One mystery solved
It took me for too long to figure out the trick. The magic that is used by people teaching mathematics. Not that mathematics is magical. Rather that we continue to provide a magical trick to virtually every student and then wait for them to figure it out. If you are still in school here is the shortcut. Every single mathematical question in your textbook has an answer. That does not mean that every single mathematical question in the world has an answer. Two different things. When you sit down and try to decipher the questions on the page before you will be aware that every one of them can be answered by a thinking human being. Perhaps not you. Do not tear out your hair if you are one of those that has not consolidated the knowledge necessary. There is a risk of going bald. I look back on my years in school and realize that every single subject with the exception of mathematics made sense. Every course came with a message to the madness. With the exception of mathematics. There someone was waiting for a student to figure out the puzzle. Hoping they would stay on message long enough to keep from going wild in the classroom. It took me years because I believed that there were not answers. Only when I went to work in the school system did I discover secret texts. The teachers kept them hidden away and the title made it blindingly clear. The book of solutions. I learned far too late to help me that every question on the page had already been answered and that someone had put forth the methodology. The teachers go to great lengths to keep that part a secret. In the same way that a magician swears to not reveal how his trick works. We are told that mathematics is there to build the mind. It might if you live long enough. At some point there will be a moment when it becomes clear to you that all of your labour is for not. That’s a nice way of saying 0. Also a way to explain chords time together. But I digress. Any magical trick keeps thousands and thousands of young people chained to their desks without revolt is legendary. Go ahead. Try to remember a single problem that was presented to you that did not have an answer. At a guess the best you will do is to realize that you had not found the answer. Think back to that small subset of people who seemed to get math in high school. They were the ones that had figured out early on in the game that the answer was irrelevant. This was just something to make them search for an answer.