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?

Why 1729 is a magic number? Answer Logically.

By including only four matchsticks in below picture, you have to make "Four Triangles And Two Squares"

A convention is held where all the big logicians are summoned. The master places a band on everyone's forehead. Now all of them can see others bands but can't see his own. Then they are told that there are different colours of bands. All the logicians sit in circle and they are further explained that a bell will ring at regular intervals. The moment when a logician knew the colour of band on his forehead, he will leave at the next bell. If anyone leaves at the wrong bell, he will be disqualified.

The master assures the logicians that the puzzle will not be impossible for anyone of them. How will the logicians manage ?

What mathematical symbol can be put between 5 and 9, to get a number bigger than 5 and smaller than 9?

When you stop to look, you can always see me. But if you try to touch me, you can never feel me. Although you walk towards me, I remain the same distance from you. What am I?

You have three orange, two pink and five purple balls in the drawer beside your bed. There is no electricity and the room is entirely dark. How many balls must you take out to ensure at least one ball of each colour at least?

I am something people love or hate. I change peoples appearances and thoughts. If a person takes care of them self I will go up even higher. To some people I will fool them. To others I am a mystery. Some people might want to try and hide me but I will show. No matter how hard people try I will Never go down. What am I?

A wooden log balances equally on the scales when weighed with three-quarters of a pound and three-quarters of a wooden log.

Can you calculate the weight of the entire wooden log?

When you say goodbye, I am what you need to tie.
I come as a couple and go wherever you run.
Who am I?