Hi, I need help to understand how to solve problems based on the pigeonhole principle. I need hints on solving them. Could you help me please?

1.

A computer network consists of 6 computers. Every computer is connected to 0 or more computers. Prove that there are 2 computers, that are connected to the same number of computers.

2.

Suppose that we have cables to connect computers to printers. Find the smallest number of cables that guarantee that if we connect 8 computers to 4 printers, there are at least 4 computers that are connected to 4 different printers. Calculate the smallest number of cables for 100 computers and 20 printers, such as 20 computers are connected to 20 different printers.

3.

The population of Greece is 11.000.000. Prove that there exists a day in the year that at least 50 people have birthday and that all of them have the same initial letters (name and surname). *alphabet consists of 24 letters.