Augie is blind. Thanks to his organized systems he is able to live alone. However, one day he finds that his laundry service has forgotten to pair his socks together. Augie has 12 black socks, 8 white socks, 6 blue socks and 4 red socks. Augie puts two random socks on and decides to take several more to work with him in his briefcase so that he can change once he gets to work and consults with his co-worker Annie if he has picked a pair that doesn’t match. How many socks must Augie put in his briefcase to ensure that he won’t go through the day with mis-matched socks?
A) 1
B) 2
C) 3
D) 5
E) 25
There are two levels to this problem. The first is recognizing this is a worst-case scenario problem. It’s more logic than math. When asked to consider how many socks you need to ensure Augie has a pair of matching socks, you should think about the maximum number of socks Augie could have without making a match. In this case, there are four different colored socks so Augie could end up with four socks and still not have a match. However, if we pull a fifth sock, no matter what color it is, that sock will match one that we already have in the worst case scenario.
That’s the first level, and students who stop there usually end up with answer choice D. The second level requires careful reading as you notice that the question asks how many socks Augie needs to put in his briefcase. Remember, he already has two socks on his feet! To get to the total of five socks that we need, we only need 3 socks in the briefcase.
Remember, the correct answers to math questions often turn on logic and careful reading rather than math skills!
In part two, I’ll show how a similar fact pattern can be used in a probability problem.
