Socks in drawer
Suppose some blue socks and the same number of red socks are in a drawer. Suppose it turns out that the minimum number of socks I must pick in order to be sure of getting at least one pair of the same color is the same as the minimum number I must pick in order to be sure of getting at least two socks of different colors. How many socks are in the drawer?
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1 solution
Let's suppose there are n socks.
the minimum number of socks I must pick in order to be sure of getting at least one pair of the same color is 3 .
the minimum number I must pick in order to be sure of getting at least two socks of different colors is 2 n + 1 . Therefore, 3 = 2 n + 1 ⇒ n = 4 since the minimum number of socks I must pick in order to be sure of getting at least one pair of the same color is the same as the minimum number I must pick in order to be sure of getting at least two socks of different colors.