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I got paid minimum wage to solve an impossible problem
(tiespetersen.substack.com)
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In retrospect it's pretty obvious that the most efficient way to traverse a grid would include no diagonals. Every time you move on an axis you move to a cell in 1 unit distance of travel. Why would you ever choose to move to a cell in √2 unit distances when you could move 1 unit distance to achieve the same result of covering one more cell?