Why 1729 is a magic number? Answer Logically.

I have branches, but no fruit, trunk or leaves. What am I?

They came out at night, without being called.
They lost at day, without being stolen.
Who are they?

A man stands on one side of a river, his dog on the other. The man calls his dog, who immediately crosses the river without getting wet and without using a bridge or a boat. How did the dog do it?

You are provided with a grid (as shown in the picture). Can you fill the squares with numbers 1-8 in a manner that none of the two consecutive numbers are placed next to each other in any direction (vertically, horizontally or diagonally?)

What does this simple rebus mean?

Can you move 2 matchsticks to form four equal sized squares.

A father's child, a mother's child, yet no one's son.

Who am I?

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?

Two guards were on duty outside a barracks. One faced up the road to watch for anyone approaching from the North. The other looked down the road to see if anyone approached from the South. Suddenly one of them said to the other, "Why are you smiling?"

How did he know his companion was smiling?