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

Take one out and scratch my head, I am now black but once was red. What am I?

Why 1729 is a magic number? Answer Logically.

A time long back, there lived a king who ruled the great kingdom of Trojan House. As a part of the renovation of the kingdom to meet future security needs, he asked his chief architect to lay down a new play in a manner that all of his 10 castles are connected through five straight walls and each wall must connect four castles together. He also asked the architect that at least one of his castles should be protected with walls. The architect could not come up with any solution that served all of King's choices, but he suggested the best plan that you can see in the picture below. Can you find a better solution to serve the king's demand?

I am never scared but became petrified and can’t live in a house but would die to make one. What am I?

A bus driver was heading down a street in Mexico. He went right past a stop sign without stopping, he turned left where there was a "no left turn" sign, and he went the wrong way on a one-way street. Then he went on the left side of the road past a cop car. Still - he didn't break any traffic laws. Why not?

A number with an interesting property:

When I divide it by 2, the remainder is 1.
When I divide it by 3, the remainder is 2.
When I divide it by 4, the remainder is 3.
When I divide it by 5, the remainder is 4.
When I divide it by 6, the remainder is 5.
When I divide it by 7, the remainder is 6.
When I divide it by 8, the remainder is 7.
When I divide it by 9, the remainder is 8.
When I divide it by 10, the remainder is 9.

It's not a small number, but it's not really big, either.
When I looked for a smaller number with this property I couldn't find one.

Can you find it?

I am not alive, but I grow; I don't have lungs, but I need air; I don't have a mouth, but water kills me. What am I?

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 ?

I speak without a mouth, and hear without ears. I have no-body, but I come alive with the wind. What am I?