Replace all '*' with digits 1, 2, 3, 4, 5 and 6 to make below statement true.

* *
x *
=====
* * *

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?

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?

A mathematics teacher took exams for his students. Out of the total students, 25% passed both the tests included in the exam. However, only 42% were able to clear the first test.

Can you find out the percentage of those students who passed the first test and also passed the second test?

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?

If one and a half boys, eat one and a half burgers in one and a half hours.

How many burgers can 9 boys eat in 3 hours?

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?

In a basket of apples,
when counted in twos, there was one extra
when counted in threes, there were two extra when counted in fours, there were three extra
when counted in fives, there were four extra
when counted in sixes, there was five extra.

However, if the apples were counted in sevens, no extra apple was left. Can you calculate the minimum number of apples that were present in the basket?

A 3 digit number is such that it's unit digit is equal to the product of the other two digits which are prime. Also, the difference between it's reverse and itself is 396.

What is the sum of the three digits?

Can you find out the smallest number that can be conveyed as the sum of three squares in three unique ways?