mountain man aha:!

at 6 a.m. a man starts hiking a path up a mountain. he walks at a variable pace, resting occasionally, but never actually reversing his direction. at 6 p.m. he reaches the top. he camps out overnight. the next morning he wakes up at 6 a.m. and starts his descent down the mountain. again he walks down the path at a variable pace, resting occassionally, but always going downhill. at 6 p.m. he reaches the bottom. what is the probability that at some time during the second day, he is in the exact same spot he was in on the first day?

solution: mountain man

answer: the probability is 100%. the easiest way to see it is, consider that on the second day when the man is going down the mountain, a ghost follows his original pace up the mountain. so even if he varies his pace as he goes down the mountain, at some point in time, he will be in the same spot as the ghost, and therefore, the same spot he was in the day before

Is it just me or is this complete hooey? It only has an "aha" rating of one exclamation point meaning it is not a "trick" question.

My answer is infinity! Provided the man follows the exact same path, he will ALWAYS be in a spot that he was yesterday. There is not enough information to determine if he was ever at the same spot at the same time.

The "answer" seems to only be answering the question "what is the probability that at some time during the second day, he is in the exact same spot he was in on the first day--at the exact same time, subtracting the total amount of time from the time he started down." In other words, if two men follow the exact same path from two directions what is the probability that they will meet? Seems to be an entirely different question, or am I missing something?