After school, I also passed the entrance exam in mathematics at one university. The task was to simplify the algebraic expression. I got the answer - the numerator is zero and some kind of denominator. I had to prove that the denominator is not zero and give an answer: the original expression is simplified to zero. But I took the zero in the numerator as a one (one point in the head!) and began to further simplify the denominator. Because of this, I did not enter this university, worked for a year at the plant, served in the army for two years, and only after that entered the university.
We never know what such experiences can be good for, and I think that it are precisely these disappointments, errors and detours that make us different and that make us to who we are. As you wrote at the beginning - the difference between machine and human.