1. Let's say that you have a drawer full of socks, 20 red socks (all identical) and 12 blue socks, and it is dark in the room. How many socks should you grab, to assure that you have at least one matching pair? The answer is below.
2. You have a draw containing 20 red socks, 12 blue socks, and 8 green socks. How many socks should you grab, to assure that you have at least one matching pair?
3. You have 10 pairs of shoes (20 shoes) in your closet, all identical! Again it is dark. And maybe your hands are numb so you can't tell if the shoes that you grab are right or left handed (footed). How may shoes should you grab to make sure you have at least one shoe for each foot?
4. In a city of 2 million people, no one has more than 1.5 million hairs on his/her head. Can you show that at least two people in the city have exactly the same number of hairs on their heads?
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