Jack Murtagh
- Indexed articles, last 90 days
- 8
- Latest publication
- Sep 26, 2026
- Outlet visibility, for Scientific American
- Top 50K sites
- Earliest in this view
- Jul 13, 2026
Latest articles
Math Puzzle: What is the longest sequence of captures in checkers? (opens the original)
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Math Puzzle: What is the longest sequence of captures in checkers? In American checkers rules, pieces only occupy the dark squares of an 8 x 8 checkerboard, and pieces can capture neighboring opposing pieces by jumping over them. A regular piece can capture an opposing piece when it is diagonally adjacent to that piece and the square directly beyond the to-be-captured piece is vacant. If capturing a different piece from this new square is legal, then the piece continues capturing until no furthe
OpenAI cracks the hidden math that keeps your texts from turning to gibberish (opens the original)
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The hidden math that keeps your texts from turning to gibberish The surprising real-world applications of high-dimensional sphere packing and the 48-year-old barrier that OpenAI just broke Spill your piggy bank on the table and try to lay out as many quarters as you can. Quarters must lie flat; they can touch at their edges as long as they don’t overlap. What’s the most efficient way to squeeze the maximum number of quarters into the space? If the tabletop extended infinitely in all directions,
Math Puzzle: A curious sequence (opens the original)
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Math’s “look-and-say” sequence goes: 1, 11, 21, 1211, 111221, 312211, 13112221, ... Each entry describes the one before it. We start with 1, then observe “we have one 1” and encode that as the next entry: 11. Now we have two 1s, encoded as 21. That in turn contains one 2 and one 1: 1211, and so forth. Which digits from 1 to 9 never appear in any number in the look-and-say sequence? You can start similar sequences with positive integers other than 1. For example, starting with 4445 yields the seq
Math Puzzle: A Tetris paradox (opens the original)
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In Tetris, players try to efficiently pack a rectangular space with pieces that can have seven different shapes. As it happens, if you have exactly one of each of those seven possible pieces, then it is impossible to arrange them into a rectangle. But there is one piece you can discard that will allow you to make such an arrangement. Which piece must be discarded? Find any rectangular arrangement of the remaining six pieces. Just as in Tetris, you may rotate pieces but not reflect them. In other
How the ‘happy ending problem’ launched a new branch of math—and a romance (opens the original)
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How the ‘happy ending problem’ launched a new branch of math—and a romance A puzzle about dots on a page led to one of the most profound areas of modern math In the early 1930s a group of bright university students held gatherings in Budapest to discuss math. Among them was Paul Erdős, an eccentric prodigy who would go on to become the most prolific mathematician in history. Other attendees included mathematicians George Szekeres and Esther Klein. One day Klein presented a puzzle to her friends:
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