I've recently started studying statistical inference. I've been working through various problems and this one has me completely stumped.
Let $X_1,\dots,X_n$ be a random sample from a discrete distribution which assigns with probability $\frac{1}{3}$ the values $\theta-1,\space\theta,\space\text{or}\space\theta+1$, where $\theta$ is an integer. Show that there does not exist a complete sufficient statistic.
Any ideas?