Groups can be very successful problem-solvers. this collective achievement crucially depends on how the group is structured, that is, how information flows between members and how individual contributions are merged. numerous methods have been proposed, which can be divided into two major categories: those that involve an exchange of information between the group members, and those that do not. Here we compare two instances of such methods for solving multi-dimensional problems: (1) transmission chains, where individuals tackle the problem one after the other, each one building on the solution of the predecessor and (2) groups of independent solvers, where individuals tackle the problem independently, and the best solution found in the group is selected afterwards. By means of numerical simulations and experimental observations, we show that the best performing method is determined by the interplay between two key factors: the individual's degrees of freedom as an aspect of skill and the complexity of the problem. We find that transmission chains are superior either when the problem is rather smooth, or when the group is composed of rather unskilled individuals with a low degree of freedom. on the contrary, groups of independent solvers are preferable for rugged problems or for groups of rather skillful individuals with a high degree of freedom. Finally, we deepen the comparison by studying the impact of the group size and diversity. our research stresses that efficient collective problem-solving requires a good matching between the nature of the problem and the structure of the group. Collective problem-solving and the related concepts of swarm intelligence and collective intelligence have been studied in a wide variety of domains. In biological systems, examples include the nest construction in eusocial insects 1,2 or collective foraging in group-living species 3. In robotics and artificial intelligence, swarms of relatively simple agents can explore and solve optimization problems efficiently 4,5. Likewise, humans can solve problems in groups during discussions 6 , by means of wisdom of crowds procedures 7 , or when creating Wikipedia articles 8,9. Despite this considerable diversity of examples and application domains, many instances of collective problem-solving come down to one central challenge: When given a specific number of individuals with a certain skill set, how should a group be structured to produce the best possible collective output? Numerous procedures have been proposed to that end. These can be divided into two major categories 10,11 : (1) those that involve an exchange of information between the group members, and (2) those that do not. In the first category, direct or indirect interactions among individuals can lead to the emergence of a collective solution 12-14. With direct interactions, group members exchange information directly via physical signals. Group-living animals, for example, communicate by means of acoustic and visual cues to detect and avoid predators 15-17. In human groups, t...