Here is a group of nine people. Can we divide the group into pairs so that everyone has a partner?
We need to know what the word “pairs” means. When we say pairs, we mean groups of two. When we talk about shoes, we say we have a pair of shoes, a group of two. Back to our group of nine people, let’s divide them into pairs: group number one, group number two, group number three, group number four. There is no one to be partners with the last person. So can we divide the group into pairs, with everyone having a partner? No, that’s not possible. Nine cannot be divided into groups of two.