Below the four parts have been reorganised. The four partitions are exactly the same in both arrangements. Why is there a hole?

I am under you when I am whole.
I shift above you if you remove the first letter.
I come all around you if you remove the second as well.

Can you tell me who I am?

An infinite number of mathematicians are standing behind a bar. The first asks the barman for half a pint of beer, the second for a quarter pint, the third an eighth, and so on. How many pints of beer will the barman need to fulfill all mathematicians' wishes?

I have some blue and red sock in my drawer. I have a total of 4 socks. I pick 2 socks and the chance that I get a pair of red socks is 1/2.

What is the chance of picking a pair of blue socks?

You walk into a room that contains a match, a kerosene lamp, a candle and a fireplace. What would you light first?

You need to climb ten stairs. At every stair, you can either take one step up or you can jump two steps up.

In how many different ways you can climb 10 stairs?

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 very interesting trivia question for all.

Why do men's shirts have their buttons on the right side and women's have buttons on the left-hand side?

You need to complete the maze by entering from the entrance marked below in the figure near the yellow circle, bottom left and leaving from the exit point near the green circle, bottom middle.

Rule of Game: You can move only by exchanging green and yellow circles.

Complete the table series riddle by finding the number that can replace "??".