I speak without a mouth, and hear without ears. I have no-body, but I come alive with the wind. 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?

Can you find out the smallest number that can be conveyed as the sum of three squares in three unique ways?

A man stands on one side of a river, his dog on the other. The man calls his dog, who immediately crosses the river without getting wet and without using a bridge or a boat. How did the dog do it?

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?

What can jump higher than a building?

There are hundred red gems and hundred blue gems. The blue gems are priceless while the red gems equal wastage. You have two sacks one labeled Heads and the other Tails. You have to distribute the gems as you want in the two sacks. Then a coin will be flipped and you will be asked to pick up a gem randomly from the corresponding sacks.

How will you distribute the gems between the sacks so that the odds of picking a Blue gem are maximum?

The following "Brain Bat" means Slow Down.
S
L
O
W

Using the same logic, can you tell us what does the following Brain Bat means ?
E
V
I
G

If an electric train is travelling south, then which way is the smoke going?

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?