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For the sake of this challenge, you can assume that the world behaves nicely (everything is continuous, differentiable etc, the world is a sphere blah blah blah) but figurative bonus points if you assume fewer things. If you're looking for a bigger challenge check out Challenge 10b.
The Challenge: Show that at any point in time there exist two points on exact opposite sides of the Earth which have the exact same temperature.
The Challenge: Show that at any point in time there exist two points on exact opposite sides of the Earth which have the exact same temperature.