Sometime on Monday, a climber ascends a mountain. Sometime on Tuesday, the climber descends from the mountain. Suppose the climber uses the same path going up as going down. Show that there is at least one point on the mountain where the climber spent the exact same time of day going up and going down.
Show that there are always two places on the Equator that are directly opposite from each other (that is, the line connecting them passes through the center of the Earth), and that have the same temperature.
I give up, show me the solution.
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