Solution:

Let us solve this problem with the help of diagonals. We know, that the sides of square are parallel. Therefore, the diagonals should also be parallel. See the picture, the yellow diagonals are drawn for referencing.

See the image, you can easily spot the four triangles highlighted with red color.

Now, in this picture, you can spot 3 blue, 3 green and 2 red squares. You can find four more rectangles but they can't be square as their diagonals are not parallel with our yellow referenced diagonals.

Therefore, total number of squares = 4 + 8 = 12.

Solution:

Let us first calculate the total number of matches that will be placed:
9C2 * 2
= 9! / (2!7!) * 2
= 8 * 9
= 72
Therefore, every team will play 16 matches.

Let us now glance over the cases that are possible.

Case 1:
Let us say that Team A, Team B and Team C wins 14 matches each (they lose 1 match each from the other two teams), then the Team D can win only (16 - 3 * 2) = 10 matches.

Case 2:
Suppose that, the top 4 teams win 13 matches each.
Team A will win 13 matches and will lose 3 matches from Team B, Team C and Team D.
Team B will win 13 matches and will lose 3 matches from Team A, Team C and Team D.
Team C will win 13 matches and will lose 3 matches from Team A, Team B and Team D.
Team D will win 13 matches and will lose 3 matches from Team A, Team B and Team C.

If this case actually happens, then the Team E will be able to win 8 matches at maximum as Team A, Team B, Team C and Team D will win all the matches played by E.

Case 3:
Suppose that, the top 5 teams win 12 matches each.
Team A will win 12 matches and will lose 3 matches from Team B, Team C, Team D and Team E.
Team B will win 12 matches and will lose 3 matches from Team A, Team C, Team D and Team E.
Team C will win 12 matches and will lose 3 matches from Team A, Team B, Team D and Team E.
Team D will win 12 matches and will lose 3 matches from Team A, Team B, Team C and Team E.
Team E will win 12 matches and will lose 3 matches from Team A, Team B, Team C and Team D.

If this case actually happens, Team E will win 12 matches but it still won't be able to get into the playoffs assuming that it has the lowest run rate among all.

This implies that from case 2, it is evident that a team must win 13 matches at the least to confirm its position in the playoffs.

Solution:

C is the top view of the given pyramid.

Solution:

This is because the queue for buying a donut is extremely long due to which the car engine becomes cool and gives trouble. While the queue for buying brownie is pretty small and thus the car gives no trouble at all.

Solution:

This puzzle is quite similar to the cheating husbands puzzle. The same logic applies here.

After the announcement, if there is only one person with green eyes, he will observe everyone and will come to the conclusion that he himself has green eyes.

If two persons have green eyes, they will see everyone and find out that there is one person with green eyes. So they will expect him to leave. But if no one leaves on that day, on the next day both of them will understand that they both have green eyes and will leave the island.

Thus if you keep going like this or apply the rules of induction, you will find that since there are 100 green eyed people on that island, all of them will leave the island on the 100th day after the announcement.

Solution:

60%

Explanation:
In all such cases where you have to find out the probability of anything with an already given situation, you have to use the formula for conditional probability.

In this case, you have to find out the probability that the second test was passed by a student given that he passed the first test already.

Therefore, P(Second/First) = P (First and Second)/ P (First)
= 0.25/0.42
=0.60
=60 %

Solution:

2/5

Explanation:
This problem can be solved with different approaches. Let us not go into the complicated generic stuff to avoid confusion and try to solve it with simpler means.

Let us find the results separately. There can be 4 different results that give the sum of 5 and there can be 6 different results that give the sum of 7.

Thus, the probability that we get the sum of 4 before the sum of 7 will be:
4/(4+6) = 4/10 = 2/5.

Solution:

It is a lateral thinking puzzle and thus it's not about anything logical.

The man who walked in the movie theater was once a father of twin brothers. Despite of the fact that they were twins, their nature was starkly opposite. While David was quite peaceful and generous, Robin was very rude and violent.

On a certain day, David came running to the man and told him that Robin had killed a man. The man rushed to the crime scene with his son and saw that the man was dead with Robin near the body. He started fighting with Robin and accidentally killed him. The police arrested the man and he was sent to prison for ten years. While in his first month at the prison, he received a letter from his son which said that he was not interested in meeting him ever and that he can't forgive his father for what he did to his brother.

After ten years, he was released and came out of the prison only to know that his son was now a small time movie star and his latest movie was running in a nearby theater. While watching the movie, he smiled when he saw his son David on screen. But the next moment, the camera shifted on his arm where he saw a birthmark that belonged to Robin. He realized that on that day the one who came to him was not David but Robin and he actually killed David.

Filled with a grief and shock he decided to take his own life. He would have never forgiven himself for what he did to his son David.

Solution:

Yes it is possible only under the following condition or situation.

When the twins were born, their mother was on a ship or boat. The elder one was born on 1st of March. But just after his birth before the younger one could be born, the boat crossed the international time zone and thus, the younger one was born on 28th of February.

Now whenever, a leap year falls, the younger brother will celebrate his birthday two days before the elder one.

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.