Despite the rich and interdisciplinary debate on the role of diversity and communication in group problem solving, as well as the recognition of the interactions between the two issues, they have been rarely treated as a joint research topic. In this paper we offer a computational model of agents in teams and we assess the impact of various levels of diversity and communication on individual and collective performance at solving problems. By communication we intend a conversation on the persuasiveness of the features characterizing the problem setting. By diversity we mean differences in how agents build problem representations that allow them to access various solutions. We deploy the concept of diversity along two dimensions: knowledge amplitude, that is the relative amount of available knowledge with respect to the complete representation of a problem, and knowledge variety, that, for a given level of knowledge amplitude, regards differences in knowledge constituents Our results highlight the peculiar role and the interactions between the different sources of variety. Regarding knowledge amplitude, when agents have an incomplete representation of the problem, communication provides just confusion as it is difficult to find a common language for sharing thoughts, and agents perform better alone. Adding knowledge variety to this scenario, effects of communication are even more devastating. Conversely, as the representation of the problem gets more and more complete, communication becomes effective and displays a clear non-monotonic effect: after an optimal point, performance declines very rapidly and gets worse than the individual behavior. In this case, the introduction of knowledge variety further increases performance in teams, since benefits from integrating partial representations of the problem occur more frequently than communication clashes. Finally, highly diverse teams seem to be less sensitive to changes in communication strength, while as diversity declines, even small discrepancies from the optimal communication strength level might account for a strong variability of performance. In particular, overestimation of the required communication effort might cause severe performance breakdowns. Our results suggest that organizations and firms should jointly consider communication intensity and different sources of diversity in teams, since interactions among these variables might result in problem solving groups resembling more a Tower of Babel than an effective and helpful workplace.