Which three-digit number, made of consecutive digits, like 567, is 2 less than a cube and 2 more than a square?

Replace the question mark with the correct number in the below-given picture?

If you're 8 feet away from a door and with each move you advance half the distance to the door. How many moves will it take to reach the door?

Eight of us go fourth, not back, to protect our king from an attack. What are we?

A network of 20 x 10 squares is given to you.

Can you calculate how many unique squares and rectangles can be formed combining two or more individual squares ?

On the dull night when the blonde was dozing, she heard an odd clamour and she saw that there was a bizarre man with a gun simply outside her home. So she raced to the telephone to call the police, however, she can't dial 911. Why?

A little girl goes to the store and buys one dozen eggs. As she is going home, all but three break. How many eggs are left unbroken?

The answer I give is yes, but what I mean is no. What was the question?

An infinite number of mathematicians are standing behind a bar. The first asks the barman for half a pint of beer, the second for a quarter pint, the third an eighth, and so on. How many pints of beer will the barman need to fulfill all mathematicians' wishes?

In the Chess Board picture below white army is arranged. You need to add a black army on the board such that no piece is under any threat.
Note: Army comprised of 1 king, 1 queen, 2 rooks, 2 bishops, 2 knights, and 8 pawns.