Can you place three balls such that the equation shown in the picture holds true?

500 women soldiers are arranged in an array of ten rows and fifty columns in accordance with their respective heights. Now, the tallest woman from each row is asked to move out in the front. From them, the shortest one is labelled as Alpha. They are then asked to resume their original position.

Now, the shortest woman in each column is asked to come out in front. The tallest among them is labelled as Beta.

Can you find out if Alpha will be taller or Beta?

Take away the whole and some still remain. What is it?

I have a head like a cat and feet like a cat, but I am not a cat. What am I?

What is the centre of gravity?

Three cars are driving on a track that forms a perfect circle and is wide enough that multiple cars can pass anytime. The car that is leading in the race right now is driving at 55 MPH and the car that is trailing at the last is going at 45 MPH. The car that is in the middle is somewhere between these two speeds.
Right now, you can assume that there is a distance of x miles between the leading car and the middle car and x miles between the middle car and the last car and also, x is not equal to 0 or 1.
The cars maintain their speed till the leading car catches up with the last car and then every car stops. In this scenario, do you think of any point when the distance between any two pairs will again be x miles i.e. the pairs will be x distance apart at the same time ?

You need to pick one entry from pot A and one from pot B to have a perfect match. Can you do it?

What number does the below three word/phrase identify and why?
1. Deck
2. Year
3. Singing in the Rain

Which three-digit number, made of consecutive digits, like 567, is 2 less than a cube and 2 more than a square?

In case you were starting to feel confident, this one was meant for third graders in Vietnam. The answer is 66, but we don't blame you for scratching your head about how they got there.