We humans are capable of solving challenging planning problems, but the range of adaptive strategies that we use to address them are not yet fully characterized. Here, we designed a series of problem-solving tasks that require planning at different depths. After systematically comparing the performance of participants and AI planners, we found that when facing manageable problems that require planning to a certain number of subgoals (from 1 to 6), participants make an adaptive use of their cognitive resources - namely, they tend to select an initial plan having the minimum required depth, rather than selecting the same depth for all problems. When facing more challenging problems that require planning up to 7 or 8 subgoals, participants tend to select a simpler (greedy) strategy wherein plans consider only the next 1 or 2 subgoals. Furthermore, we found a strong similarity between how different participants solve the same problems. These results support the view of problem solving as a bounded rational process, which adapts costly cognitive resources to task demands.