Socks and Underwear
Admittedly, this post is ripping off a conversation that happened on a work Slack channel the other week. Here’s the general idea: If you count in a particular way, there are 12 options for how to put on your underwear, and 12 (ordered) options for putting on socks and shoes. Since there are the same number of options, we can create a bijection between the two scenarios. In other words, each choice of underwear arrangement will correspond to exactly one choice for socks and shoes. The question is what bijection is “natural”, for whatever definition of natural you choose to have in this strange scenario. Let’s explore it a bit. ...