What will be the best approach to finding all the prime numbers less than 75 that leave an odd reminder when we divide them with 5?

There are 2 cops parked along a one-way street looking for traffic violations. They spot a taxi driver going in the wrong direction, yet they do nothing.

Why?

A crime was committed at baker street. Ibrahim Dakota who was shot in the stomach was the main suspect. Sherlock questioned the suspect. The conversation started as:
Sherlock: What's your story, Ibrahim?
Ibrahim: I was walking around baker street and suddenly a man from the back shot me. I ran as fast as I could to save my life".
Sherlock: That is enough (and ask the police to arrest him).

Why does Sherlock think he is the murderer?

A and B have a certain number of chocolates with them. If B gives one chocolate to A, they will have an equal number of chocolates. But if A gives one chocolate to B, then A will be left with half the number of chocolates that B has.

Can you find out the number of chocolates they have right now?

A farmer went to a market and bought a wolf, a goat, and a cabbage. On his way home, the farmer came to the bank of a river and rented a boat. But crossing the river by boat, the farmer could carry only himself and a single one of his purchases: the wolf, the goat, or the cabbage. If left unattended together, the wolf would eat the goat, or the goat would eat the cabbage. The farmer’s challenge was to carry himself and his purchases to the far bank of the river, leaving each purchase intact. How did he do it?

If I remove one from eleven it becomes Ten and if I remove one from nine also becomes Ten. How?

I have thought of a number that is made up by using all the ten digits just once. Here are a few clues for you to guess my number:

First digits is divisible by 1.
First two digits are divisible by 2.
First three digits are divisible by 3.
First four digits are divisible by 4.
First five digits are divisible by 5.
First six digits are divisible by 6.
First seven digits are divisible by 7.
First eight digits are divisible by 8.
First nine digits are divisible by 9.
The number is divisible by 10.

Can you find out the number ?

Imagine a box with two cogwheels, one big with 24 teeth and one small with 8 teeth. The big one is firmly attached to the center of the box which means it does not turn or move while the small one rotates around the big one.

How many times do you think that the smaller wheel will turn compared to the box when it turns once around the big one?

In the picture given below, can you find out which digit will take place of the question mark?

A girl was sitting in her hotel room when she heard a knock on the door. She opened the door and found that a man was standing outside.
The man said, "Oh! I am really sorry, I thought this was my room."
He then walked through the corridor to the elevator. The girl did not know the man. She closed her door and called security asking them to apprehend the man.
What made her suspicious of that man? He might have been genuinely mistaken.