What is both possible and impossible at the same time?

There are a number of books on a shelf. If one book is the 4th from the left and 6th from the right, how many books are on the shelf?

It's pretty hard to give up.
If you remove a part of it, you will be left with a bit.
Even if you remove another part, the bit still remains.
Remove one more and it still remains.

What is it?

How could a baby fall out of a twenty-story building onto the ground and live?

In a boat, the father of a sailor's son is sitting with the son of the sailor. However, the sailor is not present on the boat.

Can this even be possible?

I welcome the day with a show of light, I stealthily came here in the night. I bathe the earthy stuff at dawn, But by noon, alas! I'm gone.

Complete the given grid with valid words. You can only use the letters AAEEIIMMPPTT.

Hint: The grid reads the same across as down.

Solve below rebus puzzle?

Three cars are driving on a track that forms a perfect circle and is wide enough that multiple cars can pass anytime. The car that is leading in the race right now is driving at 55 MPH and the car that is trailing at the last is going at 45 MPH. The car that is in the middle is somewhere between these two speeds.
Right now, you can assume that there is a distance of x miles between the leading car and the middle car and x miles between the middle car and the last car and also, x is not equal to 0 or 1.
The cars maintain their speed till the leading car catches up with the last car and then every car stops. In this scenario, do you think of any point when the distance between any two pairs will again be x miles i.e. the pairs will be x distance apart at the same time ?

John's five friends Rachel, Jacob, Phoebe, Joey and Chandler live on the same road.

Rachel lives in the house: A, Jacob lives in the house: B, Phoebe lives in the house: C, Joey lives in the house:D, Chandler lives in the house: E

Mathematically
B*C*D = 1260
B + C + D = 2E
2A = E

The road numbers run from 2 to 222.

Can you tell me the house number of each of John's friends?