Some argue that the high heritability of IQ renders purely environmental explanations for large IQ differences between groups implausible. Yet, large environmentally induced IQ gains between generations suggest an important role for environment in shaping IQ. The authors present a formal model of the process determining IQ in which people's IQs are affected by both environment and genes, but in which their environments are matched to their IQs. The authors show how such a model allows very large effects for environment, even incorporating the highest estimates of heritability. Besides resolving the paradox, the authors show that the model can account for a number of other phenomena, some of which are anomalous when viewed from the standard perspective.