Solution:

{a +b +abs (a-b)}/2
It is shown that {a +b-abs (a-b)}/2 is < {a, b}

Solution:

Since the door is not visible in this picture, the bus is moving in the left direction.

Solution:

Four

three placed flat on the table in a triangle(touching each other) and put the fourth one on top of them in the middle.

Solution:

When you were inside the shed, the murderer replaced the lock with his own one that was identical to your original lock. When you locked the store room, you did not require a key and there was nothing abnormal for you. When you left, the murderer opened the lock with his key, planted the dead body inside and replaced the lock again putting the original lock in the place. He then closed it without any problem.

Solution:

This puzzle has no answer if you are considering this figure in a 2d domain. However if you follow it on a three-dimensional plane, you can do it like shown in the figure given.

Solution:

Anybody will prefer the shop in the eastern market for sure. There are two reasons for it:
Firstly, since there are only two barbers in the town, the one running the shop in eastern market must have gotten his hair done by the one running the shop in the northern market and vice versa. Thus, if the barber in the eastern market has a shabby haircut, it must be due to the incompatibility.
Secondly, the neat and clean shop can be due to the scarcity of customers as well. While the untidy place refers to the fact that so many customers get their hair done in that shop.

Thus any one will opt for the barber shop in the eastern market.

Solution:

he was genius.

Officials must have thought he was jumping with a hostage, they would never risk giving him a faulty parachute.

Solution:

Put one black rock in one sack and put all the rest in the other one. In such manner you will get about 3/4 probability of surviving.

Solution:

It can be done in 8 moves as shown in the animated image below.

Solution:

You better switch!

Your first choice has a 1/3 chance of having the car, and that does not change.<br>The other two doors HAD a combined chance of 2/3, but now a Goat has ben revealed behind one, all the 2/3 chance is with the other door.

Solution:

A
D
C
A
B