What is both possible and impossible at the same time?

The doctor advised his patient to take a tablet after every fifteen minutes. He gave him five tablets in total.

How much time will he take to have all the five tablets?

A detective visits his friend John just to discover that John's neighbour Dr Jacob was murdered. Dr Jacob, who is a mathematician wrote the murderer's name in a code word "Hcqtfz". There were five suspects
1. Ajit
2. Pankaj
3. Ganpat
4. Deenu
5. Hariya

The Detective was instantly able to find the murderer.
Can you?

Can you quickly find which two matchstick figures are identical?

I look at you, you look at me I raise my right, you raise your left. What am I?

In a stable, there are men and horses. In all, there are 22 heads and 72 feet. How many men and how many horses are in the stable

I always drive my customer away.

Who am I?

Find The Next Number in this series.
1, 2, 6, 42, 1806 ?

I am beautiful, up in the sky. I am magical, yet I cannot fly. To people I bring luck, and to some people, riches. The boy at my end does whatever he wishes. What am I?

Can you find out what is missing?

1 3 5
2 4 ?

Hint: It's not six. Think out of the box.