You need to arrange three 7 and mathematical symbols to form number 1?

We know that the number 7 is the prime followed by a cube. Which next number is also a prime followed by a cube?

A large water tank has two inlet pipes (a large one and a small one) and one outlet pipe. It takes 3 hours to fill the tank with the large inlet pipe. On the other hand, it takes 6 hours to fill the tank with the small inlet pipe. The outlet pipe allows the full tank to be emptied in 9 hours.

What fraction of the tank (initially empty) will be filled in 0.64 hours if all three pipes are in operation? Give your answer to two decimal places (e.g., 0.25, 0.5, or 0.75).

There is a square of a particular number which when doubled, becomes 7 more than its quarter.

Can you find the number?

A high school has a strange principal. On the first day, he has his students perform an odd opening day ceremony:

There are one thousand lockers and one thousand students in the school. The principal asks the first student to go to every locker and open it. Then he has the second student go to every second locker and close it. The third goes to every third locker and, if it is closed, he opens it, and if it is open, he closes it. The fourth student does this to every fourth locker, and so on. After the process is completed with the thousandth student, how many lockers are open?

While house hunting in London, I came across a very good leasehold property Discussing the lease the landlady told me:

'The property was originally on a 99 years lease and two-thirds of the time passed is equal to four-fifths of the time to come. Now work it out for yourself and see how many years are to go!

The square root of number 121 is "11". What is the square root of the number "12345678987654321."?

How many people must be gathered together in a room, before you can be certain that there is a greater than 50/50 chance that at least two of them have the same birthday?

There once were seven dwarfs who were all brothers. They were all born two years apart. The youngest dwarf is seven years old. How old is his oldest brother?

If 21x = 79x, what is the value of x?