Why 1729 is a magic number? Answer Logically.

Look at this sequence from top to bottom. What is the next number in the sequence?
1
11
21
1211
111221
312211

Mr Black, Mr Gray, and Mr White are fighting in a truel. They each get a gun and take turns shooting at each other until only one person is left. Mr Black, who hits his shot 1/3 of the time, gets to shoot first. Mr Gray, who hits his shot 2/3 of the time, gets to shoot next, assuming he is still alive. Mr White, who hits his shot all the time, shoots next, assuming he is also alive. The cycle repeats. If you are Mr Black, where should you shoot first for the highest chance of survival?

How many people must be gathered together in a room, before you can be certain that there is a greater than 50/50 chance that at least two of them have the same birthday?

A new clothing store has a unique method of pricing items. A vest costs $20, a tie costs $15, a blouse costs $30, and underwear costs $45. How much would pants cost?

Most people think of me as money. But when they find me in the water, they won’t get any money out of me. What am I?

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?

Can you count the number of blocks in the picture below?

There are two dice with empty faces in front of you and a marker. You can mark any number on each of the faces of the two dice, but you have to display all 31 days of the month using the two of them.

Which numbers will you mark on which dice so that you can easily depict all the dates of the month?

Transform the word THINK into BRAIN while changing only one letter at a time in a manner that each of the word in the process is a real word!!!