What three numbers, none of which is zero, give the same result whether they’re added or multiplied?

What is next number in the pattern below:

131 517 192 123 ?

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?

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

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

A little girl goes to the store and buys one dozen eggs. As she is going home, all but three break. How many eggs are left unbroken?

You have two jars of chocolates labelled as P and Q. If you move one chocolate from P to Q, the number of chocolates on B will become twice the number of chocolates in A. If you move one chocolate from Q to P, the number of chocolates in both the jars will become equal.

Can you find out how many chocolates are there in P and Q respectively?

A chicken farmer has figured out that a hen and a half can lay an egg and a half in a day and a half. How many hens does the farmer need to produce one dozen eggs in six days?

I throw two dice simultaneously.

What is the probability of getting a sum as 9 of the two numbers shown?

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

* *
x *
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* * *