What is both possible and impossible at the same time?

You are in a land where thirty men and two women were dressed in classic black and white dresses.
They begin to fight as soon as any of them move.

Where are you?

Fate has decided that you will only be pleased to meet me when you need me

Maybe that is why, when I am working, I start working

However annoying I may be to the regulars, the little ones are always inspired

I will always be waiting if you try to reach me

How many of you can guess my name, let me see

A car meter reading shows 72927 miles a palindromic number.
what is the minimum number of miles you would need to travel to see another palindromic number on the car meter reading?

I’m light as a feather, yet the strongest person can’t hold me for five minutes. What am I?

The Little ant seems to be always confused. Do you know why?

If,

6 / 7 = 2
3 / 9 = 7
8 / 2 = 6

Then

4 / 5 = ?

How many people must be gathered together in a room, before you can be certain that there is a greater than 50/50 chance that at least two of them have the same birthday?

How do you go from 98 to 720 using just one letter?

An equation has been laid down using a few matchsticks. However, as you can see, the equation is not correct. Can you correct the equation if you are allowed to add or remove 5 matchsticks?