There’s a new site dedicated to Perplex City: The Boardgame and it gives a much clearer picture of what the game is actually like. The general structure seems to be identical to trivial pursuit. The board is made up of multiple colored squares. Each color corresponds to a different category and each puzzle card has a question for each of the six categories. The categories are: Number Trivia, Anagrams, Pot Luck, Odd One Out (pick the thing that doesn’t belong), Word Play (the example looked like a rebus of sorts), and Visual. The goal is to collect a stone (much like a pie wedge) for each category.
In general, of course, the puzzles are easier than they are on many of the cards, as most are designed to be answered in less than a minute. There’s even a timer to hold you to it.

