A drawer contains ten identical yellow socks, eight identical blue socks and four identical pink socks. Amrita picks socks from the drawer without looking.  What is the smallest number of socks she must pick to be sure that she has at least two pairs of matching socks? 
Overseas Competition->Knowledge Point->Combinatorics->Pigeonhole Principle->Worst Case in Pigeonhole Principle Problems
Two matching pairs of socks could be obtained by choosing four socks, but this is not certain. For instance, two of one colour, one of a second colour and one of a third colour could be drawn. Combinations of five chosen socks would give two matching pairs unless three socks of one colour, one of a second colour and one of a third colour were chosen. When this is the case, drawing a sixth sock would guarantee that there would be two matching pairs as there would now be either four socks of one colour plus two other socks or three socks of one colour, two of a second colour plus one of a third colour. 