Humans are nature's most intelligent and prolific users of external props and aids (such as written texts, slide-rules and software packages). Here we introduce a method for investigating how people make active use of their task environment during problem-solving and apply this approach to the non-verbal Raven Advanced Progressive Matrices test for fluid intelligence. We designed a click-and-drag version of the Raven test in which participants could create different external spatial configurations while solving the puzzles. In our first study, we observed that the click-and-drag test was better than the conventional static test at predicting academic achievement of university students. This pattern of results was partially replicated in a novel sample. Importantly, environment-altering actions were clustered in between periods of apparent inactivity, suggesting that problem-solvers were delicately balancing the execution of internal and external cognitive operations. We observed a systematic relationship between this critical phasic temporal signature and improved test performance. Our approach is widely applicable and offers an opportunity to quantitatively assess a powerful, although understudied, feature of human intelligence: our ability to use external objects, props and aids to solve complex problems.