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Mr. Brown has 10 black gloves and 10 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? Answer:Answer:3
To find a pair, Mr. Brown must pick at least 2 gloves. But, if 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 minimally pick 3 gloves to be certain to find a pair of gloves of the same color.
Food for thought:
Would the problem change significantly if the word "gloves" was replaced by "shoes" in the problem statement? Does it matter that there are "left" and "right" shoes?
Suppose the problem statement was modified to read:
What is the minimum number of gloves Mr. Brown will have to pick to be certain to find a pair of black gloves (rather than simply gloves of the same color)? Is the minimum number still 3?