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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…
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D18. Domino Design
Posted: 2024-03-01 20:36:30In the arrangement of five dominoes shown in Figure 1, obeying the usual rule that adjacent squares have matching numbers, the two at the end total five spots, and so do the three in the middle. There are three other ways to achieve this, not counting left-right reflections as different. Can you find them?
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D12. Strange Coincidence
Posted: 2023-05-01 13:26:06Let’s listen in on a conversation between siblings divided by math, so to speak: “That’s amazing!” said Mathophila. “The squares of three consecutive positive whole numbers add up to the same number as the squares of the next two numbers.” “Oh, no big deal, that must happen all the time,” replied her brother, Innumeratus. “I…
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D5. Triple Fever
Posted: 2022-05-23 19:12:03Caught up in the excitement of the Derby and the Preakness, a buddy of yours heads to the track, and discovers that today is the running of the Medium-Rare Stakes. Only three horses have been entered: Tee Bone, New York Strip, and Rib Eye. Your buddy then notices the posted odds: Tee Bone is paying…
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D3. Zero Sum Game
Posted: 2022-01-29 16:20:46Is it possible to number the edges of a cube using each of the numbers -6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, and 6 once, so that for every vertex, the sum of the numbers on the edges that meet there is zero? (See figure 1 for a diagram of the…