A control-rod optimization problem is formulated for a one-dimensional multiregion reactor; that is, the end-of-life state surfaces are formulated in the N-dimensional bumup space, which is an N-dimensional Euclidean space, with its axis corresponding to the macroscopic fission cross section of each region. Solutions for a three-region reactor model are derived by using the principle of optimality. The investigation of these solutions reveals the existence of unique and nonunique solutions, depending on the relationship of end-of-life state surfaces. The relationship between two kinds of solution is discussed.