Solution:

45-6 = 78 / 2 = 39 * 1

Explanation:
A = 4
B = 5
C = 6
D = 7
E = 8
F = 2
G = 3
H = 9
I = 1

So below equation can be solved as:
AB - C = DE / F = GH * I
45 - 6 = 78/2 = 39 * 1
39 = 39 = 39.

Solution:

Although it looks complicated, the answer is simple. The password to his computer is JIGSAW.
1st letter of Jug = J
2nd letter of Birthdays = I
3rd letter of Fights = G
4th letter of Cars =S
2nd letter of Laptops = A
1st letter of Watch = W

Solution:

Sansa has the siamese (conjoined) twin sister.

Solution:

Karate Kid (car + at + tea + kid)

Solution:

The stranger said that he thought the room was his. If so, he must have had the keys to the room and thus he must not have knocked.

Solution:

A Spider

Solution:

White should move the rook from
A1 to D1 and hence complete the castling move.

Solution:

The brain teaser can be solved as shown in the image below.

Solution:

The husband had booked two tickets for departure and only one for the return. The travel agent told this information to the police and they immediately came to know that he had planned the murder right from the beginning.

Solution:

"World War I" was named after after "World War II"

Solution:

One of the cop will move clockwise while the other will move anti-clockwise every day. In such a manner, they will catch the thief in minimum seven days.