I've decided to go with the Logic Puzzle approach to Sunday's session. I've been looking for resources to suggest ways to construct logic puzzles, but thus far the algorithm seems to be "create the grid, create a clue, add clues until you can solve the puzzle yourself." Not terribly creative, but effective. It is also possible that I can simply hijack an existing puzzle online by replacing their category names with my own.
This latter option is the one I find myself admitting I would suggest to somebody else, which is usually my prime indicator that I should embark on that path. To that end, I found a site, http://www.logic-puzzles.org, which simply has an archive of logic puzzles known to be solvable in about 5-10 minutes. Now I just need to select one, replace the names of the categories with categories from my game, determine how to word in-game documents to contain the clues properly, and do the rest of the footwork to have this particular exercise ready to go for Session 11.
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