Numerous recent studies have investigated how animals solve means-end tasks and unraveled considerable variation in strategies used by different species. Domestic dogs (Canis familiaris) have typically performed comparably poorly in physical cognition tasks, but a recent study showed that they can solve the on-off condition of the support problem, where they are confronted with two boards, one with a reward placed on it and the other with a reward placed next to it. To explore which strategies dogs use to solve this task, we first tested 37 dogs with the on-off condition tested previously and then tested subjects that passed this condition with three transfer tasks. For the contact condition, the inaccessible reward was touching the second board. For the perceptual containment condition, the inaccessible reward was surrounded on three sides by the second board, but not supported by it, whereas for the gap condition, discontinuous boards were used. Unlike in the previous study, our subjects did not perform above chance level in the initial trials of the on-off condition, but 13 subjects learned to solve it. Their performance in the transfer tasks suggests that dogs can learn to solve the support problem based on perceptual cues, that they can quickly adopt new cues when old ones become unreliable, but also that some apparently inherent preferences are hard to overcome. Our study contributes to accumulating evidence demonstrating that animals typically rely on a variety of perceptual cues to solve physical cognition tasks, without developing an understanding of the underlying causal structure.