A drawer contains 2019 distinct pairs of socks. What is the minimum number of socks to be taken out to be sure of having taken out at least one matching pair of socks? It is specified that the drawer is so messy that it is not possible to search inside.
By the pigeonhole principle, if we have drawn 2020 socks, then we are sure to have drawn two identical socks. On the other hand, it is possible to draw 2019 distinct socks: the number sought is 2020.