I am white when I am dirty, and black when I am clean. What am I?

What does the following BrainBat signifies?

ABCDEFGHIJKLMNOPQRSTUVWYZ

QQQQQQQQQQQQQQQQQQQQQQQQQ.

You are a cab driver who pools passengers. You pick 3 people from a destination and drop 1 after an hour. 2 people climb aboard at the same time and you drop 3 at the next destination. After some time, you pick 2 passengers only to drop 1 after a short distance where 3 more passengers climb up the cab. You leave the rest of the passengers one by one to their destination and then come back home.

Can you tell the eye color of the cab driver?

Give it food and it will live; give it water and it will die.

What does a man do only once in his lifetime, but women do once a year after they are 29?

Take 9 from 6, 10 from 9, 50 from 40, and leave 6.

How Come ??

I have no life, but I can die. What am I?

As shown in the image, the nine Dogs are square fenced. By constructing just two square fences can you make sure that two Dogs cannot meet each other without crossing the fence?

Queen Elizabeth organised a royal party.

To Avoid uninvited guest royal family set a password.
Jack (an uninvited person) plan to enter the party. He stand nearby the door.

First guest comes, the security person said 'twelve' and guest replied with six.
Second guest comes , the security person said 'six' and guest replied with 'three'.

Jack thought is enough and he walked to the entry point. The security person said 'eight' , Jack replied smilingly 'four'.
He was immediately thrown out of the party. why ?

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?