We conducted three experiments on social problem solving by chimpanzees, Pan troglodytes. In each experiment a subordinate and a dominant individual competed for food, which was placed in various ways on the subordinate's side of two opaque barriers. In some conditions dominants had not seen the food hidden, or food they had seen hidden was moved elsewhere when they were not watching (whereas in control conditions they saw the food being hidden or moved). At the same time, subordinates always saw the entire baiting procedure and could monitor the visual access of their dominant competitor as well. If subordinates were sensitive to what dominants did or did not see during baiting, they should have preferentially approached and retrieved the food that dominants had not seen hidden or moved. This is what they did in experiment 1 when dominants were either uninformed or misinformed about the food's location. In experiment 2 subordinates recognized, and adjusted their behaviour accordingly, when the dominant individual who witnessed the hiding was replaced with another dominant individual who had not witnessed it, thus demonstrating their ability to keep track of precisely who has witnessed what. In experiment 3 subordinates did not choose consistently between two pieces of hidden food, one of which dominants had seen hidden and one of which they had not seen hidden. However, their failure in this experiment was likely to be due to the changed nature of the competition under these circumstances and not to a failure of social-cognitive skills. These findings suggest that at least in some situations (i.e. competition with conspecifics) chimpanzees know what conspecifics have and have not seen (do and do not know), and that they use this information to devise effective social-cognitive strategies. Copyright 2001 The Association for the Study of Animal Behaviour.