The answer to the question ‘It is dark and you walked to your wardrobe wanting to retrieve a pair of socks. If your drawer consists of 48 black socks and 28 brown socks, how many socks do you have to pull out in order to guarantee getting a matching pair?’ is 3.
Not many people got this question right and so I shall explain how I derived the answer. It is quite simple actually.
The first sock you pull out can be of either colour (black or brown) and the second sock you pull out can also be of either colour (black or brown) and therefore the answer 2 is incorrect as you might not have gotten two socks of the same colour if you are unlucky.
On the third pull, the sock will also be of one of those colours (black or brown).
Hence, you will have at your third pull either 2 brown 1 black, 2 black 1 brown, 3 blacks or 3 browns. So on your third pull, you will definitely have guaranteed pulling out at least a matching pair.
If I was to change the question to 56 red socks, 18 purple socks and 42 orange socks, the principle is still the same and the answer will be 4.
In a nutshell, even if the question is revised to have increased number of socks in the drawers or increased sock colours, the formula is always x+1.
I noticed the downfall to getting the answer to this question is the tendency to overcomplicate matters. However, if you have any queries about the answer or the explanation is not clear enough, please do leave me a message at the bottom.
If you had fun with this question, why not head on to try the question for this week ‘I spy’