There are three questions included in the document. There is no word count requirement, but the problems must be solved.EXERCISES – ANALYTICAL PROBLEMS

Analytical problems are problems that can be solved using logic to reach solutions that are certain to be correct. This means analytical problems are solved deductively. In other words, analytical problems provide a set of assumptions and the answers are derived logically based on those assumptions. If rules of deduction are followed, a solution can be proved to be correct.

Mountain Hike

You hike up a mountain trail, starting from the bottom at 9:00 AM and reaching the top at 5:00 PM. As you hike up the trail, you vary your pace, stop to rest on several occasions, and take a break for lunch. But you always stay on the trail.
After spending the night at the top of the mountain, you hike down the same trail the next day. You begin your descent at 9:00 AM and reach the bottom at 5:00 PM. Again, you vary your pace, stop to rest, and take a break for lunch, but you always remain on the trail.
The problem is the following. Were you ever at the same place on the trail at exactly the same time on each of the two days? Could you have walked down the trail on the second day so that you were never at the same spot at the same time of day? Or must you have been at the same spot at the same time of day no matter how you walked down the trail?


Brush Fire

You hike into a very long and narrow canyon that runs north to south. You enter at the southern end of the canyon because the other three sides are bounded by steep cliffs. You hike all the way to the northern end. Lightning strikes at the southern entrance to the canyon and starts a brush fire. The wind is blowing strongly to the north so the fire is burning rapidly towards you. The brush completely fills the canyon so there is no way to hike out of the canyon to the south or hide in a cave or river bed (or anything like that) without getting severely burned. And the cliffs are too steep to climb. You are stuck in the canyon. It is impossible to escape from the canyon. You have nothing with you that can be of assistance: no shovel to dig a hole, no water to douse flames, nor any other tools or supplies. How can you avoid being burned?



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