Video instruction has been widely studied and is generally considered as effective as live instruction for teaching scientific concepts and procedures. However, there is limited research on the effectiveness of prerecorded videos for teaching more challenging content. This study conducted a controlled experiment on over 300 high school students to compare the effectiveness of live instruction versus recorded video in teaching physics problem solving, a representative example of challenging content. Our results indicate that for simpler problems, there is no significant difference in student learning outcomes between live and video instruction, corroborating previous research. However, as problem complexity increases, live instruction significantly outperforms video instruction, potentially highlighting the importance of real-time adaptability, engagement, and sustained attention in face-to-face settings. We found a negative correlation between the effectiveness of video instruction and the difficulty level of the content. This study is the first to empirically investigate the use of video instruction for complex problem solving, making a significant contribution to the current body of literature. Additionally, the findings offer practical insights for school administrators or department heads, suggesting that while video instruction can effectively substitute for live teaching in simpler scenarios, live instruction remains crucial for more complex material, impacting decisions related to human resource allocation and instructional planning.