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?

Intelligence Agency need to break the vault but the problem is that they are not able to break the vault.

On the vault, a text is written as:

31 11 33 33 43 45
21 25
31 24 11 31 51 41

To Break the code Intelligence Agency brings a mathematician named Joseph.
Minutes later he deciphers the code.

Whats the code?

You are on your way to visit your Friend, who lives at the end of the hill. It is his birthday, and you want to give him the cakes you have made. Between your house and his house, you have to cross 5 bridges, and as it goes in the land of make believe, there is a troll under every bridge! Each troll, quite rightly, insists that you pay a troll toll. Before you can cross their bridge, you have to give them half of the cakes you are carrying, but as they are kind trolls, they each give you back a single cake. How many cakes do you have to leave home to make sure that you arrive at a friend's house with exactly two

You have to fill the below given grid in a manner that every row and column contains the digits 1 to 6. Also, make sure that the squares that are connected with each other must contains the same digit.

In a classic wine shop, the list of three most popular wines are:
- The cost of 1 French wine bottle: 500$
- The cost of 1 German wine bottle: 100$
- The cost of 20 Dutch wine bottles: 100$

John entered the wine shop and he needs to buy
- All three types of wine bottles.
- Needs to buy Dutch wine bottles in multiples of 20.
- Need to buy 100 wine bottles in total.

John has only 10000$. How many wine bottles of each type, John must buy?

A girl is twice as old as her brother and half as old as her father. In 50 years, her brother will be half as old as his father. How old is the daughter now?

There are people and strange monkeys on this island, and you can not tell who is who (Edit: until you understand what they said - see below). They speak either only the truth or only lies.
Who are the following two guys?
A: B is a lying monkey. I am human.
B: A is telling the truth.

In four steps you need to move the word 'cold' From 'warm' by replacing one alphabet at a time such that every word formed at each step is acceptable in English Dictionary.

There are nine dots in the picture that has been attached with this question. Can you join all the dots by drawing four straight lines without picking up your pen?

What is the unique property of the following words ?
* Revive
* Banana
* Grammar
* Voodoo
* Assess
* Potato
* Dresser
* Uneven