When I get multiplied by any number, the sum of the figures in the product is always me. What am I?

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’ll find me on Mercury, Earth, Mars, Jupiter, Saturn, and Uranus. But never Neptune, or Venus. What am I?

In a contest, four fruits (an apple, a banana, an orange, and a pear) have been placed in four closed boxes (one fruit per box). People may guess which fruit is in which box. 123 people participate in the contest. When the boxes are opened, it turns out that 43 people have guessed none of the fruits correctly, 39 people have guessed one fruit correctly, and 31 people have guessed two fruits correctly.
How many people have guessed three fruits correctly, and how many people have guessed four fruits correctly

This is a most unusual paragraph. How quickly can you find out what is so unusual about it? It looks so ordinary, you'd think nothing was wrong with it. Actually, nothing IS wrong with it. But it is not as ordinary as you might think. If you think about it for a bit, you will find out why it is truly so unusual. So what is it? What is so unordinary about this paragraph?

You have a basket containing ten apples. You have ten friends, who each desire an apple. You give each of your friends one apple.
Now all your friends have one apple each, yet there is an apple remaining in the basket.
How?

You and your two friends are working in a multinational company. How can you three find out the average salary of you all without disclosing your own salary to the other two?

On a certain day, John celebrated his birthday. Two days later, his older twin brother Jacob celebrated his birthday.

Is this even possible? How can it be?

A man embarked on a questionnaire game. He kept asking the same question to whomever he found. The answer each time was different.

Can you guess what the question was?

Take 9 from 6, 10 from 9, 50 from 40, and leave 6.

How Come ??