Solution:

30

Explanation:
It's very difficult to count an actual number of balls but it can be counted mathematically as illustrated below.

Balls in lowest level most level, say level 1 : 4 * 4 = 16
Level2 => 3 * 3 = 9
Level3 => 2 * 2 = 4
Leve4 => 1

Summing up 16+9+4+1 = 30.

Solution:

If you see the picture, they formed a pentagonal shape and achieved the required.

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:

The figure tells that B is located to the North-East of E.

Solution:

step 3 is wrong

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:

888 + 88 + 8 + 8 + 8 = 1000

Solution:

100

Series of number that do not contain albhabet 'T'

Solution:

Since each one of them gave one answer wrong, this means that each one of them gave two answers right.

Let us assume that Student A gave a wrong answer to the first question. This will mean that Student B also gave a wrong answer for the first. This will conclude that the rest of the two answers given by them are correct. However, the answers are different and thus it is not possible.

Thus both Student A and Student B must be right with the first question and the answer to the first is two.

If you keep applying the same logic, you will come to a conclusion that following are the correct answers:
Q1. Two
Q2. Three
Q3. Two

Solution:

Put one red marble in one box and all other marbles in the 2nd box.

Probability :
50 + 24/49

Solution:

Since the knife was in her hand which implies that she was planning to kill her husband "Inspector Montalbano".