Let E(x) denote the expectation of x, in other words the answer to this problem.

E(x)=(1+E(x))/6 + (2+E(x))/6 + (3+E(x))/6 + (4+E(x))/6 + (5+E(x))/6

E(x)=(15+5*E(x))/6

E(x)=15

Thanks to Nick Hobson for suggesting a similar problem.

Michael Shackleford, A.S.A.