Originally Posted by

**Yuuki** So for *a given starting condition*, there would be only be one Dn instead of n+1.

For example, if I denote the people A, B, C, X (X being the invisible person), and assign chairs 1, 2, 3, 4 to them respectively,

either 1) X sits in #4 the second time 2) X doesn't sit in #4 the second time, so in fact there are only Dn + Dn+1 possibilities, since the problem is only asking me to count the ways for one initial condition.

If I took in account all the initial conditions, would there be n!(Dn + Dn+1) possibilities?