Connect three houses to three utilities without any line crossing
Three houses each need a line running to three separate utility companies — water, gas and electricity. Can you draw all nine connecting lines on a flat sheet of paper so that no two lines ever cross?
Reveal the answer
No — it's mathematically impossible on a flat plane, though it becomes possible on a surface with a hole in it, like a doughnut. Henry Dudeney included the puzzle in his 1917 collection Amusements in Mathematics, and its impossibility became a founding example in graph theory, since it's equivalent to showing the graph K3,3 isn't 'planar.'
— Henry Dudeney, Amusements in Mathematics — 1917 — public domain
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