How can you make number one disappear by adding something to it?

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?

Two guards were on duty outside a barracks. One faced up the road to watch for anyone approaching from the North. The other looked down the road to see if anyone approached from the South. Suddenly one of them said to the other, "Why are you smiling?"

How did he know his companion was smiling?

A man who was outside in the rain without an umbrella or hat didn’t get a single hair on his head wet. Why?

I live in a bowl. I can swim. I have a tail. I also have fins and big eyes. What am I?

I can be cracked, made, told, and played. What am I?

Eight Chelsea player makes the following statements :

1. Seven of us are lying here.
2. Six of us are lying here.
3. Five of us are lying here.
4. Five of us are lying here.
5. Four of us are lying here.
6. Three of us are lying here.
7. My name is Torres.
8. My name is Lampard.

The last two are Lampard and Torres or maybe Torres and Lampard.
So can you deduce which of the last two is Lampard or Torres?

A sundial has the fewest moving parts of any timepiece. Which has the most?

What have one eye but still cannot see?

A man dies of old age on his 25 birthday. How is this possible?