How can a man go eight days without sleep?

Katniss and Peeta are liars. They both lie on some specific days.

Katniss lies on Fridays, Saturdays and Sundays. She speaks the truth on all other days.

Peeta lies on Tuesdays, Wednesdays and Thursdays. He speaks the truth on all other days.

Can you tell that one day of the week when both of them will say "Tomorrow, I will lie."?

Sherlock Holmes was challenged to make a pre-drawn line smaller without erasing it. He did it in fractions of seconds. How?

Can you find out which number multiplied by itself will give the output as 12345678987654321?

For this puzzle, you might have to find logic in something illogical. But hey, it's fun and a healthy little break from your strenuous puzzle-solving sessions.

Can you decipher the meaning in the following cluster of letters?

ITIT,NCENTCENT

Can you replace the X (both small and big x) with the numbers between 1 to 19 such that all the rows of 3 numbers between X (big x) sum to 23?

Count The number of F's in the paragraph below:

"FINISHED FILES ARE THE RESULT OF YEARS OF SCIENTIFIC STUDY COMBINED WITH THE EXPERIENCE OF YEARS"

When I asked a girl's name she told me her name is the date '07/09/2001'.

I thought for a few seconds and then I got her name. Do you?

You need to arrange three 7 and mathematical symbols to form number 1?

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.