Difficult Puzzle! Would there be a time at which he was at the same position on the mountain both day?If a mountain climber climbed up a mountain one day from midnight to midnight the next day and does the same thing the following day when coming down the mountain, would there be a time at which he was at the same position on the mountain both day?

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2015-10-18T14:52:40+05:30

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Yes. Since the mountain climber would probably have an irregular rate it would be impossible to know when but he would be at the same spot at some point. If he could walk up and down the mountain at the same time he would have to cross himself at some point, and this would be the time at which he was in the same position
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