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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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D27. Penned Out
Posted: 2025-05-12 00:31:31 Solutions will be accepted through 2025 Jul 15Figure 1 (below left) shows a perfect two-point perspective diagram of Farmer Nell’s red-roofed barn and precisely square pigpen in front of it. (“Two-point perspective” means that all lines that are vertical in three dimensions appear perfectly vertical in the diagram, while any two parallel horizontal lines intersect on the horizon line N E .)…
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D26. Aperiodic Partition
Posted: 2025-05-12 00:14:04 Solutions will be accepted through 2025 Jul 15(with thanks to Kate Stange, University of Colorado) Recall that an (infinite) arithmetic progression is the set of all numbers of the form a + n d , where a and d are fixed and n is any natural number. For example, 5, 8, 11, 14, … , and so on forever, is an arithmetic…
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D25. Whodunni’s Shuffle
Posted: 2025-05-12 00:05:48 Solutions will be accepted through 2025 Jul 15Our frequent contributor Prof. Stewart is back with a bit of permutation prestidigitation: The great stage magician Harry Whodunni shuffles a pack of (more than two) cards in the following simple way: he moves the top card to the next-to-bottom position, and then turns the whole pack over (which has the side effect of turning…