What is both possible and impossible at the same time?

Rearrange the letters in "new door" to make one word.

In the picture, you can see a chess board. On the top left position, the K marks a knight. Now, can you move the knight in a manner that after 63 moves, the knight has been placed at all the squares exactly once excluding the starting square?

In two decks of cards, what is the least amount of cards you must take to be *guaranteed* at least one four-of-a-kind?

The king of Octopuses has servants who have six, seven or eight legs. The distinguishing characteristics of the servants is that the one with seven legs always lie but the one with either six or eight legs speak the truth always.

One day, four servants meet and converse:

The black one says, 'We have 28 legs altogether.'

The green one says, 'We have 27 legs altogether.'

The yellow one says, 'We have 26 legs altogether.'

The red one says, 'We have 25 legs altogether.'


Can you identify the colour of the servant who is speaking the truth?

John and his wife were living in a rural place. On a particular day, John's wife fell ill and he called the local doctor. When the doctor picked up, he said, "Doctor, my wife is ill. She might have appendicitis."

"This can't be possible! I took out her appendix two years ago myself," the doctor explained.

When diagnosed, John's wife was found to have appendicitis. How can this be possible?

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?

We have shown you a regular water barrel as below. Without using any measuring device can you check if the barrel is more than half-filled or less than half-filled?

I come in different shapes and sizes.
Parts of me are curved, other parts are straight.
You can put me anywhere you like,
but there is only one right place for me.
What am I?

What is black when you buy it, red when you use it, and gray when you throw it away?