How Many Socks Make a Pair?

During one of our workshops Richard presented us with the question “In the dark, how many socks do we need to take out of a drawer to make a pair?” Not to my surprise, the group’s first answer was “two” because who really has the time to rummage through their sock drawer to find a matching pair of socks? However, once it had been cleared up that the socks had to be matching it soon became obvious that there was more to this problem than I first thought.

So, if we have 2 different colours of socks in our drawer, pink and blue for example(guaranteed visit from the fashion police if one of each is worn) and we have three of each colour, how many do we need to take out before we find a matching pair? it took me quite a while to get my head around this but I finally managed it.

So basically, we would need to take 3 socks out of the drawer to guarantee a pair! just 3! because if there are six socks and three of each of the two colours we could either pull out one of each colour or a pair within the first two, in the case of the first two being two different colours no matter what colour we pull out next we will make a pair! my mind is blown!

So what about writing a formula to help all of our fellow sock wearers out there? basically what we did was pull out a number one more than the number of colours of socks that we have, still with me? So if we represent the number of colours of socks with the letter “n” then the formula should be n+1.

So if were to try it with different numbers, if I have 3 colours of socks and 3 of each colour I would need to pull out 4 socks to guarantee that I had a pair, the extra sock is to support me if I am unlucky enough to pull out one of each colour within my first 3, the back up sock has to be one of the colours therefore this guarantees a matching pair!

While this is a fun concept, it is actually a great example of why having a “profound understanding of fundamental mathematics” is so important. It is easy to look at the question and come up with the answer “2” but if we really unpick the question it soon becomes obvious there is more to it. I used my previous knowledge of maths and applied it to this problem, this highlights that when teaching children about maths we should build up their conceptual understanding rather than just their procedural knowledge. This will give them better foundations for attempting problems without a set procedure and solution, it will build confidence and generate innovative thinking.

Eastaway, R.(2010) How Many Socks Make a Pair? Surprisingly Interesting Everyday Maths. London: JR Books.