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American Focus > Blog > Tech and Science > Math Puzzle: Wrangle the Rectangles
Tech and Science

Math Puzzle: Wrangle the Rectangles

Last updated: December 21, 2025 10:45 pm
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Math Puzzle: Wrangle the Rectangles
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The puzzle presented involves nine rectangles labeled A, B, C, D, E, F, G, H, and I, which overlap each other in various configurations. The relationships between the rectangles are denoted by shorthand notations, such as A\(D, F) indicating that rectangle A intersects rectangles D and F.

Further relationships between the rectangles are described as follows:
– B\(F, G)
– C\(G, H)
– D\(A, H)
– E\(H, I)
– F\(A, B, I)
– G\(B, C, I)
– H\(C, D, E)
– I\(E, F, G)

The task at hand is to correctly label each rectangle with the corresponding letters A to I based on the given information. By analyzing the relationships and intersections between the rectangles, it becomes apparent that only the four blue-shaded rectangles (F, G, H, and I) intersect with three other rectangles.

H is identified as the topmost blue-shaded rectangle that does not intersect with F, G, or I, while I intersects both F and G. This information allows for the identification of additional rectangles, such as B and E, based on their intersections with F, G, H, and I.

By following the logic and relationships between the rectangles, the correct labeling of all nine rectangles can be determined. The solution to the puzzle reveals the positioning and relationships of each rectangle within the overlapping configuration.

This challenging puzzle not only tests logical reasoning and spatial awareness but also provides an engaging exercise in problem-solving. Readers are encouraged to attempt the puzzle themselves and share their experiences by reaching out to the provided email address.

The original puzzle was sourced from Spektrum der Wissenschaft and is presented here with permission. For more engaging puzzles and intellectual challenges, stay tuned for future content updates.

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