I have teeth but i don't bite. Who Am I ?

Two men play a dice game involving roll of two standard dice. Man X says that a 12 will be rolled first. Man Y says that two consecutive 7s will be rolled first. The men keep rolling until one of them wins.

What is the probability that X will win ?

Can you find out which number multiplied by itself will give the output as 12345678987654321?

Do You See It?

There are a hundred statements.

First person says: At least one of the statements is false.

Second person says: At least two of the statements is false.

Third person says: At least three of the statements are false.

Fourth person says: At least four of the statements are false.

..

..

..

Hundredth person says: At least a hundred of the statements are false.

Analysing it, how many statements do you think are false and how many are true?

John has played 50 ODI's and his average is 50. How many runs should he score in his 51st ODI, so that his average score jumps to 51?

Three playing cards in a row. Can you name them with these clues? There is a two to the right of a king. A diamond will be found to the left of a spade. An ace is to the left of a heart. A heart is to the left of a spade. Now, identify all three cards.

In the figure, you can see nine stars. What you have to do is connect all of them by using just four line and without lifting your hand i.e. in a continuous flow.

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?

I have lakes with no water, mountains with no stone and cities with no buildings. What am I?