What is both possible and impossible at the same time?

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?

I’m tall when I’m young, and I’m short when I’m old. What am I?

What has many keys but can’t open a single lock?

Two men play a dice game involving roll of two standard dice. Man X says that a 12 will be rolled first. Man Y says that two consecutive 7s will be rolled first. The men keep rolling until one of them wins.

What is the probability that X will win ?

Your mother’s brother’s only brother-in-law is asleep on your couch. Who is asleep on your couch?

In front of you, there are 9 coins. They all look absolutely identical, but one of the coins is fake. However, you know that the fake coin is lighter than the rest, and in front of you is a balance scale. What is the least number of weightings you can use to find the counterfeit coin?

Can you find out the next digit in the following series ?

0, 0, 1, 3, 2, 6, 3, 9, 4, 12, 5, ?

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?

There was a blind beggar living on the footpath of a street. Suddenly one day, the beggar's brother died. What was the relation of the blind beggar with the person who died?

PS: Brother is not the answer.