the monk walks up a mountain-
 

Can someone give me a brief rundown of the proof for the monk walks up a mountain question?

The basic is- a monk walks up a mountain starting at time x and ending at time y - the next day he leaves to go down the mountain by the same path, again starting at time x and returning home at time y. Prove that he crosses the same point at the same time at least once.

Re: the monk walks up a mountain-
 

If you graph the monk's position versus the time of day, for both days, on the same graph, the lines should cross at least once.

Re: the monk walks up a mountain-
 

The best way to see the answer is to imagine that there are two monks- one at the top and one at the bottom of the mountain. One starts walking up the mountain at X, and one starts to descend at time X. Assuming that there is only one path along the mountain, then at some time between X and Y the two monks must cross one another's path i.e. they occupy the same point at the same time in the day. QED as they say.

John