Source: Nash Equilibrium's derivative also, in Martin's Gardener My best Mathematical and Logical Puzzles
Problem: One morning at6 am , a monk began climbing a tall mountain, which happened to only have one path to the top. He ascended the path at his leisure, taking some stops along the way. He reached the top at 8 pm .
Problem: One morning at
The next morning at 6 am , the monk descended the mountain along the same path. He took several breaks along the way, and reached the bottom at 8 pm .
The amazing result: there is some spot on the path that the monk occupied at precisely the same time of day for both trips. Why is this?
This is true even if the monk took breaks to meditate, chatted it up with a fellow traveler, or if he took some time to massage his feet. You get the point: it really does not matter what he did during the trips going up or down.
superimpose the two trips into a single day.
ReplyDeleteThat is, imagine instead that two monks are taking the journey on the same day, one climbing up and the other climbing down. Now it is clear that no matter how each monk takes the trip, there has to be some spot where they cross paths.
Now pretend those trips happened on two separate days and you have your answer–the monk is at the same spot on the path at precisely the same time of day for both trips.