Eukaryotic cells form organelles to achieve specific local chemical concentrations and conditions. In addition to membrane-bound organelles, cells possess non-membrane-bound bodies, which are now understood as phase-separated condensates. Typically, the components of these condensates have a high turnover rate and the condensates themselves are dynamic, assembling and disassembling in response to specific stimuli. We focus on a class of condensates composed of two species of polymers, where each polymer consists of repeated domains that interact in a one-to-one fashion with the domains of the other polymer. Condensates of this class are observed in living cells and in some in vitro experiments. Through analytical and numerical studies, we determined a phase diagram for such two-component polymer systems. Strikingly, the formation and dissolution of the condensates sensitively depends on the valencies of the two components, exhibiting a "magic-number" behavior. This magic-number effect provides a possible mechanism to explain the rapid dissolution and reorganization of the pyrenoid, a non-membrane-bound carbon-fixation organelle in algal cells. We examined the robustness and generality of the magic-number effect, including the importance of the rigidity and shape of the polymers, the dependence on valency, the influence of the relative concentrations of the two species, and the role that non-specific interactions play in condensate formation. To more closely relate to experimental systems, we built an off-lattice model that includes the effect of molecular sizes, molecular non-specific interactions, and bond affinities. The modeling of the algal pyrenoid provides important insights into the structure, regulation, and inheritance of this non-membrane-bound organelle. More broadly, our findings give insights into fundamental principles of the architecture and inheritance of such liquid-phase organelles.