In industry or in education, everyone keeps bringing up the importance of problem-solving skills. But what ARE some of them? After facing - and solving - problems on a continuing basis for over thirty years. a computer scientist proposes an initial solution, one which raises an even harder problem: What is the Pedagogy of Computer Science? How can such a new and complex subject be organized and taught so as to best unify its subject-matter and provide its students and its professionals with the best tool-box for dealing with problems? Over 40 curious "case studies" are presented, mostly from real-world industrial experience. Some will seem curiously antique, but then there are algorithms still in use after being invented over 2200 years ago. Ridiculous challenges due to machine or system limitations, absurdly difficult puzzles faced by co-workers, mistakes in the most unexpected places.... And a goodly number of answers, too: Why it is so important to learn LONG DIVISION. Why computers can't add. The theory which forms the nucleus of all video games. And especially a fascinating selection of errors, cautions, and the even more remarkable errors which aren't errors at all, but lampposts to larger truths - the sort of thing only a Chestertonian knows, one who has travelled with Milo in the Lands Beyond for the sake of Rhyme and Reason, and the strengthening of the Kingdom of Wisdom.