Solution:

40 balls

Solution:

31

Explanation:
Ramanujan lighting the candles in binary.
11110 =30
11111 =31

Solution:

Bond was suspicious of the women as one never knocks its own door at the hotel.

Solution:

C7 => B8
Exchange pawn for a knight

Check-Mate

GameOver

Solution:

Slumdog Millionare = Slum + Dog + Million + air

Solution:

The check was for dollars 31.63.

The bank teller gave her dollars 63.31
She spent .05, and then she had dollars 63.26, which is twice the check.

Let x be the dollars of the check, and y be the cent.

The check was for 100x + y cent
He was given 100y + x cent

Also
100y + x - 5 = 2(100x + y)
Expanding this out and rearranging, we find:
98y = 199x + 5

or 199x ≡ -5 (mod 98)
or 98*2*x + 3x ≡ -5 (mod 98)
3x ≡ -5 ≡ 93 (mod 98)
this quickly leads to x = 31

Solution:

They are matched as shown in the picture below.

Solution:

1

Explanation:
4 + 9 = 1
The trick to solve is to assume the first number as the time in AM and the second number is the number of hours you have to add to it. You'll find the time in PM when you do that.

For example
7 AM + 7 hours = 14:00 or 2 PM

4 AM + 9 hours = 13:00 or 1 PM.

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:

To do this, he must be pushing the cork inside the bottle and then taking out the coin.

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.