Why no walk can cross all seven bridges of Königsberg once: Euler's odd-places rule
30seconds
Seven bridges, two islands, two river banks: in 1700s Königsberg nobody could find a walk crossing each bridge exactly once. Euler didn't search harder, he counted. The number of bridges touching each place settles the question, and you can prove it to yourself.
Walk the map, then build and remove bridges to see exactly when a route appears and when it can't. Along the way you meet the birth of graph theory, and why a single count can beat thousands of trials.
Deep dive · 4 min
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