It walks on 4 when its young, walks on 2 when it's older, and walks on 3 when its very old?

During an experiment, a guy throws a bouncy ball from a 100 feet tall building. The ball has a specific characteristic. Every time it hits the ground, it bounces up halfway.

How many bounces do you think the ball will make before it comes to a stop ?

Place a mathematical symbol between the numerals 5 and 9 in such a way that the resulting number is greater than 5 but smaller than 9.

A convention is held where all the big logicians are summoned. The master places a band on everyone's forehead. Now all of them can see others bands but can't see his own. Then they are told that there are different colours of bands. All the logicians sit in circle and they are further explained that a bell will ring at regular intervals. The moment when a logician knew the colour of band on his forehead, he will leave at the next bell. If anyone leaves at the wrong bell, he will be disqualified.

The master assures the logicians that the puzzle will not be impossible for anyone of them. How will the logicians manage ?

Here is a mathematical expression that also secretly tells a movie name. What movie is that?

I possess a head

I flaunt a tail

But I don't have mouth or legs

Can you find out who I am?

Complete the series by replacing "?" with the correct number.

ST ND RD TH '?'

A man is found dead in his bathroom naked with blood scattered all around him. The bathroom was locked from the inside and there is no trace of any struggle. There is nothing in the bathroom except his pant with the belt still around and his shirt. Also, the medic team can't find any incision in his body that may have been the reason behind so much blood loss.

The Police department is clueless regarding this murder mystery.
Can you?

Look at me. I can bring a smile to your face, A tear to your eye, Or even a thought to your mind. But, I can't be seen. What am I?

You need to move three matchsticks to form three squares. Can you do it?