PUZZLE 3

A Buddhist monk is going up the holy mountain to pray. He sets off at dawn and walks up the long winding path from the bottom of the mountain to the top. He stops every so often to eat the nuts and raisins he has with him. He arrives at the top at dusk. He stays at the top of the mountain all night, praying. At dawn he sets off down again along the same path. The walk down is slightly easier; he doesn’t stop so often and he gets to the bottom late in the afternoon. The question is this: is there any one point on the path that he is at at the same time on both days? So, if he were to look at his watch on day two, would he be able to say "I was here yesterday at exactly this same time"? Note that it doesn’t matter when and where the time/place is, only whether there is such a time and place and how can you demonstrate that there is or isn’t such a time and place?

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