Why 1729 is a magic number? Answer Logically.

Can you find the next number in the below sequence
3 , 7 , 10 , 11 , 12 , 17 ?

I am the beginning of the end, and the end of time and space. I am essential to creation, and I surround every place. What am I?

There is a dressing drawer which contains the following coloured socks in pairs: Purple, Magenta, Crimson, White, Yellow and Turquoise. Now, the socks are paired and each pair is together in the matching set. There is no light in the room and you open the drawer and pick up a pair. Then, without noticing any colour, you keep them back and pick them up again.

Can you calculate the probability that the pair of socks was Yellow both times?

I have nine bottles of wine and one of the nine bottles is poisoned.
I need to find the poisoned bottle with two facts
(1) Poison is deadly, only a sip will cost death
(2) I have two mice to do so.

How should I do it?

A thief is convicted in Mexico. He gets the death penalty. The judge allows him to say the last sentence to determine how the penalty will be carried out. If the thief lies, he will be hanged, if he speaks the truth he will be beheaded. The thief tells the last sentence and to everybody's surprise some minutes later he is set free because the judge cannot determine his penalty. What did the thief say?

There was a blind man. He had four socks in his drawer either black or white. He opened it and took out two socks. Now the probability that it was a pair of white socks is 1/2.

Can you find out the probability that he had taken out a pair of black socks ?

All of you like to eat me. I am a five-lettered word. Remove the first two and I turn into an infamous animal. Remove just the first and I become a heinous crime. Remove the first and the last and you can groove on me.

Can you guess who am I?

I was born in a small house and I live in it all alone. No windows and no doors have been assigned to my house. The only way I can go out is by breaking through the walls of my house.

Who am I?

There is a brick of gold and a brick of iron in a boat (both 10-inch blocks), if they are both dropped into the water which will make the water level higher?