I travel all around the world but always stay in the corner. What am I?

Every words stands for unique digit that makes the arithmetic equation true

SEVEN + SEVEN + SIX = TWENTY.

What are the digits ?

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

Place the numbers from 1 to 9 in the circles in a manner that each side of the triangle sums up to 17.

A girl has as many brothers as sisters, but each brother has only half as many brothers as sisters. How many brothers and sisters are there in the family?

You need to move three matchsticks to form three squares. Can you do it?

Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not-rounded numerals equals 24.

I have a big mouth and I am also quite loud! I am NOT a gossip but I do get involved with everyone's dirty business.

Can you identify the famous TV character from the rebus below?

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