What has to be broken before you can use it?

A four-digit number (not beginning with 0) can be represented by ABCD. There is one number such that ABCD=A^B*C^D, where A^B means A raised to the B power. Can you find it?

Find the next number in the series below

21 32 54 87 131 ?

Today, I celebrated my 32nd birthday but I was born in 1972.
How is this possible?

An infinite number of mathematicians are standing behind a bar. The first asks the barman for half a pint of beer, the second for a quarter pint, the third an eighth, and so on. How many pints of beer will the barman need to fulfill all mathematicians' wishes?

Can you arrange four 9's and use at most 2 math symbols, to make the total 100?

You visit a home for specially-abled children on the occasion of Christmas where you meet with 50 children. You have a box of chocolates containing 50 chocolates exactly.

What if you were asked to one chocolate to each child in a manner that one chocolate still remains in the box? Is it possible?

When we see 2 but call 10?

What can you catch but never throw?

It's a protector.
It sits on a bridge.
One individual can see directly through it, while others wonder what it hides.

What is it?