Magic Constant Paths

Description

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 pandiagonal, bent diagonal, and zigzag.

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).

Variations

There are many variables, including:

alignment
On which cell is the 'first' crest?
direction
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?
number
How many paths are there?

REFERENCES