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D28. Tile Troubles
Posted: 2025-05-12 00:41:04 Solutions will be accepted through 2025 Jul 15Dr. Arsalan Wares’ letter this month is beautiful, as always, but sadly recounts a tale of honeycomb horror. The diagram in Figure 3 depicts a portion of a tiling of the plane by regular hexagonal tiles. All line segments shown have endpoints at the vertices of the tiling. Dr. Wares woke up one morning to…
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D19. Covid Conundrum
Posted: 2024-03-01 20:39:35Suppose you stood on line as part of a group of 30 people waiting to receive a vaccine. After everyone finished, you were told that ten members of the group turned out to have cases of Covid. You never came down with the infection, so you couldn’t have been one of the ten. If you…
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D11. Octosection
Posted: 2023-05-01 13:09:45Square A B C D in Figure 1 has been dissected into eight equal-area rectangles. The width of the rectangle shaded red in Figure 1 is 35 units. What is the area of square A B C D ? For a bonus challenge, can you devise and solve a similar problem that dissects a square…
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D6. Rectangle Pinwheel
Posted: 2022-05-26 12:09:13The outermost polygon shown in figure 2 as the region shaded in pink consists of 16 congruent rectangles placed so that their edges align (and vertices of four of the rectangles coincide at the center of the polygon). We call this polygon a 28-gon because it has 28 edges: the line segments that make up…