Take away my first letter, then take away my second letter. Then take away the rest of my letters, yet I remain the same. What am I?

Christina, Allison and Lena are 3 daughters of John a well-known Mathematician, When I asked John the age of their daughters. He replied "The current age of her daughters is prime. Also, the difference between their ages is also prime."

How old are the daughters?

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 have four wings but can't fly.
I express no emotions.
I am found on the exact spot every time you look.
I keep toiling away with a little sound.

Do you know what am I?

Can you spot the hidden girl in the picture below?

Suppose that you are trapped on the surface of a frozen lake. The surface is so smooth and ideal that there is no friction at all. You cant make any grip on the ice and no wind is blowing to help you out. You have just a mobile phone with you which has got no reception disabling you to call for help.

How will you plan your escape before you freeze to death on the frozen lake?

This is a game of Tic-Tac-Toe which you all might have played innumerable times. Here, we are playing with the black and white markers instead. Also, there is a bit change to the rules. The changed rules allow you to play just three times. After the three markers are put by each of the players, you can only slide your marker into an empty square that shares a common wall with the square that the marker is leaving. You can refer to the figure given. If this is the position of the game, the white's next move would be from 6 to 3. Now, whatever the black one does, the white one will move his marker from 5 to 2 and he will have a three in a row. What you have to decide is if both of the players are using a perfect strategy, will the white player (who plays first) always win? Or it will be the black one who will win always? Or every game will be a draw?

Three ants are going up a hill, one behind the other. The last ant then says to the other ants, 'There is an ant behind me!'' How come?

A person was found dead on a big green land with no trees or buildings around. When the police arrived, they found a piece of rock lying next to him and the man was wearing clothes comprising of red, blue and yellow colours.

Can you tell who the person is and what was the cause of death?

What breaks yet never falls, and what falls yet never breaks?