The Number of Possible Code Patterns on a 15 Disk Omnigraph 

A stack of 15 disks can be
arranged in 15! (15 factorial) ways:
Each disk can be placed on the stack in any of 5 orientations (i.e. rotated with respect to each other by 0, 72, 144, 216, or 288 degrees). Each of the possible disk stack orders can have r ^{(n1)} variations, where n = the number of disks and r = the number of possible rotations, thus the number of variations on each possible stack is:
The total number of distinct stack configurations is:
The number of "message levers" that are extended determines how many different ways the stack can be "played":
Thus, if at least one lever is extended, there are 31 ways to play the stack. So, the total number of distinct patterns possible for a specific set of 15 disks is:

