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The missing square puzzle is an optical illusion used in mathematics classes to help students reason about geometrical figures; or rather to teach them not to reason using figures, but to use only textual descriptions and the axioms of geometry. It depicts two arrangements made of similar shapes in slightly different configurations.
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Unlike other puzzle books, each page is involved in solving the book's riddle. Specifically, each page represents a room or space in a hypothetical house, and each room leads to other "rooms" in this "house". Part of the puzzle involves reaching the center of the house, Room #45 (page 45 in the book), and back to Room #1 in only sixteen steps.
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Generally, most American puzzles are 15×15 squares; if another size, they typically have an odd number of rows and columns: e.g., 21×21 for "Sunday-size" puzzles; Games magazine will accept 17×17 puzzles, Simon & Schuster accepts both 17×17 and 19×19 puzzles, and The New York Times requires diagramless puzzles to be 17×17. [90]
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Named after the number of tiles in the frame, the 15 puzzle may also be called a "16 puzzle", alluding to its total tile capacity. Similar names are used for different sized variants of the 15 puzzle, such as the 8 puzzle, which has 8 tiles in a 3×3 frame. The n puzzle is a classical problem for modeling algorithms involving heuristics.
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