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?

One absent-minded ancient philosopher forgot to wind up his only clock in the house. He had no radio, TV, telephone, internet, or any other means for telling time. So he travelled on foot to his friend's place a few miles down the straight desert road. He stayed at his friend's house for the night and when he came back home, he knew how to set his clock. How did he know?

I am thinking of a five-digit number such that:
The first and last digits are the same, their submission is an even number and multiplication is an odd number and is equal to the fourth number. Subtract five from it and we obtain the second number. Then divide into exact halves and we get the 3rd number.

What number I am thinking of?

Two batsman each on 94 runs. Seven runs needed to win in last 3 balls. Both make 100*. How?

It belongs to you, but other people use it more than you do. What is it?

What is the largest number you can write with just 3 digits?

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

There is a wide field of corn. A goose finds its way into the field and starts running. Can you find out till which point the goose can run into the field?

Two in a corner, one in a room, zero in a house, but one in a shelter. What is it?

What can run but never walk, have a mouth that never speaks, have a head that never weeps, and have a bed but never sleeps?