Sexual dimorphism in intelligence suggests that this phenotype is a sexually selected trait. This view is supported by an overrepresentation (compared to the autosomal genome) of genes affecting cognition on the X chromosome. The aim of this study is to test the hypothesis that sexual selection can explain sex and country-level differences in performance on tests of fluid intelligence. Nationally representative samples from N = 44 countries were obtained from the Programme for International Student Assessment (PISA) Creative Problem Solving (CPS), which evaluates the core of intelligence, that is novel problem solving ability. Sexual selection has the double effect of increasing the prevalence of a favored phenotype and reducing genetic variation in sexually selected traits. Matching these predictions from evolutionary theory, the average country fluid intelligence is positively correlated to sexual dimorphism after partialling out per capita GDP and the latter in turn is inversely correlated to variance in intelligence scores within populations. Males have a higher variance than females but there is a negative correlation between male-female difference in variance and sexual dimorphism in intelligence, suggesting that selection reduces variance more in the selected sex. Average country male height is negatively correlated to sexual dimorphism in intelligence, a fact that supports the notion of a trade-off between physical and intellectual competition in the context of access to females. The results of this study, if replicated, imply that genome-wide association studies of cognition may benefit from a focus on sex chromosomes, which so far have been neglected. Another implication of this study is that intelligence has continued to evolve after different human populations migrated out of Africa and possibly up to the 19th century, as suggested by the substantial variability in sex differences even between neighbouring countries.