David Leonhardt’s “A Quick Puzzle to Test Your Problem Solving” is quick, interesting, and useful. If I say anything more, I might give away the puzzle’s solution before you have a chance to try to solve it yourself, and you don’t want that. In fact, philosophy, thinking for yourself, and learning in general is like that: try to solve the puzzle on your own before you ask for the solution.

A “valid” argument is one in which the conclusion follows logically from the premises regardless of whether the premises and/or the conclusion happens to be true or false. An “invalid” argument is one in which the conclusion does not follow logically from the premises even if the conclusion happens to be a true statement. A conclusion may be true or false regardless of whether it follows from a valid argument or not.  Got it? See if you can spot the valid and invalid arguments in this “valid or invalid” quiz. Warning: a favorite trick of logicians is to test students with some valid arguments that have false conclusions and some invalid arguments that have true conclusions.