smc

We must place the classes into the periods such that no two classes are in the same period or in consecutive periods. Ignoring distinguishability, we can thus list out the ways that three periods can be chosen for the classes when periods cannot be consecutive: Periods $1,3,5$ Periods $1,3,6$ Periods $1,4,6$ Periods $2,4,6$ There are $4$ ways to place $3$ nondistinguishable classes into $6$ periods such that no two classes are in consecutive periods. For each of these ways, there are $3!=6$ orderings of the classes among themselves. Therefore, there are $4\cdot 6=\boxed{24}$ ways to choose the classes.