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

In the given figure, move three matchsticks so that the resulting figure contains two rectangles.

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.

If you say my name, I will no longer exist. What am I?

I know a 5-digit number having a property that With a 1 after it, it is three times as large as it would be with a one before it.

Guess the number?

A lion and its tamer are standing inside a cage that measures 1 unit in radius. Both of them can effortlessly run at the speed of 1 unit maximum.

1) Suppose the lion is hungry, will he be able to eat up the tamer?
2) If yes, how long can the tamer survive?

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?

Can you find a seven digit number which describes itself. The first digit is the number of zeros in the number. The second digit is the number of ones in the number, etc. For example, in the number 21200, there are 2 zeros, 1 one, 2 twos, 0 threes and 0 fours.

I am a prime number.
The double of myself is equal to the square of me.

which number am I?

I possess a head

I flaunt a tail

But I don't have mouth or legs

Can you find out who I am?