Finding A Pair of Socks in the Dark: Recreational Mathematics and Using the Pigeonhole Principle with Young Children

Matthew Oldridge
2 min readNov 3, 2021

A piece I wrote about recreational mathematics inspired by (of course) Martin Gardner, is far and away the most popular thing I have ever written on Medium. Every week, it just keeps going, with hundreds of people reading it. To this day, I do not know why that is. Lots of recreational math enthusiasts out there, maybe?

A problem I believe attributable to Gardner, which I will be trying with primary-aged children, concerns two different colours of socks in a drawer, and a “picker” trying to make a pair in the dark?

Here is the problem formulation:

There are 20 black socks, and 20 white socks in a drawer. If I get up and get dressed in the dark, to avoid waking my family, how many socks must I pick out of the drawer, to be sure I have a pair?

You may find it likely that the common misconception here is simply to say: 4. As in, we might be thinking of picking two pairs worth of socks, and therefore being sure we have one pair. This logic does not work.

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Matthew Oldridge

Writing about creativity, books, productivity, education, particularly mathematics, music, and whatever else “catches my mind”. ~Thinking about things~