Intelligence is an ability to design a solution to a problem one has never solved before, and express that using a language (including symbolic). BTW: this is what AI professionals do not want to admit. The most general approach for designing a solution is scientific thinking. One of the crucial features of it is learning from mistakes.
Teaching how to learn from mistakes separates common mass education from the actual/"elite" one.
Recently I saw a publication about a "three-problem intelligence test" invented by an MIT professor. Those problems are from my list, too, and they have nothing to do with intelligence, and everything to do with having a good teacher.