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?

You are playing a game with your friend Jack. There are digits from 1 to 9. You both will take turn erasing one digit and adding it to your score. The first one to score 15 points will win the game.

Would you want to play first or second?

PS: The sum should be exactly 15.

In a competitive exam, each correct answer could win you 10 points and each wrong answer could lose you 5 points. You sat in the exam and answered all the 20 questions, which were given in the exam.
When you checked the result, you scored 125 marks on the test.

Can you calculate how many answers given by you were wrong?

James ordered a fishing rod, priced at $3.56. Unfortunately, James is an Eskimo who lives in a very remote part of Greenland and the import rules forbid any package longer than 4 feet to be imported. The fishing rod was 4 feet and 1 inch, just a little too long, so how can the fishing rod be mailed to James without breaking the rules? Ideally James would like the fishing rod to arrive in one piece!

Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not-rounded numerals equals 24.

A man is walking down a road with a basket of eggs. As he
is walking he meets someone who buys one-half of his eggs
plus one-half of an egg.
He walks a little further and meets another person who buys
one-half of his eggs plus one-half of an egg.
After proceeding further he meets another person who buys
one-half of his eggs plus one half an egg. At this point, he
has sold all of his eggs, and he never broke an egg.
How many eggs did the man have to start with?

You have two jars of chocolates labelled as P and Q. If you move one chocolate from P to Q, the number of chocolates on B will become twice the number of chocolates in A. If you move one chocolate from Q to P, the number of chocolates in both the jars will become equal.

Can you find out how many chocolates are there in P and Q respectively?

In the below-given picture of a pretty girl, there is something wrong. Can you find out what it is?

Considering the below equation:

V + II - VI = 10
IV - X + VIII = 20
IV - VII + VI = 30

Then, I + II + III = ?

There is one thing that goes round the house and also inside the house but never even share a brief touch. What is it?