You have 60 red socks and 30 blue socks unpaired in a drawer. You can not see the socks, they are in a drawer and it is dark. What is the minimum number of socks that you have to pull out before you have a matching pair?
two, of course.
Now, if you want to be sure you have a matching pair, then 3. There are only two colors, so if you pull 3 socks, at least two of them must be the same color.
To determine the minimum number of socks you need to pull out before you have a matching pair, you can use a concept known as the pigeonhole principle.
The pigeonhole principle states that if you have more items (socks in this case) than available categories (colors in this case) to place them in, then there must be at least one category (color) that contains more than one item (more than one sock).
In this case, you have a total of 60 red socks and 30 blue socks. Since there are only two categories (red and blue), and you have more red socks than blue socks, it means that there must be at least one matching pair of red socks, as there are more red socks available to choose from.
Therefore, you only need to pull out a minimum of 2 socks in order to have a matching pair, as the second sock you pull out is guaranteed to match the first sock, since there are more of that color available.