik's cube, you must rotate numbered disks so that every row and column add up to the magic number. The most common magic cube is a semi-perfect order three puzzle where each face of the cube comprises three numbers by three numbers, or nine numbers, per face. Unlike magic squares, not every diagonal line will add up to the magic number in a semi-perfect puzzle. An order three magic cube has 27 numbers (1--27) where one is hidden inside the cube.

• 1

  Practice solving two-dimensional magic square worksheets first to become comfortable with filling in numbers so that all rows, columns and diagonal lines add up to the same total. With a 3-by-3 magic square, the central number is always 5 and the magic number (or sum of each row, column and diagonal) is 15.

• 2

  Begin solving your 3-by-3 magic cube by knowing that the magic number, the total of each row and column, is 42. Space diagonals also add up to 42. A space diagonal is a three-dimensional diagonal that goes through the middle of the cube. For example, a diagonal line starting from the top right number on the top face of the cube, going through the inside of the cube and ending on the bottom face at the bottom left number is a space diagonal.Diagonal lines on each of the six flat faces of the cube do not add up to 42.

• 3

  Arrange numbers bearing in mind that the center number inside the cube that you cannot see is 14. This will help you determine what the corner numbers should be. For example, the number on the top right corner of one of the cube's faces added to the bottom left corner of the opposite face added to 14 should equal 42, since the sum of space diagonals equals the magic number. Another way to put this is that the top right corner added to the bottom left corner on the opposite face should add up to 28. For example, if the top right corner is 19, the bottom left number on the opposite face must be 9, since 19+9+14=42.

• 4

  Arrange the corner numbers so that each of the cube's faces have three even numbered corners and one odd-numbered corner.

• 5

  Arrange numbers so that the central number of each face added to the central number of the opposite face adds up to 28, since when added to the invisible number 14, the three numbers would total 42.

• 6

  Check to see if each row and column on each face adds up to 42. If you need to make further adjustments, write down the values of faces that are close to solved; this will help you remember potential solutions after shifting numbers around.