When faced with a hard problem, break it down into smaller subproblems, and try to simplify the problem. If you're stuck, move on to another problem and return with fresh perspective later.

Hard problems in competitive programming can be daunting, but with the right strategies, you can tackle them effectively. One approach is to break the problem into smaller subproblems. If the problem seems too complex, try to simplify it by removing some constraints or solving a simpler version first. This can help you understand the underlying structure of the problem and identify a pattern or strategy that works. Another strategy is to draw diagrams or sketches if the problem involves graphs, grids, or geometric shapes, as visualizing the problem often leads to new insights. If you're stuck after spending considerable time on a problem, it can be helpful to move on to another problem and return later with a fresh perspective. Sometimes stepping away allows your subconscious mind to work on the problem in the background. Additionally, discussing the problem with peers or looking at hints (if available) can trigger new ideas without directly giving away the solution. Finally, practice is key—many hard problems are variations of common themes, so the more you practice, the more likely you'll recognize these themes in future problems. After solving a tough problem, take time to reflect on your approach and learn from any mistakes, as this will improve your problem-solving abilities over time.