Something about this concept—two sets of synonyms (PUB and BAR, QUIZ and EXAM), which when paired together, form phrases that themselves are not synonyms (PUB QUIZ and BAR EXAM)—captured the minds of Crosscord.
If you’re a creative person, square theory is a useful framework to keep in mind. If you’re coming up with a title for a paper or a brand name, try to see if you can think of one that completes the square. If you’re writing puns for a popsicle stick or a Laffy Taffy wrapper, you can use squares to model your setups and punchlines. If you’re constructing a crossword, consider whether your theme or your question mark clues can form squares.