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There are three different types of symmetrical puzzles that may be created:
Cross-Symmetrical
There is about a 33% chance that the puzzle will be symmetrical about the two diagonals between the corners of the puzzle.
Plus-Symmetrical
There is about a 33% chance that the puzzle will be symmetrical about the two bisectors between the midpoints of the puzzle edges.
Origin-Symmetrical
There is about a 33% chance that the puzzle will be symmetrical about the origin (center) of the puzzle, meaning that if rotated 180 degrees the puzzle will maintain its shape.
Symmetrical puzzles are more aesthetically pleasing than Random puzzles which is why they are far more common in puzzle books and newspapers. However, they do typically take slightly longer to converge on a solution of higher skill level than Random puzzles do.
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