I agree with this. It really is putting on a show. Ideally you get a problem that you are familiar with. Even more so if you know the exact problem and optimal

I agree with this. It really is putting on a show. Ideally you get a problem that you are familiar with. Even more so if you know the exact problem and optimal solution. If not exactly, then at least similar to something you've solved before. Then you put on a show acting as if this is the first time you're seeing the problem. With practiced confidence, you roughly outline a naive solution, then quickly and smoothly iterate your way to the ideal optimal solution. All the while explaining your "thought processes" as if you serendipitously saw the solution materialize before your eyes. By practicing (say, grinding leetcode), you ensure that you have the confidence to smoothly put on this show, and also not waste your precious interview minutes meandering down suboptimal dead-end paths.