Can you find a number that lies one third of the distance between 1/3 and 2/3?

Replace the letters of words with a number so that the below equation holds true

BASE +
BALL
---------
GAMES
----------

A girl was sitting in her hotel room when she heard a knock on the door. She opened the door and found that a man was standing outside. The man said, "Oh! I am really sorry, I thought this was my room." He then walked through the corridor to the elevator. The girl did not know the man. She closed her door and called security asking them to apprehend the man. What made her suspicious of that man? He might have been genuinely mistaken.

A mathematician couple was having a Frappuccino in Starbucks sitting opposite to each other. Suddenly the guy noticed the text written on the paper in front of them and exclaimed that it was wrong. The girl denied it and said it is appropriate. Both are correct. What is written on the paper?

Can you decipher the below rebus?

PBLUESAISNUERSES

It spends most of its day eating white, but when it’s quick enough, it gets to eat fruit and sometimes some blue things. It’s in a dark room, where the walls are blue, it runs from a ghost that roams the halls and haunts it all the time. What is it?

Can you replace the question mark with the correct number in the below table sequence?

How can you write nineteen in a manner that if we take out one, it becomes twenty?

Three doctors said that Bill was their brother. Bill says he has no brothers. How many brothers does Bill actually have?

See the given image carefully. What you have to do is move the blue checkers in the position of the black checkers and vice versa. You are only allowed to move the checker to an adjacent empty space. Do it in the least possible moves.