Hexagram Triage

Any hexagram may be transformed into any other by changing certain lines.  A hexagram with between 1 and 5 moving lines divides all other hexagrams into three groups:  those that are formed by changing all combinations of moving lines, those that are formed by changing all combinations of non-moving lines, and those that may only be formed by changing a combination of moving and non-moving lines.

For example:  if lines 1, 2, and 4 are moving, the combinations of moving lines are 1, 2, 1&2, 4, 1&4, 2&4, and 1&2&4.  The combinations of non-moving lines are 3, 5, 3&5, 6, 3&6, 5&6, and 3&5&6.  The other combinations are those such as 1&3.  Note that the steps of change and transitional hexagrams are subsets of the first group.

One could call the hexagrams formed by changing the moving lines “positive,” those formed by changing the non-moving lines “negative,” and the rest “mixed,” although these terms refer only to which group of lines are changed, not the content of the hexagrams themselves.

 movinglines negative mixed positive 0 63 0 0 1 31 31 1 2 15 45 3 3 7 49 7 4 3 45 15 5 1 31 31 6 0 0 63

In general, for n moving lines, the number of positive hexagrams is 2n - 1, the number of negative is 26-n - 1, and the number of mixed is 63 - (2n - 1) - (26-n - 1).

Here is an example.  For hexagram 51 with moving lines 1 and 3, the positive hexagrams are 16, 55, and 62; the negative hexagrams are 3, 10, 17, 19, 21, 24, 25, 27, 38, 41, 42, 54, 58, 60, and 61; and the mixed are all the rest.