Mr Brown has 8 black gloves and 8 brown gloves in his closet

Mr. Brown has 8 black gloves and 8 brown gloves in his closet. He blindly picks up some gloves from the closet. What is the minimum number of gloves Mr. Brown will have to pick to be certain to find a pair of gloves of the same color?

Solution

To find a pair, Mr. Brown has to pick at least 2 gloves. He picks 2 gloves blindly, then they may be of different colors. If he picks 3 gloves blindly, then there are only 2 possibilities: all 3 gloves are of the same color, or 2 gloves are of the same color and 1 is of a different color. Both these possibilities guarantee Mr. Brown a pair of gloves of the same color. Thus, Mr. Brown should pick atleast 3 gloves to be certain to find a pair of gloves of the same color.