I shave every day, but my beard stays the same. What am I?

A man plots the murder of his wife. His plan is full proof. Nobody saw them leaving their house. He stabbed her with a knife while driving. She died on the spot. He threw her body in a valley. He threw the knife carefully wiping his finger prints on a random garbage bin. Then he went back to his home and no one was watching him this time as well.

After an hour, he was called by the local police department who informed him that his wife was murdered. They asked him to reach the scene of crime immediately. But as soon as he arrived at the crime scene, he was arrested by them.

How did the police know that he himself is the murderer?

Find the Next Number in the Sequence

2 9 3 1 8 4 3 6 5 7 ?

Begin with a word, five letters to my name,
Remove the first and last but I am the same
Take out my middle and still, I remain.
What word am I?

In the addition below, all digits have been replaced by letters. Equal letters represent equal digits and different letters represent different digits.
ABCABA
BBDCAA
ABEABB
ABDBAA
------- +
AAFGBDH
What does the complete addition look like in digits?

A chicken farmer has figured out that a hen and a half can lay an egg and a half in a day and a half. How many hens does the farmer need to produce one dozen eggs in six days?

Why do people go to bed?

Why is it against the law for a man living in Delhi to be buried in Mumbai?

How many pluses should we put between the digits of 987654321 to get a total of 99, and where?

What English word has three consecutive double letters?