what does this below rebus represent identXQQQQQME

What number divided by 4 is the same as that number minus 4?

I am a seven-letter word but if you remove four of my letters I will have one left. What word am I?

O_er_t_o_

Complete the missing letters of the given word.

100 prisoners are stuck in the prison in solitary cells. The warden of the prison got bored one day and offered them a challenge. He will put one prisoner per day, selected at random (a prisoner can be selected more than once), into a special room with a light bulb and a switch which controls the bulb. No other prisoners can see or control the light bulb. The prisoner in the special room can either turn on the bulb, turn off the bulb or do nothing. On any day, the prisoners can stop this process and say "Every prisoner has been in the special room at least once". If that happens to be true, all the prisoners will be set free. If it is false, then all the prisoners will be executed. The prisoners are given some time to discuss and figure out a solution. How do they ensure they all go free?

Christina, Allison and Lena are 3 daughters of John a well-known Mathematician, When I asked John the age of their daughters. He replied "The current age of her daughters is prime. Also, the difference between their ages is also prime."

How old are the daughters?

Arrange the numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9 above and below the division line in a manner that the thus formed fractions equal to 1/3.

(You can use one number only once)

I have an eye but still cannot see.

Who am I?

The product of three consecutive numbers is 7980.
Then the sum of these consecutive numbers would be?

81 x 9 = 801. What must you do to make the this equation true?