What's the only room from which no one can enter or leave

Can you find out the number that should replace the question mark with a valid reason?

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 ?

In the figure that has been attached to this question, each digit represents a digit. The similar letters carry the same integer value. Can you expose the original digits?

If in a car race, the man who came two places in front of the last man finished one ahead of the man who came fifth, how many contestants were there?

You knock a Table over in the library, and suddenly 20 eyes are looking at you.

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?

Find the next number in the series.
1 10 24 43 67 ?

In The 1st month of this year(the year 2013), I noticed that the date 13-1-13 (13 January 2013) is special.

This date is special as:

Date * Month = Year.

Can you figure out which year of this century has a maximum number of such dates?

Solve below rebus puzzle?