Valid entries for the empty slot are 1, 2, 4, and 5. All others are either a mirror image of that starting position or can be duplicated by rotating the triangle 120 degrees.
The starting solution number depends on the empty slot that was chosen since the number of solutions vary depending upon the empty slot. The maximums are:
1 29760 2 14880 4 85258 5 1550
The number of solutions must be at least 1 but no greater than 100.