A drawer contains ten identical yellow socks, eight identical blue socks and one hundred 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
Consider the worst case scenario: first 3 are drawn, all of different colors, when the fourth is drawn, no matter which color is drawn, a pair of the same color will definitely be matched. Continue to draw the fifth one. The worst case is that the last color socks are drawn again, and at this point there are three socks of the same color and one sock of each of the other two colors. If you continue to draw the sixth one, no matter which color you draw, you will be able to form two pairs of socks of the same color. So the answer is to draw 6 times. 