Cathy has six pairs of black socks and six pairs of white socks in her drawer. In complete darkness, and without looking, how many socks must she take from the drawer in order to be sure to get a pair that match?
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3
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6
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2
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4
With only 2 colors (black and white), taking 3 socks guarantees a matching pair by the pigeonhole principle. In the worst case, you pick one black and one white sock - the third sock must match one of them. You need only 3, not 6 or more.
To answer this question, we need to consider the worst-case scenario. In order to be sure to get a pair that matches, Cathy must take the maximum number of socks required.
Let's go through each option to determine the correct answer:
Option A) 3 - This option is correct. If Cathy takes three socks, there are two possible scenarios:
- She could have taken one black sock and two white socks. In this case, the next sock she takes will definitely match one of the socks she already has.
- She could have taken two black socks and one white sock. In this case, the next sock she takes will definitely match one of the socks she already has.
Option B) 6 - This option is incorrect. If Cathy takes six socks, there is a chance that she could have taken three black socks and three white socks. In this case, she does not have a guaranteed matching pair.
Option C) 2 - This option is incorrect. If Cathy takes only two socks, there is a chance that she could have taken one black sock and one white sock. In this case, she does not have a guaranteed matching pair.
Option D) 4 - This option is incorrect. If Cathy takes four socks, there is a chance that she could have taken two black socks and two white socks. In this case, she does not have a guaranteed matching pair.
The correct answer is Option A) 3. This option is correct because, in the worst-case scenario, Cathy will have taken two socks of different colors, and the next sock she takes will definitely match one of the socks she already has.