Magic Constant Paths
There are many paths that can sum to the magic constant.
The minimum requirement is all rows, all columns, and the two main diagonals.
Some other commonly referred to groups of paths are
bent diagonal, and
The paths can be thought of as triangle wave patterns of different
heights from 0, (the rows and columns), to n - 1, (the main diagonals).
There are many variables, including:
- On which cell is the 'first' crest?
- Does the 'first' crest point left, right, up, or down?
- wave height
- How many row or column boundaries are crossed from trough to crest?
- wave length
- How many row or column boundaries are crossed from crest to crest?
- path length, segment length
- How many row or column boundaries are crossed from start to end?
For an entire path, (summing to the magic constant), this is n - 1.
- homogeneous or mixed
- Do the waves of the path all have the same height?
- How many paths are there?