I shave every day, but my beard stays the same. What am I?

A professor thinks of two consecutive numbers between 1 and 10.
'A' knows the 1st number and 'B' knows the second number

A: I do not know your number.
B: Nor do I know your number.
A: Now I know.

What are the four solutions for this?

There are two insects on a tile. Insect X is sitting on one side of the tile (point A) and Insect Y is sitting opposite on the other side of the tile (point B). Now both of them decide to change their position and thus X starts crawling to point B and Y starts crawling to point A. When they meet and pass each other in between, X takes 20 seconds to reach B and Y takes just 5 seconds to reach A.

Can you calculate the total time each of the insects took to change their positions?

Once upon a time, there was a castle on a square island. The entire island was surrounded by a 14m wide trench. The Romans had wanted to invade the castle and had brought a few wooden planks along with them to facilitate themselves in crossing the moat. The planks were however found to be only 13m long.

The Romans still managed to cross the trench. How did they do it?

A landlord calls both of his sons and tells them that their horses will now decide who will transfer the inheritance. He tells them to race along the land till the end and the one whose horse will be slower will win and be the heir to all the property.

Both of them keep wandering for days but to no result. Then they ask a wise man regarding it. The man advises them on the matter after which they jump on the horses and race as fast as they can till the end. Why did they do it?

What did the wise man say?

Find the number of squares in the below-given picture.

This is a simple one. You just have to count the number of Fs in the given sentence.

Finished Files are the result of years of scientific study combined with the experience of years.

How many did you count?

James bond was pushed out of an aeroplane without any parachute.
He survived, How come?

They are the five precious gems of an everyday sort and all can be found on a Tennis Court. Who are they?

John was drowned by he was not wet. How?