A mountain climber is journeying up a mountain trail. He starts out with the sunrise, and gets to the peak just as the sun is setting. Throughout the day, he moves with inconsistent speed, slowing down to rest a few times.
He spends the night at the top, and in the morning sets out downward, reaching basecamp by nightfall. (Even though the going is easier, he stops a number of times to admire the scenery and rest.)
Is there an altitude on the mountain slope for which the climber was at that exact altitude at the same point during both days? Why or why not?
This is a great puzzle because it doesn't take much reasoning or logic to determine that the climber must have been at the same spot on both days. The real problem is how to show it or prove it. I agree with jasper. A graph is the best way to solve this puzzle. No matter how you change the speed of the climber, the two lines will have to cross proving that he was at the same spot AND AT THE SAME TIME on both days.
Edited on August 23, 2004, 1:11 am
Great Puzzle
