It is no doubt that these type of problems are very different to problems one would find in a maths textbook. I find them extremely challenging even after done a Master degree in mathematics. However, the solutions make a lot of sense after reading them. I am coaching a high school student in these problems at the moment and she is getting a lot of them wrong despite being the top in her (normal) math class and started math tuition very young at 2 years of age. My question is to be successful at doing these problems, is coaching necessary? Are there kids who can do these problems without coaching and without having done them in the past (e.g without having read many solutions to these problems)? My feeling is no since this is like saying are there kids who can play the piano without a teacher and without reading piano instruction books. Is this analogy correct or not?