Problem #1

You are on a hiking trip and you start at the base of a mountain and start climbing it to go to the top. You start exactly at sunrise and take the narrow winding path which spirals upwards towards the summit. You ascend at varying rates of speed, stopping and resting on the way and finally you reach the top in the evening just before sunset. After an overnight rest at a camp on the top the next morning, exactly at sunrise you start descending to the base of the mountain by taking exactly the same path that you took on your way up. Again, you descend at varying speed and rest on the way. Obviously, your average speed of descent on the way down is lot greater than your average speed up. Which of the following is true?

1. There is a unique spot along the path that you will occupy on both trips - on the way up and on the way down – at precisely the same time of the day;
2. There are two unique spots along the path that you will occupy on both trips – on the way up and down – at precisely the same time of the day;
3. There cannot be any single unique spot along the path that you will occupy on both trips – on the way up and on the way down – at precisely the same time of the day;
4. If your average speed on the way up and on the way down is the same then there will be a single spot that you’ll occupy on both trips at precisely the same time of the day.

Problem #2

If 0 (zero) is opposite of 1 (one) and therefore, 1 (one) is opposite of 0 (zero), then by this logic which of the following pairs are opposites of each other:

1. 3/4 and 1/4
2. 2/3 and 1/3
3. 1/2 and 1/2
4. All the above;

Problem #3

Which number will come next in this sequence: 6, 28, 496, .........

1. 852
2. 1,656
3. 8,128
4. 17,212

Problem #4

If there exists are super computer that can do more calculations simultaneously than there are particles in the universe, then it stands out to reason that:

1. the Universe is finite;
2. the Universe is infinite;
3. the Universe has insufficient computing resources to carry all the calculations;
4. the Universe itself becomes a super-computing machine;

Problem #5

According to the generalized version of Uncertainty principle in physics and engineering it is impossible to determine all properties of a particle at any point in time. Therefore, it stands to reason that if there is a particle (an object) P, then:

1. it is possible to make a perfect copy of this particle (object);
2. it is impossible to make a perfect copy of this particle (object);
3. the particle (object), P, will exist with its twin particle (object), P*;
4. the particle (object), P, after an infinite point of time will not exist;

Answers:

1. a
2. d
3. c
4. c
5. b

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