Problem solving from a distributed cognitive system perspective is an emergent product of the strategic and opportunistic manipulation of artefacts populating a physical space. In the present study, insight problem solving was investigated with matchstick algebra problems. Participants were split in two groups. In the first, the paper group, they examined a static two-dimensional representation of the false algebraic expressions and told the experimenter which matchstick should be moved. The non-interactive procedure was similar to the one employed in Knoblich, Ohlsson, Haider, and Rhenius (1999). In the second group, the interactive group, participants manipulated a concrete three-dimensional representation of the false equations. Solution rates for participants in the interactive group were significantly higher than in the paper group. Problem solving success in the paper group was best predicted by performance on a numeracy test, whereas in the interactive group, it was best predicted by performance on a visuo-spatial reasoning test.