What is both possible and impossible at the same time?

My sock drawer has 26 blue socks, 13 pink socks, 33 green socks, and 12 red socks, how many socks would I have to pull out in the dark to be sure I had a matching pair?

What does below chemistry rebus means?

Find The Next Number in this series.
1, 2, 6, 42, 1806 ?

what does the below rebus means?

You are given 2 eggs.
You have access to a 100-storey building.
Eggs can be very hard or very fragile means it may break if dropped from the first floor or may not even break if dropped from 100th floor, Both eggs are identical.
You need to figure out the highest floor of a 100-storey building an egg can be dropped without breaking.
Now the question is how many drops you need to make. You are allowed to break 2 eggs in the process

A man and a dog were going down the street. The man rode, yet walked. What was the dog’s name?

Known by all without exception, Forever here, for your protection, Sometimes strong, sometimes weak, Right after the night I come - hot and chic. And while millions of miles away, I always get to you, I find my way. No life around could do without me, Can you guess what I might be?

Twenty frogs are sitting on a log floating on the surface of a river. Two of them decide to jump off into the water.

How many frogs are there on the log at this moment?

What breaks yet never falls, and what falls yet never breaks?