Optimal solution found for the most fragile picture-hanging arrangement

Mathematicians have solved a puzzle about hanging a painting on multiple nails so that removing any one causes it to fall. They reduced the number of string wraps for a four-nail, two-removal scenario from 80 to the absolute minimum of 16, using computer verification. The result provides the shortest known explicit solutions for a family of such problems.
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Original headline: “Mathematicians discover the worst way to hang a painting.” Browse more stories.