What is both possible and impossible at the same time?

Rebus Puzzle Definition: A rebus is an illusion device that uses pictures to represent words or parts of words.
What does This Rebus Puzzle Identify?

How can a man go eight days without sleep?

Can you find the odd number in the following?

2716, 4135, 5321 and 7145

A wealthy man lives alone in a small cottage. Being partially handicapped he had everything delivered to his cottage. The mailman was delivering a letter one Thursday when he noticed that the front door was ajar. Through the opening he could see the man's body lying in a pool of dried blood. When a police officer arrived he surveyed the scene. On the porch were two bottles of warm milk, Monday's newspaper, a catalog, flyers, and unopened mail. The police officer suspects it was foul play. Who does he suspect and why?

Can you solve the photo plexer logic ?

A landlord calls both of his sons and tells them that their horses will now decide who will transfer the inheritance. He tells them to race along the land till the end and the one whose horse will be slower will win and be the heir to all the property.

Both of them keep wandering for days but to no result. Then they ask a wise man regarding it. The man advises them on the matter after which they jump on the horses and race as fast as they can till the end. Why did they do it?

What did the wise man say?

They are the five precious gems of an everyday sort and all can be found on a Tennis Court. Who are they?

Three doctors said that Bill was their brother. Bill says he has no brothers. How many brothers does Bill actually have?

A mile-long train is moving at sixty miles an hour when it reaches a mile-long tunnel. How long does it take the entire train to pass through the tunnel?