Solution:

This problem can be solved with algebra as well as logical reasoning. We are going to tell you how it is logically possible.

Be it any quantity that was present in the beginning and any liquid as well. We know that we have taken a spoonful from one glass and put it into another. Then, we have taken a spoonful from the other glass and put it into the first glass. So, at the end of it, the quantity of liquid in either glass remains same as it was in the beginning.

Therefore, we can conclude the fact that any amount of coke that is missing in the glass with coke will be present in the lemonade glass. Also, the same quantity of lemonade will be missing from the lemonade glass and will be present in the coke glass.

Solution:

You might be laughing by looking at the answer now. This is how you would have trashed the figure if you were unable to solve it right? But did you know that this could possibly give you the required solution?

Solution:

Yes, some people are going get really tiny pieces but you were allowed for that right. Also, there is another way of doing it. Can you think of it?

Solution:

The last missing throw will have 3 as the result. This is because, with each pair of the throws you can find that the total sum is increasing by three and then decreasing by one. Therefore the missing throw be 3.

Solution:

100

Series of number that do not contain albhabet 'T'

Solution:

Q

Explanation:
First Square:
6 + 4 + 4 = 14
N is the 14th letter.

Second Square:
4 + 1 + 7 = 12
L is the 12th letter.

Third Square:
5 + 6 + 10 = 21
U is the 21st letter.

Fourth Square:
14 + 2 + 1 = 17
Q is the 17th letter.

Solution:

4

Explanation:
Now if you go on calculating 2^300, you will lose so much time and it might not even be feasible to carry out so long of calculations. Thus we will make use of a trick here. We will calculate the remainder of each power of 2 till we come across a pattern.

2^1 divided by 4 leaves the remainder 2.
2^2 divided by 4 leaves the remainder 0.
2^3 divided by 4 leaves the remainder 0.
2^4 divided by 4 leaves the remainder 0.

You can see that all the following powers of two will be divisible by 4. Therefore the remainder when 2^300 is divided by 4 will be 0 only.

Solution:

First fill the 8 liters jug complete - 4, 8, 0
Fill the 5 liters jug with 8 liters jug - 4, 3, 5
Pour back the beer from 5 liters jug to 12 liters jug - 9, 3, 0
Pour the 3 liters from 8 liters jug to 5 liters jug - 9, 0, 3
Fill the 8 liters jug completely from 12 liters jug - 1, 8, 3
Fill the 5 liters jug from the 8 liters jug - 1, 6, 5
Pour the entire 5 liters jug back in 12 liters jug - 6, 6, 0

You have successfully split the beer into two equal parts.

Solution:

Paradise

Solution:

The guy threw a boomerang in the air from his window. It flew away and looped around to return back with high velocity. It hit his head and he died on the spot due to the injury. This can be the only logical explanation.