The problem of the equilibrium state of an isolated composite system with a movable internal adiabatic wall is a recurrent one in the literature. Classical equilibrium thermodynamics is unable to predict the equilibrium state, unless supplemented with information about the process taking place. This conclusion is clearly demonstrated in this article. In addition, some simple methods for estimating the constrained equilibrium point are proposed. These methods are accessible to first- or second-year college students; they provide physical insights, and constitute a good practice of basic principles and relations of thermodynamics. (Contains 1 figure and 3 tables.)