Category Archives: problems and puzzles

The Chromatic Number of Liechtenstein

Four colors suffice for any planar map: We’ve known that since 1977. If a map is divided into countries or provinces or other regions, and you want to color the map so that no two adjacent regions have the same … Continue reading

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Hung over

The drawing below, brazenly swiped from a 1964 Martin Gardner column, illustrates the solution to a well-known puzzle. If you stack n bricks on a table, how far can you make them extend over the edge without toppling? The answer … Continue reading

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Twenty-six twiddles suffice

Among the 250 million Rubik’s cubes manufactured since 1980, how many lie abandoned in a scrambled state, having never regained their original configuration since being taken out of the box? Most of them, I would guess. Now comes word that … Continue reading

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Working on the railroad

The March-April issue of American Scientist is now available on the Web; paper copies should be on their way soon. My column is about hump yards and turnouts and wyes—in other words, about algorithms for railroad workers. “Computing with locomotives … Continue reading

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Jacobsthal numbers, part 3

Our story so far: Having stumbled upon the Jacobsthal numbers, 1, 3, 5, 11, 21, 43, 85, 171, 341,…, I idly asked, “Who was Jacobsthal?” Keith Matthews promptly responded with a wealth of biographical information, even arranging to have an … Continue reading

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