What is harder to catch the faster you run?

A convention is held where all the big logicians are summoned. The master places a band on everyone's forehead. Now all of them can see others bands but can't see his own. Then they are told that there are different colours of bands. All the logicians sit in circle and they are further explained that a bell will ring at regular intervals. The moment when a logician knew the colour of band on his forehead, he will leave at the next bell. If anyone leaves at the wrong bell, he will be disqualified.

The master assures the logicians that the puzzle will not be impossible for anyone of them. How will the logicians manage ?

What runs around the whole yard without moving?

Place a mathematical symbol between the numerals 5 and 9 in such a way that the resulting number is greater than 5 but smaller than 9.

There are seven sisters in a house in a village where there is no electricity or any gadget.

Sister-1: Reading Novel
Sister-2: Cooking
Sister-3: Playing Chess
Sister-4: Playing Sudoku
Sister-5: Washing clothes
Sister-6: Gardening

what is Sister-7 doing ?

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

Imagine you are in a room with no windows or doors. How will you get out?

You have $100 with you and you have to buy 100 balls with it. 100 is the exact figure and you can't go below or above the numbers and you have to use the entire $100. If there is no kind of tax applied how many of each of the following balls will you be able to buy:

Green Balls costing $6
Yellow Balls costing $3
Black Balls costing $0.10

Now, how many of each must you buy to fulfil the condition given?

It is a nine-letter word.
The exact opposite of the phrase "friendly and outgoing"
It contains the word "over".
It starts will a vowel.

What is it?

Nine marbles are arranged in the image below. Can you slide two marbles to form a square?