What is both possible and impossible at the same time?

What has hands, but can’t clap?

You order chicken wings at KFC in the boxes of 6, 9 and 20. What is the largest number of wings that you cannot obtain by buying in any combination of the boxes?

Three people enter a room and have a green or blue hat placed on their heads. They cannot see their own hat but can see the other hats.
The colour of each hat is purely random. They could all be green, blue, or any combination of green and blue.
They need to guess their own hat colour by writing it on a piece of paper, or they can write 'pass'.
They cannot communicate with each other in any way once the game starts. But they can have a strategy meeting before the game.
If at least one of them guesses correctly they win $10,000 each, but if anyone guesses incorrectly they all get nothing.
What is the best strategy?

The square root of number 121 is "11". What is the square root of the number "12345678987654321."?

An artist while painting a scenic beauty, decides to paint three layers of blue colour on the sky.

Which layer will go on the first?

John has played 50 ODI's and his average is 50. How many runs should he score in his 51st ODI, so that his average score jumps to 51?

You know three triplets: Frank John and Wayne (need to return your money). Frank always tells the truth while John and Wayne always lie. You meet one of them on the road and can ask him a three-word question.
Which question, will you ask?

What does below science rebus mean?

Ag Ag Ag
Ag SPOON Ag
Ag Ag Ag

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.