Discrete Mathematics
# Pigeonhole Principle

It was around 4 in the morning, and I'm all dressed up, ready for school, when the electricity was cut off. Too bad, I haven't put on my socks yet.

I have 2343 pairs of gray socks, 3212 pairs of pink socks and 6525 pairs of blue socks. Everything is mixed in my drawer (I'm a bit of irresponsible, sorry about that.). As there was no light, I was not able to identify the color of the socks. How many of the socks did I need to take to match one pair?

$5$ of them to make sure at least one of them is red and you have to grab at least $10$ of them to make sure both colors appear among the balls selected. How many balls are there in the box?

In a box there are red and blue balls. If you select a handful of them with eyes closed, you have to grab at least