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The following may not quite count as "everyday life," but in the 2013 MIT Mystery Hunt, one of the most elaborate team puzzle-solving contests in the world, one of the puzzles involved solving a crossword on the surface of a CW complex. As explained in the solution, to figure out which edges were identified, you had to complete the grid; this caused the dotted lines on the surface to join up into loops, and you had to figure out which loops were trivial. No algebraic topology is really needed to solve the puzzle, but it is needed to prove the correctness of the intended solution.