Solution:

12 minutes

Explanation:
Yes, surely they can all make it out of the cave.

First, father and mother will go. Time taken = 2 minutes.
Father comes back. Time taken = 2 + 1 = 3 minutes.
Both children go. Time taken = 3 + 5 = 8 minutes.
Mother comes back. Time taken = 8 + 2 = 10 minutes.
Mother and Father go. Time taken = 10 + 2 = 12 minutes.

Thus in 12 minutes, all of them will be out of the cave through the tunnel.

Solution:

When he took the first bite of the salmon, he realized that what he ate at the island was not salmon but his friend

Solution:

There are sixty marks in the given figure, thus it is safe to assume that each mark represents a minute.

Now, the hour hand is on a mark when the minute hand is on [0, 12, 24, 36, 48]. When the minute hand is on a mark, the second hand is on noon. But the orange hand cannot be the second hand. (It would be onnoon and it would be eighteen minutes past/before a full hour.)

a) Purple is on 12. Green indicates twenty four minutes. orange indicates forty two [minutes] = 8 + 2/5 [hours] = 8:24
b) Purple is on 12. Green indicates thirty six minutes. orange indicates eighteen [minutes] = 3 + 3/5 [hours] = 3:36
c) Green is on 12 = 3:36
d) Green is on 12 = 8:24.

Please note that the watch could be rotated upside down as well.

Solution:

If you look into the picture, you can see the cut lines. If the four people cut along with the lines, each one of them will have 1/5th of the cake.

Solution:

512

Explanation:
The cube that remains will be 8 x 8 x 8. This will make a total of 512. This is because, when a layer is taken, it will be taken from all sides of the cube which will reduce the dimension be two and not one.

Solution:

If you take a look closely, you will acknowledge the fact that every symbol in the given figure is somehow associated with the surrounding one’s position. The upside-down spade is used to the left of a right-side-up heart every time.

Solution:

He should draw any chit of paper and before unfolding it, he must eat and swallow the chit. In this manner, to determine the judgment of the god, they will have to look at the other chit which will have 'Guilty' written over it. Thus everyone will believe that the chit which he ate had innocent written over it and thus they will believe that he is innocent.

Solution:

The 100th statement for sure is incorrect because it says that at least 100 of the statements are incorrect.

Suppose if that is correct, then 100 statements cannot be true.
This suggests that the 100th statement is incorrect and that the first statement is true.

Similarly 99 statements cannot be true because if they were true, then two statements would become correct i.e. the 1st and the 99th.
But the 99th statement says that at least 99 are incorrect.
This suggests that the 99th statement is incorrect and that 2ndone is true.

If we keep analyzing is the same way till the end, we will find out that only the first fifty statements are true and all the remaining ones are incorrect.

Solution:

At every floor, the detective had to open the window himself. If the man had committed suicide, then at least one of the windows must have been open. A person who is committing suicide won’t close the window behind him. Thus he knows that someone pushed him off the edge and closed the window afterwards.

Solution:

The Pink servant is the truthful one.

In order to prove the same, let us take all of them one by one assuming that the selected one is telling the truth. This is because all of them are disagreeing with each other which means that three servants are lying while one is telling the truth.

Assume that the Orange servant is the truthful one. Under this condition, the orange one is having either 6 or 8 legs. And each of the other octopus is lying will then have 7 legs. Under this condition, the total number of legs will be 6 + 7 + 7 + 7 = 27 legs or 8 + 7 + 7 + 7 = 29 legs. But the Orange servant said that they have 28 legs all together. Thus he is lying.

Now if we simply follow the same logic with all other servants as well, we will come up to the conclusion that only the Pink servant is truthful.