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mountain man

I guess I don't really understand the point of the question. Of course if you walk a path one and then walk it back you'll be in the same spot. It doesn't seem worded properly or maybe it's just a "duh!". On what read you immediately think 100% but think there must be something more because that is too obvious. What am I missing?

pb
Thursday, October 10, 2002

Let me try that again:

I guess I don't really understand the point of the question. Of course if you walk a path one way and then walk it back you'll be in the same spot at some point. It doesn't seem worded properly or maybe it's just a "duh!". On one read you immediately think 100% but then think there must be something more because that is too obvious. What am I missing?

pb
Thursday, October 10, 2002

The question isn't perfectly clear unless you're thinking about puzzles.

What the question asks is "What is the probability
that at some time during the second day, the
mountain man is in the same place that he was
in on the first day, at the same time both days.

Fred Garber
Thursday, October 10, 2002

If that's the case, then my answer would something like "infintessimally small probability".

pb
Monday, October 14, 2002

Yet the correct answer is 100%

Bill
Monday, October 21, 2002

Think of it this way. Suppose walking up the mountain is the same as moving from (0,0) to (1,1) on a Cartesian graph. Suppose walking down the mountain is the same as moving from (0,1) to (1,0) on the same Cartesian graph. (That is, the vertical axis represents a position on the mountain and the horizontal represents the time.)  Then it's pretty clear that at some point, the line from (0,0) to (1,1) will cross the line from (0,1) to (1,0). The point of intersection represents when he is at the same position at the same time but on two different hikes.

Hugh Brown
Wednesday, October 23, 2002

Or also: Imagine that you start walking up the mountain at a certain time of the day. Exactly at the same time, your alter-ego is at the top of the mountain and starts walking down. Both of you will follow the same path. There's no way you could avoid meeting your alter-ego somewhere along the way!

Bill
Wednesday, October 23, 2002

The whole trick of the question is that the wording encourages you to consider the same person hiking up one day and down another day.

However, if you want to make it easier on yourself, just imagine two people hiking on the same day. Hiker A is going up the mountain, Hiker B is going down the mountain They start hiking at the same time, both taking 12 hours to make the trip. Will they run into each other? Of course they will! Once you think about it this way, the solution IS obvious.

This is a good example of how the original wording of a problem can bog you down, and how useful it can be to think of it in slightly different terms.

AS
Monday, October 28, 2002

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