Is the statement valid that it does not matter how much older a sibling is, eventually the younger one will be half as old as the older one?

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?

Make eight squares by moving only two matchsticks.
Note- Square can be of different sizes.

Sachin bought a car with a strange 5 digit numbered plate.The water image of the number is 78633 more than my car number. All the digits of car number are distinct.

What is the original number on number plate?

You may enter, but you may not come in. I have space, but no room. I have keys, but open no lock. What am I?

In the given picture, in how many ways can you read the word "Tiger"?

An infinite number of mathematicians are standing behind a bar. The first asks the barman for half a pint of beer, the second for a quarter pint, the third an eighth, and so on. How many pints of beer will the barman need to fulfill all mathematicians' wishes?

What does the following represent?

N N N N N N N

A A A A A A A

C C C C C C C

Sherlock Holmes was challenged to make a pre-drawn line smaller without erasing it. He did it in fractions of seconds. How?

Begin with a word, five letters to my name,
Remove the first and last but I am the same
Take out my middle and still, I remain.
What word am I?