This paper treats the problem of maximum stiffness topology optimization for discrete structures and makes two extensions to include unilateral contact. It is demonstrated how a saddle point approach to these problems gives a clear and concise theory which results in simple proofs of existence of a solution and optimality conditions. The extensions to include unilateral contact are, firstly, the direct one where unilateral contact conditions are simply allowed alongside classical boundary conditions and, secondly, a problem where initial gaps between contact nodes and obstacles are treated as design variables in addition to the volume ones.