What is more useful when it is broken?

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 ?

A mother bought three dress for her triplets daughters(one for each) and put the dresses in the dark. One by one the girls come and pick a dress.
What is the probability that no girl will choose her own dress?

In the given figure, move three matchsticks so that the resulting figure contains two rectangles.

An express train takes 3 seconds to enter the tunnel which is 1 km long.
If it is travelling at 120 km an hour, how long will it take to pass completely through the tunnel?

Can it be possible to build a house that has all its four walls facing towards the South?

After teaching his class all about Roman numerals (X = 10, IX=9 and so on) the teacher asked his class to draw a single continuous line and turn IX into 6. The teacher's only stipulation was that the pen could not be lifted from the paper until the line was complete.

I am 5 letters long.
My first two tell you who I am
My first 3 could be a medicine
My last three reversed could be a young boy.
My 4th, 3rd and 2nd in that order could be a fruit drink.
If you have me you may hang me round your neck
WHAT AM I ?

Astrology starts with the alphabet A, Biology starts with B, Psychology with P and Limnology with L.

Can you find an "ology" that begins with a P?

What four weights can be used to balance from 1 to 30 pounds?